Set Datang di SMAN 8 Batam Starting with maths
W e lcom e t o M a t h s Ch oice s w e bsit e
This sit e is about your choices if you wish t o st art st udying m at hem at ics wit h t he Open
Universit y. I t describes courses and possible st udy rout es, and gives you inform at ion which
you m ight t ake int o considerat ion when m aking your decision. I t also gives you help in
j udging which of t he possible rout es is best for you.
The m at hem at ics ent ry suit e consist s of t he following courses:
St art ing wit h m at hs ( Y162) - 10 point s
Discovering m at hem at ics ( MU123) - 30 point s
Using m at hem at ics ( MST121) - 30 point s
Exploring m at hem at ics ( MS221) - 30 point s
Which of t hese you choose t o st udy will depend largely on your previous m at hem at ics
experience and what you m ight want t o st udy lat er.
I f you haven't st udied recent ly and feel uncert ain about your m at hem at ics, we recom m end
st art ing wit h our short Openings course St art ing wit h m at hs ( Y162) which will help build
up your st udy skills, and is part icularly appropriat e if you t hink your m at hs background is
weak ( if, say, you left school at 16 wit hout a form al qualificat ion in m at hem at ics) .
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Starting with maths (Y162) leads onto MU123
I f you're confident about your st udy skills, and have st udied m at hs successfully at school
up t o or beyond GCSE ( or equivalent ) , we recom m end you st art eit her wit h Discovering
m at hem at ics ( MU123) or Using m at hem at ics ( MST121) . Bot h will get you accust om ed t o
OU st udy and t each you som e m at hem at ics.
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Discovering mathematics (MU123)
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Using mathematics (MST121)
Discovering m at hem at ics ( MU123) leads ont o MST121
Using m at hem at ics ( MST121) leads ont o MS221. Alt ernat ively, Using m at hem at ics
( MST121) and Exploring m at hem at ics ( MS221) can be t aken t oget her assum ing you are
adequat ely prepared and have plent y of st udy t im e
Regardless of previous m at hem at ical knowledge, it is sensible for new st udent s t o m at hs
at t he OU t o st art at Level 1. Most st udent s find it t akes t im e t o organise t heir st udy and
deadlines alongside t he dem ands of t he rest of t heir lives. Our courses are designed t o
help you get accust om ed t o st udying m at hs wit h t he OU.
Most of our st udent s do st art at Level 1, choosing t heir course on t he basis of t he advice at
t his websit e. A sm all num ber of st udent s st art at a higher level, alt hough Level 2 and 3
courses not only assum e prior t echnical knowledge and experience, but t hat st udent s are
also used t o st udying t he OU way. Even if t he courses you require are at a higher level,
t hen it is usually sensible t o consider st art ing at a lower level as advised in Mat hs Choices.
See St art ing at a higher level for m ore inform at ion.
W h a t is a va ila ble t o you
The courses in t he m at hem at ics ent ry suit e share a com m on approach t o m at hem at ics and
it s st udy, and t here is a nat ural progression bet ween t hem , wit h a planned developm ent of
t he skills you need t o acquire. They are designed for flexibilit y, giving you a choice of
where t o st art and how m uch t o st udy, depending on your needs. They cat er for t hose who
wish t o st udy m ainly m at hem at ics courses and for t hose who need som e m at hem at ics t o
underpin t heir st udies in ot her areas, or who j ust have a personal int erest in m at hem at ics.
St a r t in g w it h m a t h s Y1 6 2 - 1 0 point s
I f you are part icularly int erest ed in m at hs, or you want t o st udy a m at hs- based subj ect or
one where m at hs will feat ure significant ly, St art ing wit h m at hs offers a friendly
int roduct ion. The course w ill help you feel m ore confident in using m at hs in a variet y of
different sit uat ions - at hom e, in work or in your ot her st udies. There are t hr ee m ain
t hem es developed in t he course:
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im proving your m at hem at ical skills including using a calculat or effect ively;
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developing problem - solving st rat egies so t hat you know what t o do when you get
st uck;
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pract ising general learning skills t o help you becom e an effect ive learner.
Using m at hem at ics in t he real world is som et im es quit e different t o t ackling a clearlyst at ed problem in a t ext book. During t he course, you will consider several real- life
exam ples, including a case st udy based on a conservat ion issue, so t hat you can see t he
differences yourself, and feel m ore confident in using m at hem at ics in your own life t o solve
problem s and m ake decisions. Being able t o com m unicat e using m at hem at ical ideas is
im port ant , whet her you are reading t he work of ot hers or explaining your own solut ions.
The course w ill help you develop t hese skills, in part icular using not at ion and language
appropriat ely and writ ing good m at hem at ical solut ions t hat are easy t o underst and. As well
as m at hs t hat is useful in everyday sit uat ions, t he course also includes puzzles, bit s of
hist ory and som e m at hem at ical ideas t hat are fascinat ing in t heir own right .
You will find t he course useful whet her you are building up t owards regular, st ruct ured
st udy or are sim ply int erest ed in finding out about m at hem at ics and it s place in our lives.
I n t his course t he m at hem at ical ideas are em phasised m ore t han t he t echnological and
scient ific ones, alt hough t he skills are equally appropriat e for anyone who int ends t o st udy
t echnology or science.
The course m at erials have been prepared wit h t he needs of new learners in m ind. They
assum e no special knowledge and no experience of st udying. Taking exam ples from
everyday life, t hey enable you t o st art from your general knowledge and int er est s and
gradually build up t o degr ee- level st udy. Learning skills are key t o t he course, and skills
such as t im e m anagem ent , not e t aking, reading for st udy purposes and reflect ion on your
own learning are explored.
St art ing wit h m at hs st art s four t im es a year, in March, June, Sept em ber and Novem ber.
Each course last s for a m axim um of 20 weeks alt hough you can t ake less t im e if you
prefer.
D iscove r ing m a t h e m a t ics M U1 2 3 - 3 0 poin t s
This course int roduces som e fundam ent al m at hem at ical ideas and will form a relevant part
of m any st udy profiles, including t hose in t he sciences and in t he hum anit ies. I t covers
statistical, graphical, algebraic, trigonometric and numerical concepts and techniques, and
introduces mathematical modelling. I t does assum e arit hm et ical, but not algebraic, skills.
MU123 is t herefore less m at hem at ically dem anding t han MST121, but will help you to
integrate mathematical ideas into your everyday thinking and build your confidence in using
and learning mathematics. The developm ent of skills in interpreting and explaining
mathematics is an im port ant aspect of t he course.
Providing you have the appropriate background knowledge, you should expect to spend
about eight hours a week studying the course. There are five t ut or- m arked assignm ent s and
a num ber of short int eract ive com put er- based assignm ent s, all of which count t owards t he
final course result .
The course st art s at t he beginning of February and Oct ober each year, and last s about nine
m ont hs.
M ST1 2 1 Usin g m a t h e m a t ics - 3 0 poin t s
This provides a broad int roduct ion t o t he nat ure of m at hem at ics and it s uses in t he m odern
world. I t shows how m at hem at ics can be used t o invest igat e and answer quest ions from
science, t echnology and everyday life. This course assum es good skills in algebra,
t rigonom et ry and geom et r y, and fam iliarit y wit h t he m ain funct ions on a scient ific
calculat or, such as t he sine and exponent ial funct ions. ( Successful st udy of MU123 or t he
highest level GCSE could provide t he required skills.)
On average t he course needs at least 8 hours of st udy each week. I t t eaches t he use of
m at hem at ical and st at ist ical com put er soft ware packages. There are four t ut or- m arked
assignm ent s and t wo com put er- m arked assignm ent s, all of which count t owards t he final
course result . I n addit ion t here is a pract ice t ut or- m arked assignm ent and com put erm arked assignm ent at t he beginning of t he course.
The course st art s in lat e January and lat e Sept em ber each year, and last s about nine
m ont hs.
M ST1 2 1 / M S2 2 1 com bine d - a t ot a l of 6 0 poin t s
Usin g m a t h e m a t ics M ST1 2 1
Ex plor in g m a t h e m a t ics M S2 2 1
This com binat ion com prises of t he t wo courses, MST121 and MS221, which have been
designed so t hat t hey can be t aken essent ially as a single 60 point course wit hin one year.
The prer equisit e m at hem at ical knowledge for t he pair of courses is m ore t han t he
m inim um background for MST121 as m ore advanced concept s are included in MS221, such
as t he role of reasoning in m at hem at ics, so a relevant A- level or equivalent is desirable
before st udying t he t wo courses at t he sam e t im e. By t he end of MS221 you will have
encount ered m any of t he t opics t hat are developed in lat er m at hem at ics courses, and bot h
use t he sam e m at hem at ical soft ware package.
On average, t hese courses t oget her need at least 16 hours of st udy each week. I n addit ion
t o t he assessm ent on MST121, MS221 has four t ut or- m arked assignm ent s t oget her wit h a
t hree- hour writ t en exam at t he end of t he course, all of which count t owards t he final
course result .
MS221 st art s in February each year, and last s about nine m ont hs.
H ow do you ch oose
M a in r e com m e n da t ion s
I f you have com plet ed an A- level ( or Higher in Scot land) in m at hs or an HNC/ D in an
engineering subj ect , and you have at least 16 hours st udy t im e per week, you should cope
reasonably well wit h MST121 and MS221 t oget her : t he m ore experience you have of
reading and writ ing m at hem at ics and of using a com put er t he easier you will find it . You
m ay need m ore t im e if you have not st udied at t his level for a num ber of years.
I f you have an AS- level in m at hs, or st udied but failed at A- level m at hs ( or Higher in
Scot land) , or HNC/ D, or you have good algebra and t rigonom et ry skills and gained a good
grade in t he highest level GCSE or 'O' Level ( or, in Scot land, SCE 'O' Grade or St andard
Grade) , unless you have a lot of t im e you are advised t o do MST121 on it s own, and follow
it wit h MS221 in a lat er year.
I f you have less m at hem at ical background or would like a course t o build up skills and
knowledge at a slower pace, consider MU123, whet her you are current ly cont em plat ing
t aking furt her courses in m at hem at ics or not .
I f you need t o im prove your m at hem at ics in order t o t ake courses in science, t echnology
or social science, consider MU123 or MST121. I f you have sufficient st udy t im e, eit her of
t hese can be t aken at t he sam e t im e as anot her Level 1 course. However, in order t o boost
your m at hem at ical confidence, you m ight t ake a 30- point m at hs course befor e em barking
on science or t echnology courses.
I f you have already passed S151 confident ly and are int ending t o st udy m at hem at ics,
physics or t echnology courses t hen you should be in a good posit ion t o t ake MST121, but
do t ry t he MST121 quiz first . I f you were less confident wit h your work on S151,
part icularly wit h t he algebr a, you should consider MU123 as t his will give you t im e t o
consolidat e your underst anding.
I f your m ain int erest is in com put ing, you m ight reasonably st art your st udies wit h MU123,
MST121 and/ or a Level 1 course in Com put ing or I nform at ion Technology.
Com bin a t ion s of cou r se s
You m ay choose t o st udy MST121 and MS221 t oget her, st art ing in February, if you have
sufficient m at hem at ical background, and at least 16 hours st udy t im e a week. These t wo
courses have been designed for t his purpose.
I f you st art MST121, you can choose t o st art MS221 lat er, eit her overlapping wit h MST121
or aft er you have com plet ed MST121. MS221 cannot sensibly be st udied unless it is st art ed
at t he sam e t im e as, or aft er st art ing, MST121.
I t is recom m ended t hat MST121 be t aken aft er MU123, as MST121 relies on a very good
underst anding of all of t he cont ent of MU123.
You can t ake a 10- , 30- or 60- point course alongside any of t he t hree m at hem at ics
courses. For st udent s who do so, t he ot her course would usually be a Level 1 course in a
different subj ect area. However, you should t hink very carefully and seek adv ice from your
OU Regional Cent re before em barking on m ore t han 60 point s in your first year of st udy.
Ot h e r fa ct or s t o con side r
MU123 requires t he use of a scient ific calculat or, which you will need t o know how t o use
before t he course st art s. Recom m ended calculat ors are eit her t he Casio fx- 83ES or t he
Texas inst rum ent s TI - 30XA, alt hough any m odel can be used providing you have t he
inst ruct ion booklet .
MST121 and MS221 require t he use of a scient ific or graphics calculat or ( any m odel) which
you will need t o know how t o use before t he course st art s.
You need regular online com put er access t o st udy any of t he courses and you should be
fam iliar wit h t he basics of using a com put er and t he int ernet before t he course st art s.
Each MU123 and MST121 t ut or offers t heir group, as a whole, about 20 hours of learning
support , which is spread t hroughout t he course present at ion. MS221 t ut ors offer about 12
hours. The support m ay be provided in face- to- face or online t eaching sessions, and be
supplem ent ed by occasional em ail or t elephone cont act .
W h a t w ill you st u dy
D iscove r in g m a t h e m a t ics M U1 2 3
As well as giving you 30 point s at Level 1 successful com plet ion of MU123 offers t he
following benefit s.
A sound and broad int roduct ion t o st udy at Universit y level, t oget her wit h t he opport unit y
t o im prove your skills in m at hem at ical com m unicat ion and independent learning.
An appreciat ion of how m at hem at ics pervades aspect s of our everyday lives.
A good foundat ion in m at hem at ical ideas, such as:
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int roduct ory st at ist ics, algebra, geom et ry and t rigonom et ry
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describing problem s m at hem at ically
m at hem at ical vocabulary and not at ion
select ion and use of m at hem at ical t echniques for solving problem s
int erpret at ion of result s in t he cont ext of real life sit uat ions
sim ple m at hem at ical argum ent s
how t o explain m at hem at ical ideas from t he course in writ ing
developm ent of skills in learning m at hem at ics
use of relevant I CT t ools for learning and for working on m at hem at ical
problem s
analysing m at hem at ical reasoning.
The oppor t unit y t o learn t o use bespok e soft ware t o help invest igat e m at hem at ical ideas.
An 'equivalent accept able qualificat ion' t o GCSE grade C in m at hs for t eacher t raining,
t hough t his is at t he discret ion of each t eacher t raining inst it ut ion.
During your st udy of MU123 you will cover t he following t opics.
D u r in g your st u dy of M U1 2 3 you w ill cove r t h e follow in g t opics.
Unit 1
I nt roduct ion t o t he course.
St a r t in g poin t s
St udy st rat egies for m at hem at ics.
Brief revision of som e key num erical skills such as rounding,
negat ive num bers and percent ages.
Mat hem at ical invest igat ions.
I nt roduct ion t o fract als.
Unit 2
M a t h e m a t ica l m ode ls
I nt roduct ion t o m at hem at ical m odelling
Rout e planning including speed, dist ance, t im e calculat ions.
Creat ing and using form ulas.
Using num ber inequalit ies.
Unit 3
N u m be r s
I nt roduct ion t o t he num ber syst em .
Mult iples, fact ors and prim es.
Pow ers and scient ific not at ion.
Rat ional num bers and reciprocals.
I rrat ional num bers and surds.
Rat io.
Unit 4
St a t ist ica l su m m a r ie s
Types of dat a.
St at ist ical invest igat ions.
Averages and m easures of spread.
Accuracy and precision.
Unit 5
Alge br a
Algebraic language.
Sim plifying expressions.
Solving linear equat ions.
Unit 6
Gr a ph s
I nt erpret ing graphs.
Gradient , int ercept and equat ion of a st raight - line graph.
Linear m odels from dat a.
Unit 7
Changing t he subj ect of an equat ion.
Equ a t ion s a n d
Solving equat ions in t wo unknowns.
in e qu a lit ie s
I nequalit ies involving one variable.
Unit 8
Ge om e t r y
Angles and Pyt hagoras’ t heorem .
Geom et rical proof.
Areas and perim et ers.
Congruency and sim ilarit y.
Circles.
Solids.
Unit 9
Ex pa n din g a lge br a
Num ber pat t erns and proof.
Bracket s and quadrat ic expressions.
Fact orisat ion and quadrat ic equat ions.
Algebraic fract ions and rearranging form ulas.
Unit 10
Qu a dr a t ics
Parabolas and t heir key feat ures.
Com plet ing t he square and t he quadrat ic form ula.
Quadrat ic m odels.
Unit 11
St a t ist ica l pict u r e s
Dot plot s and boxplot s.
Hist ogram s.
Random num bers and variat ion.
St at ist ical invest igat ions.
Unit 12
Tr igon om e t r y
Trigonom et ric rat ios and funct ions.
Solving t riangles and equat ions.
Radians and circles.
Unit 13
Ex pon e n t ia ls
Growt h and decay.
The exponent ial funct ion.
Exponent ial m odels.
Logarit hm s.
Unit 14
M a t h e m a t ics
e ve r yw he r e
More on funct ions and t heir use in m odelling.
I nt roduct ion t o num ber t heory and encrypt ion.
Usin g m a t h e m a t ics M ST1 2 1
As well as giving you 30 point s at Level 1 successful com plet ion of MST121 offers t he
following benefit s.
Experience of a range of m at hem at ical t opics em ployed in m any areas of science and
t echnology. This includes:
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applying sequences of num bers, coordinat e syst em s and form ulas t o solve
problem s;
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expressing m at hem at ical ideas and procedures clear ly;
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using vect ors and m at rices t o express and solve equat ions;
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using calculus t o solve a range of problem s;
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deepening ideas about chance and using t hese t o solve probabilit y problem s;
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using st at ist ics t o com par e dat a set s and t o est im at e likely m easures.
Expert ise in using a personal com put er, t he Windows environm ent and power ful
m at hem at ical soft ware beyond t he usual applicat ions ( such as word- processing) . These
skills can t hen be t ransfer red t o m any ot her courses, and t o ot her areas of life.
A required m at hem at ical com ponent for professional engineering inst it ut e recognit ion.
Please visit ht t p: / / www3.open.ac.uk/ courses/ essent ial/ rils.sht m
During your st udy of MST121 you will cover t he following t opics.
D u r in g your st u dy of M ST1 2 1 you w ill cove r t h e follow in g t opics.
Block A - M a t h e m a t ics a n d m ode llin g
Chapter A1 deals wit h cert ain t ypes of recurrence sequences and exam ines t heir longt erm behaviour. Such sequences arise in various real- world cont ext s, and
so t hey can be used for m at hem at ical m odelling
Chapter A2
uses an algebraic approach in order t o solve problem s about lines and
circles, and int roduces basic t rigonom et ry. Various applicat ions of lines,
circles and t rigonom et ry are included
Chapter A3
int roduces t he m at hem at ical funct ions, used t o m odel m any real- world
processes. I n part icular, t he graphs of funct ions are used t o provide
inform at ion about t he nat ure of t he solut ions of equat ions
Block B - D iscr e t e m ode ls
Chapter B1
develops t he t hem e of m at hem at ical m odelling, and in part icular working
wit h discret e m odels, by considering t wo m odels for anim al populat ions.
The chapt er also invest igat es what is m eant by t he convergence of a
sequence t o a lim it
Chapter B2
develops a m odel for a populat ion wit h specified int ernal st ruct ure by using
m at hem at ical ent it ies known as vect ors and m at rices
Chapter B3
pursues t he t opic of vect ors, but t hrough t heir geom et ric propert ies:
m agnit ude and direct ion. By applying t rigonom et ry t o vect ors, t he chapt er
shows how t hey can be used t o m odel forces act ing on a body
Block C - Con t in u ou s m ode ls
Chapter C1
concerns t he rat e at which variables change, whet her t he change is an
increase or decrease and whet her t he change st ops. The process called
different iat ion is int roduced t o help in analysing t hese m at t ers
Chapter C2
t akes a different view of change, by considering how t o m easure an
accum ulat ion of inst ant aneous changes. This is achieved by using
int egrat ion, which is t he reverse process t o different iat ion
Chapter C3
considers an applicat ion of int egrat ion t o cert ain first - order different ial
equat ions
Block D - M ode llin g u n ce r t a in t y
Chapter D1
considers a concept which is fundam ent al t o all m odels for chance event s
and w hich underpins st at ist ical t hinking: probabilit y
Chapter D2
looks at t wo m odels for t he variat ion observed in a variable are discussed one m odel for a discret e variable and one for a cont inuous variable
Chapter D3
looks at est im at ing an unknown quant it y
Chapter D4
invest igat es differences bet ween populat ions by com paring sam ples of
dat a, and relat ionships bet ween variables.
Usin g m a t h e m a t ics M ST1 2 1 w it h Ex plor in g m a t h e m a t ics M S2 2 1
I n addit ion t o t he benefit s of MST121, successful com plet ion of MS221 offers t he following.
The opport unit y t o gain 60 point s in one year of st udy from a pair of courses which
nat urally fit t oget her.
St udy at Level 2, providing t he necessary experience for m any ot her courses in
m at hem at ics, t echnology and science at t his level.
A deeper underst anding of m any of t he m at hem at ical t opics covered in MST121.
During your st udy of MS221 you will cover t he following t opics.
During your study of MS221 you will cover the following topics.
Block A - Mathematical exploration
Chapter A1 introduces linear second-order recurrence sequences, in particular the Fibonacci
sequence, which has numerous intriguing properties, and is connected with the
so-called golden ratio
Chapter A2
is concerned with the curves called conics which arise as cross-sections of a
cone in particular ellipses, hyperbolas and parabolas. These have many elegant
properties that lead to applications, for example in optics
Chapter A3
introduces a general notion of function, concentrating on functions, such as
rotations, reflections and translations, which arise in geometry. These functions
are used to show that all so-called quadratic curves are in fact conics
Block B - Exploring iteration
Chapter B1
looks at the long-term behaviour of iteration sequences by considering the
geometric properties of the related functions
Chapter B2
explores linear transformations such as rotations, reflections and shears by using
the associated matrices
Chapter B3
brings the themes of the two earlier chapters together by considering the effect of
iterating a linear transformation and by studying which points and lines in the
plane remain invariant
Block C - Exploring continuous models
Chapter C1 and explore the topics of differentiation and integration, respectively, covering basic
C2
techniques and related topics such as the Newton-Raphson method for solving
equations, and calculation of volumes of revolution
Chapter C3
introduces the topic of Taylor approximations and Taylor series. This provides
one answer to the question of how we can evaluate functions such as exp, cos
and arctan, using only addition and multiplication
Block D - Structure in mathematics
Chapter D1
looks at complex numbers, which are a ‘new’ type of number. Within the set of
real numbers, R, certain algebraic equations, such as x2 + 1 = 0, have no
solutions. But if we supplement R then we obtain a system within which all
polynomial equations have solutions
Chapter D2
considers numbers of the simplest type, integers. Over the years, these have
provided many intriguing conjectures, the study of which has contributed to the
development of mathematical ideas of much wider relevance, such as
cryptography
Chapter D3
topic is: addition and multiplication of real numbers are examples of operations. A
set with an operation satisfying particular properties is called a group
Chapter D4
concerns ‘effective argument’, a topic that has been a theme throughout MS221.
Proving that results hold is an important pillar of pure mathematics
W h a t a bou t qua lifica t ion s
It is important to note that you do not need to be aiming towards any particular qualification whilst
studying these courses. You can take courses from a range of subject areas and achieve a BA or
BSc degree which is tailored to your own requirements. However, if you think you may wish to
study towards a degree or other qualification in a particular subject area, then it is a good idea to
plan for this as early as possible. Below is a list of the qualifications which the maths entry courses
can be counted towards, and more qualifications are being introduced all the time. If you would like
further advice about qualifications, then please contact your OU Regional Centre or look at the
Open University’s qualifications website.
Ce r t ifica t e s
The Cert ificat e in Mat hem at ics is awarded upon successful com plet ion of any t wo of
MU123, MST121 and MS221.
The Cert ificat e in Com put ing and Mat hem at ics is awarded upon successful com plet ion of
Dat a, com put ing and inform at ion ( M150) , and eit her MU123 or MST121.
D iplom a s
MS221 m ay be count ed t owards t he Diplom a in Physical Science
D e gr e e s in clu din g M U1 2 3
MU123 m ay specifically be count ed t owards t he following degrees:
BA ( Hons) Business St udies
BSc ( Hons) Com put ing
Foundat ion Degree in I nform at ion and Com m unicat ion Technologies
BSc ( Hons) I nform at ion and Com m unicat ion Technologies
BSc ( Hons) I T and Com put ing ( in cert ain circum st ances)
BSc ( Hons) Physical Science
BA/ BSc Mat hem at ics and it s Learning
I t m ay also be count ed t owards t he ‘free choice’ elem ent of m any ot her qualificat ions.
D e gr e e s in clu din g M ST1 2 1
MST121 should be st udied at t he st art of any nam ed degr ee wit h ‘m at hem at ics’ in it s t it le.
I n part icular, MST121 is t he com pulsory Level 1 course in t he following degrees:
BA / BSc ( Hons) Com put ing and St at ist ics
BA / BSc ( Hons) Econom ics and Mat hem at ical Sciences
BA / BSc ( Hons) Mat hem at ics
BA / BSc ( Hons) Mat hem at ics and St at ist ics
BA / BSc ( Hons) Mat hem at ics and it s Learning
MST121 m ay specifically be count ed t owards t he following degrees:
BA ( Hons) Business St udies
BSc ( Hons) Com put ing
BA / BSc ( Hons) Com put ing and Mat hem at ical Sciences
Foundat ion Degree in I nform at ion and Com m unicat ion Technologies
BS ( Hons) I nform at ion and Com m unicat ion Technologies
BS ( Hons) I T and Com put ing ( in cert ain circum st ances)
BS ( Hons) Physical Science
I t m ay also be count ed t owards t he ‘free choice’ elem ent of m any ot her qualificat ions.
D e gr e e s in clu din g M S2 2 1
MS221 is eit her com pulsory or highly desirable for any nam ed degree wit h ‘m at hem at ics’
in it s t it le.
I n part icular, MS221 is com pulsory in t he following degr ees:
BA / BSc ( Hons) Com put ing and St at ist ics
BA / BSc ( Hons) Mat hem at ics
BA / BSc ( Hons) Mat hem at ics and St at ist ics
MS221 m ay specifically be count ed t owards t he following degrees:
BA / BSc ( Hons) Com put ing and Mat hem at ical Sciences
BA / BSc ( Hons) Econom ics and Mat hem at ical Sciences
BSc ( Hons) Physical Science
I t m ay also be count ed t owards t he ‘free choice’ elem ent of m any ot her qualificat ions.
W hat next
Br ie f gu ide t o st u dy r ou t e s
This diagram shows how t he t hree cour ses relat e t o each ot her, and t he various st udy
rout es t hey m ay lead t o.
Addit ion a l in for m a t ion
I f you wish t o st udy higher level courses in applied or pure m at hem at ics, you are st rongly
advised t o have st udied MS221 first .
I f your m ain int erest is in com put ing, t hen MU123 or MST121 would provide t he
appropriat e m at hem at ical background for st udy in t his area, but you will also need t o a
relevant Level 1 course in com put ing.
I f your m ain int erest is in physics, it is advisable t o include MS221 in your profile.
I f your m ain int erest is in st at ist ics, t hen MST121 ( or MST121 and MS221) pr ovide t he
necessary m at hem at ical knowledge for Analysing dat a ( M248) and Pract ical Modern
St at ist ics ( M249) and m ost Level 3 courses in st at ist ics.
I f your int ent ion is t o t ake a profile of courses in areas out side m at hem at ics, but wit h a
significant m at hem at ical cont ent ( such as elect ronics or engineering m echanics) , MST121
will provide you wit h m any of t he necessary m at hem at ical skills, but you m ight t hink about
t aking MS221 as well.
For ot her subj ect areas in science and t echnology, MU123 will provide you wit h t he
necessary m at hem at ical skills.
I f you are st udying m ost ly science courses and need a brief refresher of t he m ain
m at hem at ical t echniques, you m ight consider t he 10- point Mat hs for Science ( S151) . This
course could be st udied aft er com plet ion of MU123, or alongside MST121.
For subj ect areas such as art s, m anagem ent or social science MU123 will provide st at ist ical
and m at hem at ical skills t hat will enhance your st udies, as well as helping you t o im prove
your generic st udy skills.
Your choice m ight also depend on your em ploym ent and career plans - see
www.open.ac.uk/ careers for furt her advice
MU123 or MST121 provides t he basic m at hem at ics requirem ent for I nit ial Teaching
Training via t he Open Universit y's Post graduat e Cert ificat e in Educat ion ( for England and
Wales) . Bot h courses are also usually accept ed as an equivalent accept able qualificat ion t o
GCSE grade C in m at hem at ics by ot her t eacher t raining inst it ut ions. You can ask your OU
Regional Cent re for a copy of t he relevant Recognit ion Leaflet .
St a r t in g a t a h igh e r le ve l
I f you have som e m at hem at ics background, it m ay be feasible t o st art your OU st udy at
Level 2. All our Level 2 courses have a diagnost ic quiz t hat would give you an idea of t he
m at hem at ics required.
However, long experience at t he OU shows t hat only a relat ively sm all proport ion of new
m at hem at ics st udent s do st art at a higher level. For such st udent s t he percent age
com plet ion rat e on t heir first course is usually t wo t hirds of t he rat e for st udent s who have
previously t aken t he relevant OU prerequisit e courses.
Feedback from st udent s who st art t he OU at Level 2 suggest s t hat m any find it difficult t o
com bine t he st udy of m at hem at ics at t hat level wit h est ablishing t heir work rout ine for OU
st udy alongside ot her com m it m ent s.
I f you do decide t o st art at Level 2, t ake advant age of our advice about Mat hem at ical
St udy Skills.
For fut ure advice we suggest t hat you cont act your OU Regional Cent re.
Ar e you r e a dy
This sect ion is designed t o help you decide which is t he best st udy rout e for you. There are
short quizzes on what is assum ed for st udy of each of MU123, MST121, and
MST121/ MS221 com bined so t hat you can check if you have t he m at hem at ical skills t o
st art t he course.
For st udent s int ending t o st udy a num ber of courses in m at hem at ics, t he Open Universit y
has produced a Success wit h Mat hem at ics book ( I SBN: 0415 298 61 X) published in
conj unct ion wit h Rout ledge as part of t heir St udy Guide Series. Success wit h Mat hem at ics
includes bot h general st udy skills, such as m aking best use of t im e, preparing for
assignm ent s and exam s, and specific help wit h learning m at hem at ics. There are chapt ers
on how t o present your m at hem at ics effect ively, what t o do when you get st uck, and
appropriat e use of t echnology.
When you at t em pt each quiz, it doesn't m at t er if you cannot do absolut ely every quest ion.
I f you can do m ost of t he quest ions, or could do t hem wit h a rem inder ( because t he t opic
is fam iliar t o you but you can't quit e rem em ber t he det ails) , t hen you are probably ready
t o st art t he course. Bot h MU123 and MST121 have som e prepar at ory m at erials, which are
available before t he course st art s.
M U1 2 3
I f you t hink MU123 m ay be appropriat e for you, t ry t he MU123 quiz. You can always t ry
t he ot her quizzes lat er t o check t hat your choice is appropriat e.
Before starting the course it is recommended that you work through some of the free and
open educational resources from the OU’s OpenLearn website (www.open.ac.uk/openlearn),
These resour ces will also enable you t o revise t he t ypes of skills t hat are needed t o answer
t he quest ions in t he quiz. There is a module to help you to refresh your knowledge of each of
the following topics:
•
Numbers, units and arithmetic
•
Rounding and estimation
•
Ratio, proportion and percentages
•
Squares, roots and powers
•
Diagrams, charts and graphs
•
Language, notation and formulas
•
Geometry
Alt ernat ively, consider one of t he following.
Teach yourself basic m at hs, by Alan Graham , and published by Hodder and St ought on
( I SBN–10: 0071429735; I SBN–13: 978- 0071429733) .
A Key St age 3 ( or possibly Key St age 4) or equivalent , m at hem at ics book.
You could also help yourself by ensuring t hat you are fam iliar wit h how your scient ific
calculat or works.
M ST1 2 1 or M ST1 2 1 / M S2 2 1 com bine d
I f you are considering MST121 as t he best st art ing point , t hen look at t he MST121 quiz.
MST121 and MS221 are designed so t hat t hey m ay be t aken in t he sam e year, so if you
are t hinking of com bining t hem t hen also t ry t he slight ly m ore challenging quest ions in t he
MST121 and MS221 com bined quiz. However, if you have never encount ered any of t he
cont ent of MST121 and MS221 before, you m ay find it difficult t o assim ilat e all of t he
m at erial in one year. I n t hat case you m ay wish t o consider t aking MST121 and t hen
st art ing MS221 at a lat er dat e, t o allow yourself t im e t o consolidat e new m at hem at ical
ideas.
MST121 has som e prepar at ory m at erials which are available before t he course st art s. I f
you wish t o do som e work before t hen,we suggest t hat you look at one of t he following
books, which m ay be available in a local library.
I f you need t o refresh your skills in algebra, or if t his is your first Open Universit y
m at hem at ics course, t hen t ry Count down t o m at hem at ics: Volum e 1 by Lynne Graham and
David Sargent ( 1981) , published by Addison- Wesley, I SBN 0 201 13730 5. [ However, if
you have problem s wit h algebra, you should consider doing MU123 before MST121.]
To gain great er fluency wit h algebra, and also t rigonom et ry, use t he com panion book:
Count down t o m at hem at ics: Volum e 2 by Lynne Graham and David Sargent ( 1981) ,
published by Addison- Wesley, I SBN 0 201 13731 3. There is a lot of m at erial, som e of
which goes beyond what is needed t o st art MST121, but it is wort h t rying exam ples from
each of t he m odules.
A GCSE- t ype m at hem at ics t ext book which includes algebra and t rigonom et ry.
You could also help yourself by ensuring t hat you are t horoughly fam iliar wit h how your
scient ific or graphics calculat or works.
Cou r se qu izze s
These are designed t o help you decide which is t he best st udy rout e for you. There are
short quizzes on what is assum ed for st udy of each of MU123, MST121 and
MST121/ MS221 com bined so t hat you can check if you have t he m at hem at ical skills t o
st art t he course.
When you at t em pt each quiz, it doesn't m at t er if you cannot do absolut ely every quest ion.
I f you can do m ost of t he quest ions, or could do t hem wit h a rem inder ( because t he t opic
is fam iliar t o you but you can't quit e rem em ber t he det ails) , t hen you are probably ready
t o st art t he course. To prepare yourself well for MU123 it is recommended that you work
through some of the free and open educational resources from the OU’s OpenLearn website
(www.open.ac.uk/openlearn), MST121 has preparat or y m at erial, which is sent out before
t he course st art s, and which will enable you t o revise t he t ypes of skills t hat are needed t o
answer t he quest ions in t he MST121 quiz.
I f t he MU123 quiz seem s t oo advanced, consider st udying St art ing wit h m at hs ( Y162)
before m oving ont o MU123.
M U1 2 3 Qu iz
MU123 will assum e t hat you can answer m ost of t he quest ions in t he quiz correct ly before
you st art t he course. To help you revise exist ing skills for MU123 it is recommended that
you work through Maths Help.
I t should also be not ed t hat MU123 involves m ore reading and writ ing t han m any st udent s
ant icipat e on a m at hem at ics course. I f you are not able t o read a docum ent such as t his
Mat hs Choices websit e reasonably fluent ly, t hen it m ay t ake you m ore t im e t o st udy t he
course.
I f t he MU123 quiz seem s t oo advanced, consider st udying St art ing wit h Mat hs ( Y162)
before m oving ont o MU123.
Try t o answer each of t he following quest ions. You can do t hem in any order and t ake as
m uch t im e as you like. I f need be, use a calculat or t o help you wit h Quest ions 4, 5 and 6.
MU123 quiz
Question 1
If the temperature at 2 am on Wednesday is −5◦ C and 12 hours later it is
3â—¦ C, by how many degrees has the temperature risen?
Question 2
You are considering buying carpet tiles for a room you are decorating. In
which of the following sizes are the tiles likely to be available? Give a
reason for your choice.
(a) 15 mm by 15 mm
(b) 3 m by 3 m
(c) 30 cm by 30 cm
(d) 1.5 km by 1.5 km
Question 3
Calculate the following.
(a) (−2) × (−1.5)
(b)
2 3
+
5 4
(c)
2
4
×1
3
5
(d) 2.13 + (−5.74)
(e) (−27) ÷ 3
(f) 52
Question 4
A store is offering 15% off all electrical goods during its summer sale.
What would you pay for a washing machine that usually costs £310?
Question 5
A family on holiday in Florida is considering buying a souvenir which is on
sale for $22. If the rate of exchange at the time is £1 = $1.42
approximately how much does the souvenir cost in pounds?
Question 6
This is a plan of a garden.
7m
1.5 m
5m
The owner intends to have a circular flower bed in the middle of a lawn. If
400 grams of grass seed covers 8 square metres, how much grass seed will
be needed to re-seed the lawn? (Give your answer to the nearest
100 gram.) The area of a circle is π × radius2 , where π is 3.14159. . . .
Question 7
A plan from a DIY booklet shows a shelf and its metal bracket. The shelf
makes a right angle with the wall.
28°
The size of one of the angles is given; what are the sizes of the other two
angles in this triangle?
[END OF QUESTIONS]
MU123 answers
Answer 1
3◦ − (−5◦) = 8◦ C.
Answer 2
(c) 30 cm by 30 cm is probably the best choice, as this size would give the
most flexibility as generally rooms are at least 2 m by 3 m.
Reasons for rejecting the others are:
(a) too small
(b) too large (may be larger than the room!)
(d) much too large, more like a very large field.
Answer 3
(a) (−2) × (−1.5) = 2 × 1.5 = 3
8
15
23
3
+
=
=1
20 20
20
20
2 9
18
6
1
(c) × =
= =1
3 5
15
5
5
(b)
(d) 2.13 + (−5.74) = 2.13 − 5.74 = −3.61
(e) (−27) ÷ 3 = −9
(f) 52 = 5 × 5 = 25
Answer 4
15% of 310 =
15
100
× 310 = 0.15 × 310 = 46.5.
So you would pay £310 − £46.50 = £263.50.
Answer 5
22 ÷ 1.42 = 15.49295775, so the cost is about £15.49.
Answer 6
Area of the garden is 7 × 5 = 35 m2
Area of the flower bed is
π × (1.5)2 = 3.14159 . . . × (1.5)2 = 7.0685 . . . ≈ 7.069 m2
Area of lawn is 35 − 7.069 = 27.931 m2
Amount of seed required is
27.931
= 1396.5 . . . = 1400 g (to the nearest 100 g).
400 ×
8
Answer 7
Since it is a right-angled triangle, one angle is 90â—¦. The angles of a triangle
add to 180◦ which gives 180◦ − (28◦ + 90◦) = 62◦ as the size of the third
angle.
[END OF ANSWERS]
I f you m anaged t o get m ost ly correct answers, or at least t he m et hod of solut ion given
here m akes sense t o you, t hen consider st art ing wit h MU123. However you m ight also like
t o look at t he quest ions in t he MST121 quiz.
I f you decide t o st art your st udies wit h MU123, you can do som e addit ional preparat ion
using Maths Help.
You m ight also like t o look at t he quest ions in t he MST121 quiz and MST121 and MS221
com bined quiz.
I f you found t hese quest ions quit e challenging t hen you m ight be able t o do MU123 aft er a
considerable am ount of preparat ion. Try using Mat hs Help.
Alt ernat ively consider t aking St art ing wit h m at hs ( Y162) first . Y162 includes t opics such as
fract ions, decim als and percent ages, using form ulas and working wit h dat a and graphs. I t
also discusses st rat egies for solving problem s and writ ing m at hem at ics. This course would
be part icularly relevant if you have not used or st udied m at hem at ics for som e t im e and
would be very useful preparat ion for MU123. The course last s 14 - 20 weeks, and provides
a gent ler int roduct ion t o t he skills of successful learning at a dist ance, as well as giving a
good grounding in m at erial relevant t o MU123. On successful com plet ion of a final
assignm ent you gain 10 point s at Level 1, which m ay be count ed t owards a degree.
Your Regional Cent re m ay be able t o give you furt her advice on ot her access or
preparat ory courses.
M ST1 2 1 Qu iz
MST121 will assum e t hat you can do m ost of t he following quest ions before you st art t he
course. Ther e is a preparat ory package t o help you prepare for MST121 but it s m ain aim is
t o help you t o revise exist ing skills.
Try t o answer t he following quest ions. Do t hem in any order and t ake as m uch t im e as you
like. I f need be, use a calculat or t o help you wit h Quest ions 1, 2, 3, 5, 8 and 10.
MST121 quiz
Question 1
The mean height of a sample of sunflowers was 1 m. The grower then tried
a new fertiliser which claimed to increase the average height of a plant by
at least 10%. The heights that the sunflowers reached (in metres) were:
1.12
1.26
1.34
1.25
0.96
1.04
0.95
1.21
1.11
1.24
1.02
0.99
0.87
1.27
1.28
0.98
1.29
1.22
Calculate the mean (average) height of the sunflowers, and say whether it
is consistent with the claim given for the fertiliser or not.
Question 2
Straight in front of me is Fred at a distance of 100 m. Directly to my right
is Gillian at a distance of 200 m. How far apart are Fred and Gillian?
Question 3
The mass, m, of the Earth, in kilograms, can be calculated by using the
gR2
, where g = 9.8 ms−2 , R = 6.37 × 106 m and
formula m =
G
G = 6.67 × 10−11 m3 s−2 kg−1 .
Find the Earth’s mass in scientific notation, correct to 3 significant figures.
Question 4
(a) Factorise x2 − 8x + 15.
(b) Expand (3y − 2)(2y + 4) by multiplying out the brackets.
(c) These two pieces of metal have the same area. What are the actual
dimensions of each piece?
( y + 12) cm
( y + 5) cm
y cm
( y + 5) cm
Question 5
The road sign below shows that the road rises 1 m for every 10 m along the
road. Calculate the angle between the road and the horizontal.
10%
Question 6
Make s the subject of the formula
p=
100(s − c)
.
c
Question 7
(a) Sketch the two lines represented by the equations
y = 5 − x and y = 2x + 14.
(b) Using algebra, find the coordinates of the point where the two lines
meet.
Question 8
(a) Sketch the graph of y = sin(2x).
(b) Give the values of cos x when x = 0.5 radians and when x = 23â—¦.
Question 9
Solve each of the following.
(a) 5t + 4 = 3t
(b) 3y + 2 ≥ 5
(c) 2(x − 1) < 3
Question 10
Solve, using the quadratic equation formula, each of the following
equations.
(a) x2 − 5x + 2 = 0
(b) 3x2 + 4x − 5 = 0
The quadratic formula is x =
−b ±
√
b2 − 4ac
.
2a
[END OF QUESTIONS]
MST121 answers
Answer 1
20.4
= 1.1333 . . . = 1.13 m (to three significant figures).
18
Previous mean height was 1 m so there has been an increase in mean
height of 0.13 m. 10% of 1 m is 0.10 m. This result supports the claim.
Mean =
Answer 2
Since the triangle formed by Fred, Gillian and me is right-angled,
Pythagoras’ Theorem can be applied. 1002 + 2002 = 50 000. Taking the
square root of this value gives 223.6068 so the distance is 223.6 m (to one
decimal place).
Answer 3
5.96 × 1024 kg (to three significant figures).
Answer 4
(a) x2 − 8x + 15 = (x − 3)(x − 5).
(b) (3y − 2)(2y + 4) = 6y 2 + 12y − 4y − 8 = 6y 2 + 8y − 8.
(c) Since the areas are equal,
y(y + 12) = (y + 5)(y + 5)
y 2 + 12y = y 2 + 10y + 25
12y = 10y + 25
2y = 25
y = 12.5
Dimensions are 12.5 cm by 24.5 cm and 17.5 cm by 17.5 cm.
Answer 5
10
1
Let x be the angle between the road and the horizontal.
Then sin x =
figures).
1
10
= 0.1; thus x = 5.74â—¦ (or 0.10 radians) (to three significant
Answer 6
100(s − c)
.
c
pc = 100(s − c)
pc
=s−c
100
pc
+c=s
100
p
pc
So s =
+c=c
+1 .
100
100
p=
Answer 7
(a)
y
(0,14)
(0,5)
(5,0)
(–7,0)
y = 2x + 14
x
y=5–x
(b) At the point (x, y) where the two lines meet, both y = 5 − x and
y = 2x + 14 hold, so that
5 − x = 2x + 14
5 − 14 = 3x
−9 = 3x.
So x = −3.
When x = −3, y = 5 − (−3) = 8.
So the lines meet at the point (−3, 8).
Answer 8
(a)
y = sin 2x
1
–90°
0
90°
180°
270°
360°
–1
(b) cos 0.5 = 0.878 (to three decimal places);
cos 23â—¦ = 0.921 (to three decimal places).
Answer 9
(a) t = −2
(b) y ≥ 1
(c) x < 2.5
Answer 10
√
5 ± 25 − 8
(a) x =
2
which gives 0.438 and 4.562 (to three decimal places).
√
16 + 60
6
which gives −2.120 and 0.786 (to three decimal places).
(b) x =
−4 ±
[END OF ANSWERS]
x
I f you m anaged t o get m ost ly correct answers, or at least t he m et hod of solut ion given
here m akes sense t o you, t hen consider st art ing wit h MST121.
I f you are planning t o st udy MST121 t hen you m ight like t o consider t aking MS221 at t he
sam e t im e. I f you haven't already done so, t ry t he quiz for t he com bined courses. You
should be ready t o st udy MS221 if you can answer 'yes' t o t he following quest ions.
1.
Do you feel t hat you will be able t o devot e no less t han 16 hours t o your st udies
each week?
2.
Does your m at hem at ical background include an A- Level or Higher in m at hs or an
HNC/ D in an engineering subj ect , or have you obt ained t his level of knowledge
som e ot her way?
3.
When you st udy m at hem at ics, do you like t o underst and t he principles behind
what you are doing rat her t han j ust learn how t o do it ?
I f you decide t o st art your st udies wit h MST121, you will be sent a preparat or y pack t o
work t hrough before t he course begins. However, you can do som e addit ional preparat ion
by working t hrough one or m ore of t he books recom m ended for MST121 in t he Are you
ready? sect ion.
I f you found t he MST121 quiz quest ions quit e challenging t hen you m ight be able t o do
MST121 aft er a considerable am ount of preparat ion. However you m ay need t o st art wit h
MU123 inst ead, so have a look at t he MU123 quiz. Ot herwise you should consult your
Regional Cent re for furt her advice on access or preparat ory courses.
M ST1 2 1 / M S2 2 1 com bine d Qu iz
I f you are considering doing MST121 and MS221 t oget her at t he sam e t im e, t hen you will
need t o be m ore confident wit h algebra and t rigonom et ry t han if you were t aking MST121
alone. You should t herefore be able t o do m ost of t he following quest ions before you
em bark on t he t wo courses at t he sam e t im e. There is a preparat ory package t o help you
revise exist ing skills for MST121, but t here is no separat e pr eparat ory pack for MS221.
Try t o answer t he following quest ions. Do t hem in any order and t ake as m uch t im e as you
like. You should at t em pt t he quest ions wit hout use of a calculat or.
MST121/MS221 combined
quiz
Question 1
Given that ap × aq = ap+q , a−p =
1
and (ap )q = apq simplify.
ap
(a) 93/2
(b) a2 ÷ a−7 × a−12 ÷ a−4
Question 2
Find the area of the triangle.
5
4
Question 3
Fill in the two correct numbers in the places denoted by (∗):
(x + (∗))2 − (∗) = x2 + 8x + 13.
Question 4
Change the subject of the equation to the letter given in brackets.
l
(l)
(a) T = 2Ï€
g
x+a
(x)
(b) m =
b−x
Question 5
Find the coordinates of the points of intersection of the line y = 2 − x and
the parabola y = x2 − 4.
Question 6
By multiplying out the brackets, simplify
√
5+
√ √
√
2
5− 2 .
1
Question 7
Find tan θ (as an exact fraction) from the following triangle.
Ö13
q
3
[END OF QUESTIONS]
2
MST121/MS221 combined
answers
Answer 1
3
(a) 93/2 = 91/2 = 33 = 27.
(b) a2 ÷ a−7 × a−12 ÷ a−4 = a2 × a7 × a−12 × a4 = a(2+7−12+4) = a1 = a.
Answer 2
The base of the triangle is
1
2
× base × height =
1
2
√
52 − 42 = 3, so the area of the triangle is:
× 3 × 4 = 6 square units.
Answer 3
(x + (4))2 − (3) = x2 + 8x + 16 − 3 = x2 + 8x + 13.
Hence the two numbers required are 4 and 3.
Answer 4
l
(a) T = 2Ï
This sit e is about your choices if you wish t o st art st udying m at hem at ics wit h t he Open
Universit y. I t describes courses and possible st udy rout es, and gives you inform at ion which
you m ight t ake int o considerat ion when m aking your decision. I t also gives you help in
j udging which of t he possible rout es is best for you.
The m at hem at ics ent ry suit e consist s of t he following courses:
St art ing wit h m at hs ( Y162) - 10 point s
Discovering m at hem at ics ( MU123) - 30 point s
Using m at hem at ics ( MST121) - 30 point s
Exploring m at hem at ics ( MS221) - 30 point s
Which of t hese you choose t o st udy will depend largely on your previous m at hem at ics
experience and what you m ight want t o st udy lat er.
I f you haven't st udied recent ly and feel uncert ain about your m at hem at ics, we recom m end
st art ing wit h our short Openings course St art ing wit h m at hs ( Y162) which will help build
up your st udy skills, and is part icularly appropriat e if you t hink your m at hs background is
weak ( if, say, you left school at 16 wit hout a form al qualificat ion in m at hem at ics) .
•
Starting with maths (Y162) leads onto MU123
I f you're confident about your st udy skills, and have st udied m at hs successfully at school
up t o or beyond GCSE ( or equivalent ) , we recom m end you st art eit her wit h Discovering
m at hem at ics ( MU123) or Using m at hem at ics ( MST121) . Bot h will get you accust om ed t o
OU st udy and t each you som e m at hem at ics.
•
Discovering mathematics (MU123)
•
Using mathematics (MST121)
Discovering m at hem at ics ( MU123) leads ont o MST121
Using m at hem at ics ( MST121) leads ont o MS221. Alt ernat ively, Using m at hem at ics
( MST121) and Exploring m at hem at ics ( MS221) can be t aken t oget her assum ing you are
adequat ely prepared and have plent y of st udy t im e
Regardless of previous m at hem at ical knowledge, it is sensible for new st udent s t o m at hs
at t he OU t o st art at Level 1. Most st udent s find it t akes t im e t o organise t heir st udy and
deadlines alongside t he dem ands of t he rest of t heir lives. Our courses are designed t o
help you get accust om ed t o st udying m at hs wit h t he OU.
Most of our st udent s do st art at Level 1, choosing t heir course on t he basis of t he advice at
t his websit e. A sm all num ber of st udent s st art at a higher level, alt hough Level 2 and 3
courses not only assum e prior t echnical knowledge and experience, but t hat st udent s are
also used t o st udying t he OU way. Even if t he courses you require are at a higher level,
t hen it is usually sensible t o consider st art ing at a lower level as advised in Mat hs Choices.
See St art ing at a higher level for m ore inform at ion.
W h a t is a va ila ble t o you
The courses in t he m at hem at ics ent ry suit e share a com m on approach t o m at hem at ics and
it s st udy, and t here is a nat ural progression bet ween t hem , wit h a planned developm ent of
t he skills you need t o acquire. They are designed for flexibilit y, giving you a choice of
where t o st art and how m uch t o st udy, depending on your needs. They cat er for t hose who
wish t o st udy m ainly m at hem at ics courses and for t hose who need som e m at hem at ics t o
underpin t heir st udies in ot her areas, or who j ust have a personal int erest in m at hem at ics.
St a r t in g w it h m a t h s Y1 6 2 - 1 0 point s
I f you are part icularly int erest ed in m at hs, or you want t o st udy a m at hs- based subj ect or
one where m at hs will feat ure significant ly, St art ing wit h m at hs offers a friendly
int roduct ion. The course w ill help you feel m ore confident in using m at hs in a variet y of
different sit uat ions - at hom e, in work or in your ot her st udies. There are t hr ee m ain
t hem es developed in t he course:
•
im proving your m at hem at ical skills including using a calculat or effect ively;
•
developing problem - solving st rat egies so t hat you know what t o do when you get
st uck;
•
pract ising general learning skills t o help you becom e an effect ive learner.
Using m at hem at ics in t he real world is som et im es quit e different t o t ackling a clearlyst at ed problem in a t ext book. During t he course, you will consider several real- life
exam ples, including a case st udy based on a conservat ion issue, so t hat you can see t he
differences yourself, and feel m ore confident in using m at hem at ics in your own life t o solve
problem s and m ake decisions. Being able t o com m unicat e using m at hem at ical ideas is
im port ant , whet her you are reading t he work of ot hers or explaining your own solut ions.
The course w ill help you develop t hese skills, in part icular using not at ion and language
appropriat ely and writ ing good m at hem at ical solut ions t hat are easy t o underst and. As well
as m at hs t hat is useful in everyday sit uat ions, t he course also includes puzzles, bit s of
hist ory and som e m at hem at ical ideas t hat are fascinat ing in t heir own right .
You will find t he course useful whet her you are building up t owards regular, st ruct ured
st udy or are sim ply int erest ed in finding out about m at hem at ics and it s place in our lives.
I n t his course t he m at hem at ical ideas are em phasised m ore t han t he t echnological and
scient ific ones, alt hough t he skills are equally appropriat e for anyone who int ends t o st udy
t echnology or science.
The course m at erials have been prepared wit h t he needs of new learners in m ind. They
assum e no special knowledge and no experience of st udying. Taking exam ples from
everyday life, t hey enable you t o st art from your general knowledge and int er est s and
gradually build up t o degr ee- level st udy. Learning skills are key t o t he course, and skills
such as t im e m anagem ent , not e t aking, reading for st udy purposes and reflect ion on your
own learning are explored.
St art ing wit h m at hs st art s four t im es a year, in March, June, Sept em ber and Novem ber.
Each course last s for a m axim um of 20 weeks alt hough you can t ake less t im e if you
prefer.
D iscove r ing m a t h e m a t ics M U1 2 3 - 3 0 poin t s
This course int roduces som e fundam ent al m at hem at ical ideas and will form a relevant part
of m any st udy profiles, including t hose in t he sciences and in t he hum anit ies. I t covers
statistical, graphical, algebraic, trigonometric and numerical concepts and techniques, and
introduces mathematical modelling. I t does assum e arit hm et ical, but not algebraic, skills.
MU123 is t herefore less m at hem at ically dem anding t han MST121, but will help you to
integrate mathematical ideas into your everyday thinking and build your confidence in using
and learning mathematics. The developm ent of skills in interpreting and explaining
mathematics is an im port ant aspect of t he course.
Providing you have the appropriate background knowledge, you should expect to spend
about eight hours a week studying the course. There are five t ut or- m arked assignm ent s and
a num ber of short int eract ive com put er- based assignm ent s, all of which count t owards t he
final course result .
The course st art s at t he beginning of February and Oct ober each year, and last s about nine
m ont hs.
M ST1 2 1 Usin g m a t h e m a t ics - 3 0 poin t s
This provides a broad int roduct ion t o t he nat ure of m at hem at ics and it s uses in t he m odern
world. I t shows how m at hem at ics can be used t o invest igat e and answer quest ions from
science, t echnology and everyday life. This course assum es good skills in algebra,
t rigonom et ry and geom et r y, and fam iliarit y wit h t he m ain funct ions on a scient ific
calculat or, such as t he sine and exponent ial funct ions. ( Successful st udy of MU123 or t he
highest level GCSE could provide t he required skills.)
On average t he course needs at least 8 hours of st udy each week. I t t eaches t he use of
m at hem at ical and st at ist ical com put er soft ware packages. There are four t ut or- m arked
assignm ent s and t wo com put er- m arked assignm ent s, all of which count t owards t he final
course result . I n addit ion t here is a pract ice t ut or- m arked assignm ent and com put erm arked assignm ent at t he beginning of t he course.
The course st art s in lat e January and lat e Sept em ber each year, and last s about nine
m ont hs.
M ST1 2 1 / M S2 2 1 com bine d - a t ot a l of 6 0 poin t s
Usin g m a t h e m a t ics M ST1 2 1
Ex plor in g m a t h e m a t ics M S2 2 1
This com binat ion com prises of t he t wo courses, MST121 and MS221, which have been
designed so t hat t hey can be t aken essent ially as a single 60 point course wit hin one year.
The prer equisit e m at hem at ical knowledge for t he pair of courses is m ore t han t he
m inim um background for MST121 as m ore advanced concept s are included in MS221, such
as t he role of reasoning in m at hem at ics, so a relevant A- level or equivalent is desirable
before st udying t he t wo courses at t he sam e t im e. By t he end of MS221 you will have
encount ered m any of t he t opics t hat are developed in lat er m at hem at ics courses, and bot h
use t he sam e m at hem at ical soft ware package.
On average, t hese courses t oget her need at least 16 hours of st udy each week. I n addit ion
t o t he assessm ent on MST121, MS221 has four t ut or- m arked assignm ent s t oget her wit h a
t hree- hour writ t en exam at t he end of t he course, all of which count t owards t he final
course result .
MS221 st art s in February each year, and last s about nine m ont hs.
H ow do you ch oose
M a in r e com m e n da t ion s
I f you have com plet ed an A- level ( or Higher in Scot land) in m at hs or an HNC/ D in an
engineering subj ect , and you have at least 16 hours st udy t im e per week, you should cope
reasonably well wit h MST121 and MS221 t oget her : t he m ore experience you have of
reading and writ ing m at hem at ics and of using a com put er t he easier you will find it . You
m ay need m ore t im e if you have not st udied at t his level for a num ber of years.
I f you have an AS- level in m at hs, or st udied but failed at A- level m at hs ( or Higher in
Scot land) , or HNC/ D, or you have good algebra and t rigonom et ry skills and gained a good
grade in t he highest level GCSE or 'O' Level ( or, in Scot land, SCE 'O' Grade or St andard
Grade) , unless you have a lot of t im e you are advised t o do MST121 on it s own, and follow
it wit h MS221 in a lat er year.
I f you have less m at hem at ical background or would like a course t o build up skills and
knowledge at a slower pace, consider MU123, whet her you are current ly cont em plat ing
t aking furt her courses in m at hem at ics or not .
I f you need t o im prove your m at hem at ics in order t o t ake courses in science, t echnology
or social science, consider MU123 or MST121. I f you have sufficient st udy t im e, eit her of
t hese can be t aken at t he sam e t im e as anot her Level 1 course. However, in order t o boost
your m at hem at ical confidence, you m ight t ake a 30- point m at hs course befor e em barking
on science or t echnology courses.
I f you have already passed S151 confident ly and are int ending t o st udy m at hem at ics,
physics or t echnology courses t hen you should be in a good posit ion t o t ake MST121, but
do t ry t he MST121 quiz first . I f you were less confident wit h your work on S151,
part icularly wit h t he algebr a, you should consider MU123 as t his will give you t im e t o
consolidat e your underst anding.
I f your m ain int erest is in com put ing, you m ight reasonably st art your st udies wit h MU123,
MST121 and/ or a Level 1 course in Com put ing or I nform at ion Technology.
Com bin a t ion s of cou r se s
You m ay choose t o st udy MST121 and MS221 t oget her, st art ing in February, if you have
sufficient m at hem at ical background, and at least 16 hours st udy t im e a week. These t wo
courses have been designed for t his purpose.
I f you st art MST121, you can choose t o st art MS221 lat er, eit her overlapping wit h MST121
or aft er you have com plet ed MST121. MS221 cannot sensibly be st udied unless it is st art ed
at t he sam e t im e as, or aft er st art ing, MST121.
I t is recom m ended t hat MST121 be t aken aft er MU123, as MST121 relies on a very good
underst anding of all of t he cont ent of MU123.
You can t ake a 10- , 30- or 60- point course alongside any of t he t hree m at hem at ics
courses. For st udent s who do so, t he ot her course would usually be a Level 1 course in a
different subj ect area. However, you should t hink very carefully and seek adv ice from your
OU Regional Cent re before em barking on m ore t han 60 point s in your first year of st udy.
Ot h e r fa ct or s t o con side r
MU123 requires t he use of a scient ific calculat or, which you will need t o know how t o use
before t he course st art s. Recom m ended calculat ors are eit her t he Casio fx- 83ES or t he
Texas inst rum ent s TI - 30XA, alt hough any m odel can be used providing you have t he
inst ruct ion booklet .
MST121 and MS221 require t he use of a scient ific or graphics calculat or ( any m odel) which
you will need t o know how t o use before t he course st art s.
You need regular online com put er access t o st udy any of t he courses and you should be
fam iliar wit h t he basics of using a com put er and t he int ernet before t he course st art s.
Each MU123 and MST121 t ut or offers t heir group, as a whole, about 20 hours of learning
support , which is spread t hroughout t he course present at ion. MS221 t ut ors offer about 12
hours. The support m ay be provided in face- to- face or online t eaching sessions, and be
supplem ent ed by occasional em ail or t elephone cont act .
W h a t w ill you st u dy
D iscove r in g m a t h e m a t ics M U1 2 3
As well as giving you 30 point s at Level 1 successful com plet ion of MU123 offers t he
following benefit s.
A sound and broad int roduct ion t o st udy at Universit y level, t oget her wit h t he opport unit y
t o im prove your skills in m at hem at ical com m unicat ion and independent learning.
An appreciat ion of how m at hem at ics pervades aspect s of our everyday lives.
A good foundat ion in m at hem at ical ideas, such as:
•
•
•
•
•
•
•
•
int roduct ory st at ist ics, algebra, geom et ry and t rigonom et ry
•
•
describing problem s m at hem at ically
m at hem at ical vocabulary and not at ion
select ion and use of m at hem at ical t echniques for solving problem s
int erpret at ion of result s in t he cont ext of real life sit uat ions
sim ple m at hem at ical argum ent s
how t o explain m at hem at ical ideas from t he course in writ ing
developm ent of skills in learning m at hem at ics
use of relevant I CT t ools for learning and for working on m at hem at ical
problem s
analysing m at hem at ical reasoning.
The oppor t unit y t o learn t o use bespok e soft ware t o help invest igat e m at hem at ical ideas.
An 'equivalent accept able qualificat ion' t o GCSE grade C in m at hs for t eacher t raining,
t hough t his is at t he discret ion of each t eacher t raining inst it ut ion.
During your st udy of MU123 you will cover t he following t opics.
D u r in g your st u dy of M U1 2 3 you w ill cove r t h e follow in g t opics.
Unit 1
I nt roduct ion t o t he course.
St a r t in g poin t s
St udy st rat egies for m at hem at ics.
Brief revision of som e key num erical skills such as rounding,
negat ive num bers and percent ages.
Mat hem at ical invest igat ions.
I nt roduct ion t o fract als.
Unit 2
M a t h e m a t ica l m ode ls
I nt roduct ion t o m at hem at ical m odelling
Rout e planning including speed, dist ance, t im e calculat ions.
Creat ing and using form ulas.
Using num ber inequalit ies.
Unit 3
N u m be r s
I nt roduct ion t o t he num ber syst em .
Mult iples, fact ors and prim es.
Pow ers and scient ific not at ion.
Rat ional num bers and reciprocals.
I rrat ional num bers and surds.
Rat io.
Unit 4
St a t ist ica l su m m a r ie s
Types of dat a.
St at ist ical invest igat ions.
Averages and m easures of spread.
Accuracy and precision.
Unit 5
Alge br a
Algebraic language.
Sim plifying expressions.
Solving linear equat ions.
Unit 6
Gr a ph s
I nt erpret ing graphs.
Gradient , int ercept and equat ion of a st raight - line graph.
Linear m odels from dat a.
Unit 7
Changing t he subj ect of an equat ion.
Equ a t ion s a n d
Solving equat ions in t wo unknowns.
in e qu a lit ie s
I nequalit ies involving one variable.
Unit 8
Ge om e t r y
Angles and Pyt hagoras’ t heorem .
Geom et rical proof.
Areas and perim et ers.
Congruency and sim ilarit y.
Circles.
Solids.
Unit 9
Ex pa n din g a lge br a
Num ber pat t erns and proof.
Bracket s and quadrat ic expressions.
Fact orisat ion and quadrat ic equat ions.
Algebraic fract ions and rearranging form ulas.
Unit 10
Qu a dr a t ics
Parabolas and t heir key feat ures.
Com plet ing t he square and t he quadrat ic form ula.
Quadrat ic m odels.
Unit 11
St a t ist ica l pict u r e s
Dot plot s and boxplot s.
Hist ogram s.
Random num bers and variat ion.
St at ist ical invest igat ions.
Unit 12
Tr igon om e t r y
Trigonom et ric rat ios and funct ions.
Solving t riangles and equat ions.
Radians and circles.
Unit 13
Ex pon e n t ia ls
Growt h and decay.
The exponent ial funct ion.
Exponent ial m odels.
Logarit hm s.
Unit 14
M a t h e m a t ics
e ve r yw he r e
More on funct ions and t heir use in m odelling.
I nt roduct ion t o num ber t heory and encrypt ion.
Usin g m a t h e m a t ics M ST1 2 1
As well as giving you 30 point s at Level 1 successful com plet ion of MST121 offers t he
following benefit s.
Experience of a range of m at hem at ical t opics em ployed in m any areas of science and
t echnology. This includes:
•
applying sequences of num bers, coordinat e syst em s and form ulas t o solve
problem s;
•
expressing m at hem at ical ideas and procedures clear ly;
•
using vect ors and m at rices t o express and solve equat ions;
•
using calculus t o solve a range of problem s;
•
deepening ideas about chance and using t hese t o solve probabilit y problem s;
•
using st at ist ics t o com par e dat a set s and t o est im at e likely m easures.
Expert ise in using a personal com put er, t he Windows environm ent and power ful
m at hem at ical soft ware beyond t he usual applicat ions ( such as word- processing) . These
skills can t hen be t ransfer red t o m any ot her courses, and t o ot her areas of life.
A required m at hem at ical com ponent for professional engineering inst it ut e recognit ion.
Please visit ht t p: / / www3.open.ac.uk/ courses/ essent ial/ rils.sht m
During your st udy of MST121 you will cover t he following t opics.
D u r in g your st u dy of M ST1 2 1 you w ill cove r t h e follow in g t opics.
Block A - M a t h e m a t ics a n d m ode llin g
Chapter A1 deals wit h cert ain t ypes of recurrence sequences and exam ines t heir longt erm behaviour. Such sequences arise in various real- world cont ext s, and
so t hey can be used for m at hem at ical m odelling
Chapter A2
uses an algebraic approach in order t o solve problem s about lines and
circles, and int roduces basic t rigonom et ry. Various applicat ions of lines,
circles and t rigonom et ry are included
Chapter A3
int roduces t he m at hem at ical funct ions, used t o m odel m any real- world
processes. I n part icular, t he graphs of funct ions are used t o provide
inform at ion about t he nat ure of t he solut ions of equat ions
Block B - D iscr e t e m ode ls
Chapter B1
develops t he t hem e of m at hem at ical m odelling, and in part icular working
wit h discret e m odels, by considering t wo m odels for anim al populat ions.
The chapt er also invest igat es what is m eant by t he convergence of a
sequence t o a lim it
Chapter B2
develops a m odel for a populat ion wit h specified int ernal st ruct ure by using
m at hem at ical ent it ies known as vect ors and m at rices
Chapter B3
pursues t he t opic of vect ors, but t hrough t heir geom et ric propert ies:
m agnit ude and direct ion. By applying t rigonom et ry t o vect ors, t he chapt er
shows how t hey can be used t o m odel forces act ing on a body
Block C - Con t in u ou s m ode ls
Chapter C1
concerns t he rat e at which variables change, whet her t he change is an
increase or decrease and whet her t he change st ops. The process called
different iat ion is int roduced t o help in analysing t hese m at t ers
Chapter C2
t akes a different view of change, by considering how t o m easure an
accum ulat ion of inst ant aneous changes. This is achieved by using
int egrat ion, which is t he reverse process t o different iat ion
Chapter C3
considers an applicat ion of int egrat ion t o cert ain first - order different ial
equat ions
Block D - M ode llin g u n ce r t a in t y
Chapter D1
considers a concept which is fundam ent al t o all m odels for chance event s
and w hich underpins st at ist ical t hinking: probabilit y
Chapter D2
looks at t wo m odels for t he variat ion observed in a variable are discussed one m odel for a discret e variable and one for a cont inuous variable
Chapter D3
looks at est im at ing an unknown quant it y
Chapter D4
invest igat es differences bet ween populat ions by com paring sam ples of
dat a, and relat ionships bet ween variables.
Usin g m a t h e m a t ics M ST1 2 1 w it h Ex plor in g m a t h e m a t ics M S2 2 1
I n addit ion t o t he benefit s of MST121, successful com plet ion of MS221 offers t he following.
The opport unit y t o gain 60 point s in one year of st udy from a pair of courses which
nat urally fit t oget her.
St udy at Level 2, providing t he necessary experience for m any ot her courses in
m at hem at ics, t echnology and science at t his level.
A deeper underst anding of m any of t he m at hem at ical t opics covered in MST121.
During your st udy of MS221 you will cover t he following t opics.
During your study of MS221 you will cover the following topics.
Block A - Mathematical exploration
Chapter A1 introduces linear second-order recurrence sequences, in particular the Fibonacci
sequence, which has numerous intriguing properties, and is connected with the
so-called golden ratio
Chapter A2
is concerned with the curves called conics which arise as cross-sections of a
cone in particular ellipses, hyperbolas and parabolas. These have many elegant
properties that lead to applications, for example in optics
Chapter A3
introduces a general notion of function, concentrating on functions, such as
rotations, reflections and translations, which arise in geometry. These functions
are used to show that all so-called quadratic curves are in fact conics
Block B - Exploring iteration
Chapter B1
looks at the long-term behaviour of iteration sequences by considering the
geometric properties of the related functions
Chapter B2
explores linear transformations such as rotations, reflections and shears by using
the associated matrices
Chapter B3
brings the themes of the two earlier chapters together by considering the effect of
iterating a linear transformation and by studying which points and lines in the
plane remain invariant
Block C - Exploring continuous models
Chapter C1 and explore the topics of differentiation and integration, respectively, covering basic
C2
techniques and related topics such as the Newton-Raphson method for solving
equations, and calculation of volumes of revolution
Chapter C3
introduces the topic of Taylor approximations and Taylor series. This provides
one answer to the question of how we can evaluate functions such as exp, cos
and arctan, using only addition and multiplication
Block D - Structure in mathematics
Chapter D1
looks at complex numbers, which are a ‘new’ type of number. Within the set of
real numbers, R, certain algebraic equations, such as x2 + 1 = 0, have no
solutions. But if we supplement R then we obtain a system within which all
polynomial equations have solutions
Chapter D2
considers numbers of the simplest type, integers. Over the years, these have
provided many intriguing conjectures, the study of which has contributed to the
development of mathematical ideas of much wider relevance, such as
cryptography
Chapter D3
topic is: addition and multiplication of real numbers are examples of operations. A
set with an operation satisfying particular properties is called a group
Chapter D4
concerns ‘effective argument’, a topic that has been a theme throughout MS221.
Proving that results hold is an important pillar of pure mathematics
W h a t a bou t qua lifica t ion s
It is important to note that you do not need to be aiming towards any particular qualification whilst
studying these courses. You can take courses from a range of subject areas and achieve a BA or
BSc degree which is tailored to your own requirements. However, if you think you may wish to
study towards a degree or other qualification in a particular subject area, then it is a good idea to
plan for this as early as possible. Below is a list of the qualifications which the maths entry courses
can be counted towards, and more qualifications are being introduced all the time. If you would like
further advice about qualifications, then please contact your OU Regional Centre or look at the
Open University’s qualifications website.
Ce r t ifica t e s
The Cert ificat e in Mat hem at ics is awarded upon successful com plet ion of any t wo of
MU123, MST121 and MS221.
The Cert ificat e in Com put ing and Mat hem at ics is awarded upon successful com plet ion of
Dat a, com put ing and inform at ion ( M150) , and eit her MU123 or MST121.
D iplom a s
MS221 m ay be count ed t owards t he Diplom a in Physical Science
D e gr e e s in clu din g M U1 2 3
MU123 m ay specifically be count ed t owards t he following degrees:
BA ( Hons) Business St udies
BSc ( Hons) Com put ing
Foundat ion Degree in I nform at ion and Com m unicat ion Technologies
BSc ( Hons) I nform at ion and Com m unicat ion Technologies
BSc ( Hons) I T and Com put ing ( in cert ain circum st ances)
BSc ( Hons) Physical Science
BA/ BSc Mat hem at ics and it s Learning
I t m ay also be count ed t owards t he ‘free choice’ elem ent of m any ot her qualificat ions.
D e gr e e s in clu din g M ST1 2 1
MST121 should be st udied at t he st art of any nam ed degr ee wit h ‘m at hem at ics’ in it s t it le.
I n part icular, MST121 is t he com pulsory Level 1 course in t he following degrees:
BA / BSc ( Hons) Com put ing and St at ist ics
BA / BSc ( Hons) Econom ics and Mat hem at ical Sciences
BA / BSc ( Hons) Mat hem at ics
BA / BSc ( Hons) Mat hem at ics and St at ist ics
BA / BSc ( Hons) Mat hem at ics and it s Learning
MST121 m ay specifically be count ed t owards t he following degrees:
BA ( Hons) Business St udies
BSc ( Hons) Com put ing
BA / BSc ( Hons) Com put ing and Mat hem at ical Sciences
Foundat ion Degree in I nform at ion and Com m unicat ion Technologies
BS ( Hons) I nform at ion and Com m unicat ion Technologies
BS ( Hons) I T and Com put ing ( in cert ain circum st ances)
BS ( Hons) Physical Science
I t m ay also be count ed t owards t he ‘free choice’ elem ent of m any ot her qualificat ions.
D e gr e e s in clu din g M S2 2 1
MS221 is eit her com pulsory or highly desirable for any nam ed degree wit h ‘m at hem at ics’
in it s t it le.
I n part icular, MS221 is com pulsory in t he following degr ees:
BA / BSc ( Hons) Com put ing and St at ist ics
BA / BSc ( Hons) Mat hem at ics
BA / BSc ( Hons) Mat hem at ics and St at ist ics
MS221 m ay specifically be count ed t owards t he following degrees:
BA / BSc ( Hons) Com put ing and Mat hem at ical Sciences
BA / BSc ( Hons) Econom ics and Mat hem at ical Sciences
BSc ( Hons) Physical Science
I t m ay also be count ed t owards t he ‘free choice’ elem ent of m any ot her qualificat ions.
W hat next
Br ie f gu ide t o st u dy r ou t e s
This diagram shows how t he t hree cour ses relat e t o each ot her, and t he various st udy
rout es t hey m ay lead t o.
Addit ion a l in for m a t ion
I f you wish t o st udy higher level courses in applied or pure m at hem at ics, you are st rongly
advised t o have st udied MS221 first .
I f your m ain int erest is in com put ing, t hen MU123 or MST121 would provide t he
appropriat e m at hem at ical background for st udy in t his area, but you will also need t o a
relevant Level 1 course in com put ing.
I f your m ain int erest is in physics, it is advisable t o include MS221 in your profile.
I f your m ain int erest is in st at ist ics, t hen MST121 ( or MST121 and MS221) pr ovide t he
necessary m at hem at ical knowledge for Analysing dat a ( M248) and Pract ical Modern
St at ist ics ( M249) and m ost Level 3 courses in st at ist ics.
I f your int ent ion is t o t ake a profile of courses in areas out side m at hem at ics, but wit h a
significant m at hem at ical cont ent ( such as elect ronics or engineering m echanics) , MST121
will provide you wit h m any of t he necessary m at hem at ical skills, but you m ight t hink about
t aking MS221 as well.
For ot her subj ect areas in science and t echnology, MU123 will provide you wit h t he
necessary m at hem at ical skills.
I f you are st udying m ost ly science courses and need a brief refresher of t he m ain
m at hem at ical t echniques, you m ight consider t he 10- point Mat hs for Science ( S151) . This
course could be st udied aft er com plet ion of MU123, or alongside MST121.
For subj ect areas such as art s, m anagem ent or social science MU123 will provide st at ist ical
and m at hem at ical skills t hat will enhance your st udies, as well as helping you t o im prove
your generic st udy skills.
Your choice m ight also depend on your em ploym ent and career plans - see
www.open.ac.uk/ careers for furt her advice
MU123 or MST121 provides t he basic m at hem at ics requirem ent for I nit ial Teaching
Training via t he Open Universit y's Post graduat e Cert ificat e in Educat ion ( for England and
Wales) . Bot h courses are also usually accept ed as an equivalent accept able qualificat ion t o
GCSE grade C in m at hem at ics by ot her t eacher t raining inst it ut ions. You can ask your OU
Regional Cent re for a copy of t he relevant Recognit ion Leaflet .
St a r t in g a t a h igh e r le ve l
I f you have som e m at hem at ics background, it m ay be feasible t o st art your OU st udy at
Level 2. All our Level 2 courses have a diagnost ic quiz t hat would give you an idea of t he
m at hem at ics required.
However, long experience at t he OU shows t hat only a relat ively sm all proport ion of new
m at hem at ics st udent s do st art at a higher level. For such st udent s t he percent age
com plet ion rat e on t heir first course is usually t wo t hirds of t he rat e for st udent s who have
previously t aken t he relevant OU prerequisit e courses.
Feedback from st udent s who st art t he OU at Level 2 suggest s t hat m any find it difficult t o
com bine t he st udy of m at hem at ics at t hat level wit h est ablishing t heir work rout ine for OU
st udy alongside ot her com m it m ent s.
I f you do decide t o st art at Level 2, t ake advant age of our advice about Mat hem at ical
St udy Skills.
For fut ure advice we suggest t hat you cont act your OU Regional Cent re.
Ar e you r e a dy
This sect ion is designed t o help you decide which is t he best st udy rout e for you. There are
short quizzes on what is assum ed for st udy of each of MU123, MST121, and
MST121/ MS221 com bined so t hat you can check if you have t he m at hem at ical skills t o
st art t he course.
For st udent s int ending t o st udy a num ber of courses in m at hem at ics, t he Open Universit y
has produced a Success wit h Mat hem at ics book ( I SBN: 0415 298 61 X) published in
conj unct ion wit h Rout ledge as part of t heir St udy Guide Series. Success wit h Mat hem at ics
includes bot h general st udy skills, such as m aking best use of t im e, preparing for
assignm ent s and exam s, and specific help wit h learning m at hem at ics. There are chapt ers
on how t o present your m at hem at ics effect ively, what t o do when you get st uck, and
appropriat e use of t echnology.
When you at t em pt each quiz, it doesn't m at t er if you cannot do absolut ely every quest ion.
I f you can do m ost of t he quest ions, or could do t hem wit h a rem inder ( because t he t opic
is fam iliar t o you but you can't quit e rem em ber t he det ails) , t hen you are probably ready
t o st art t he course. Bot h MU123 and MST121 have som e prepar at ory m at erials, which are
available before t he course st art s.
M U1 2 3
I f you t hink MU123 m ay be appropriat e for you, t ry t he MU123 quiz. You can always t ry
t he ot her quizzes lat er t o check t hat your choice is appropriat e.
Before starting the course it is recommended that you work through some of the free and
open educational resources from the OU’s OpenLearn website (www.open.ac.uk/openlearn),
These resour ces will also enable you t o revise t he t ypes of skills t hat are needed t o answer
t he quest ions in t he quiz. There is a module to help you to refresh your knowledge of each of
the following topics:
•
Numbers, units and arithmetic
•
Rounding and estimation
•
Ratio, proportion and percentages
•
Squares, roots and powers
•
Diagrams, charts and graphs
•
Language, notation and formulas
•
Geometry
Alt ernat ively, consider one of t he following.
Teach yourself basic m at hs, by Alan Graham , and published by Hodder and St ought on
( I SBN–10: 0071429735; I SBN–13: 978- 0071429733) .
A Key St age 3 ( or possibly Key St age 4) or equivalent , m at hem at ics book.
You could also help yourself by ensuring t hat you are fam iliar wit h how your scient ific
calculat or works.
M ST1 2 1 or M ST1 2 1 / M S2 2 1 com bine d
I f you are considering MST121 as t he best st art ing point , t hen look at t he MST121 quiz.
MST121 and MS221 are designed so t hat t hey m ay be t aken in t he sam e year, so if you
are t hinking of com bining t hem t hen also t ry t he slight ly m ore challenging quest ions in t he
MST121 and MS221 com bined quiz. However, if you have never encount ered any of t he
cont ent of MST121 and MS221 before, you m ay find it difficult t o assim ilat e all of t he
m at erial in one year. I n t hat case you m ay wish t o consider t aking MST121 and t hen
st art ing MS221 at a lat er dat e, t o allow yourself t im e t o consolidat e new m at hem at ical
ideas.
MST121 has som e prepar at ory m at erials which are available before t he course st art s. I f
you wish t o do som e work before t hen,we suggest t hat you look at one of t he following
books, which m ay be available in a local library.
I f you need t o refresh your skills in algebra, or if t his is your first Open Universit y
m at hem at ics course, t hen t ry Count down t o m at hem at ics: Volum e 1 by Lynne Graham and
David Sargent ( 1981) , published by Addison- Wesley, I SBN 0 201 13730 5. [ However, if
you have problem s wit h algebra, you should consider doing MU123 before MST121.]
To gain great er fluency wit h algebra, and also t rigonom et ry, use t he com panion book:
Count down t o m at hem at ics: Volum e 2 by Lynne Graham and David Sargent ( 1981) ,
published by Addison- Wesley, I SBN 0 201 13731 3. There is a lot of m at erial, som e of
which goes beyond what is needed t o st art MST121, but it is wort h t rying exam ples from
each of t he m odules.
A GCSE- t ype m at hem at ics t ext book which includes algebra and t rigonom et ry.
You could also help yourself by ensuring t hat you are t horoughly fam iliar wit h how your
scient ific or graphics calculat or works.
Cou r se qu izze s
These are designed t o help you decide which is t he best st udy rout e for you. There are
short quizzes on what is assum ed for st udy of each of MU123, MST121 and
MST121/ MS221 com bined so t hat you can check if you have t he m at hem at ical skills t o
st art t he course.
When you at t em pt each quiz, it doesn't m at t er if you cannot do absolut ely every quest ion.
I f you can do m ost of t he quest ions, or could do t hem wit h a rem inder ( because t he t opic
is fam iliar t o you but you can't quit e rem em ber t he det ails) , t hen you are probably ready
t o st art t he course. To prepare yourself well for MU123 it is recommended that you work
through some of the free and open educational resources from the OU’s OpenLearn website
(www.open.ac.uk/openlearn), MST121 has preparat or y m at erial, which is sent out before
t he course st art s, and which will enable you t o revise t he t ypes of skills t hat are needed t o
answer t he quest ions in t he MST121 quiz.
I f t he MU123 quiz seem s t oo advanced, consider st udying St art ing wit h m at hs ( Y162)
before m oving ont o MU123.
M U1 2 3 Qu iz
MU123 will assum e t hat you can answer m ost of t he quest ions in t he quiz correct ly before
you st art t he course. To help you revise exist ing skills for MU123 it is recommended that
you work through Maths Help.
I t should also be not ed t hat MU123 involves m ore reading and writ ing t han m any st udent s
ant icipat e on a m at hem at ics course. I f you are not able t o read a docum ent such as t his
Mat hs Choices websit e reasonably fluent ly, t hen it m ay t ake you m ore t im e t o st udy t he
course.
I f t he MU123 quiz seem s t oo advanced, consider st udying St art ing wit h Mat hs ( Y162)
before m oving ont o MU123.
Try t o answer each of t he following quest ions. You can do t hem in any order and t ake as
m uch t im e as you like. I f need be, use a calculat or t o help you wit h Quest ions 4, 5 and 6.
MU123 quiz
Question 1
If the temperature at 2 am on Wednesday is −5◦ C and 12 hours later it is
3â—¦ C, by how many degrees has the temperature risen?
Question 2
You are considering buying carpet tiles for a room you are decorating. In
which of the following sizes are the tiles likely to be available? Give a
reason for your choice.
(a) 15 mm by 15 mm
(b) 3 m by 3 m
(c) 30 cm by 30 cm
(d) 1.5 km by 1.5 km
Question 3
Calculate the following.
(a) (−2) × (−1.5)
(b)
2 3
+
5 4
(c)
2
4
×1
3
5
(d) 2.13 + (−5.74)
(e) (−27) ÷ 3
(f) 52
Question 4
A store is offering 15% off all electrical goods during its summer sale.
What would you pay for a washing machine that usually costs £310?
Question 5
A family on holiday in Florida is considering buying a souvenir which is on
sale for $22. If the rate of exchange at the time is £1 = $1.42
approximately how much does the souvenir cost in pounds?
Question 6
This is a plan of a garden.
7m
1.5 m
5m
The owner intends to have a circular flower bed in the middle of a lawn. If
400 grams of grass seed covers 8 square metres, how much grass seed will
be needed to re-seed the lawn? (Give your answer to the nearest
100 gram.) The area of a circle is π × radius2 , where π is 3.14159. . . .
Question 7
A plan from a DIY booklet shows a shelf and its metal bracket. The shelf
makes a right angle with the wall.
28°
The size of one of the angles is given; what are the sizes of the other two
angles in this triangle?
[END OF QUESTIONS]
MU123 answers
Answer 1
3◦ − (−5◦) = 8◦ C.
Answer 2
(c) 30 cm by 30 cm is probably the best choice, as this size would give the
most flexibility as generally rooms are at least 2 m by 3 m.
Reasons for rejecting the others are:
(a) too small
(b) too large (may be larger than the room!)
(d) much too large, more like a very large field.
Answer 3
(a) (−2) × (−1.5) = 2 × 1.5 = 3
8
15
23
3
+
=
=1
20 20
20
20
2 9
18
6
1
(c) × =
= =1
3 5
15
5
5
(b)
(d) 2.13 + (−5.74) = 2.13 − 5.74 = −3.61
(e) (−27) ÷ 3 = −9
(f) 52 = 5 × 5 = 25
Answer 4
15% of 310 =
15
100
× 310 = 0.15 × 310 = 46.5.
So you would pay £310 − £46.50 = £263.50.
Answer 5
22 ÷ 1.42 = 15.49295775, so the cost is about £15.49.
Answer 6
Area of the garden is 7 × 5 = 35 m2
Area of the flower bed is
π × (1.5)2 = 3.14159 . . . × (1.5)2 = 7.0685 . . . ≈ 7.069 m2
Area of lawn is 35 − 7.069 = 27.931 m2
Amount of seed required is
27.931
= 1396.5 . . . = 1400 g (to the nearest 100 g).
400 ×
8
Answer 7
Since it is a right-angled triangle, one angle is 90â—¦. The angles of a triangle
add to 180◦ which gives 180◦ − (28◦ + 90◦) = 62◦ as the size of the third
angle.
[END OF ANSWERS]
I f you m anaged t o get m ost ly correct answers, or at least t he m et hod of solut ion given
here m akes sense t o you, t hen consider st art ing wit h MU123. However you m ight also like
t o look at t he quest ions in t he MST121 quiz.
I f you decide t o st art your st udies wit h MU123, you can do som e addit ional preparat ion
using Maths Help.
You m ight also like t o look at t he quest ions in t he MST121 quiz and MST121 and MS221
com bined quiz.
I f you found t hese quest ions quit e challenging t hen you m ight be able t o do MU123 aft er a
considerable am ount of preparat ion. Try using Mat hs Help.
Alt ernat ively consider t aking St art ing wit h m at hs ( Y162) first . Y162 includes t opics such as
fract ions, decim als and percent ages, using form ulas and working wit h dat a and graphs. I t
also discusses st rat egies for solving problem s and writ ing m at hem at ics. This course would
be part icularly relevant if you have not used or st udied m at hem at ics for som e t im e and
would be very useful preparat ion for MU123. The course last s 14 - 20 weeks, and provides
a gent ler int roduct ion t o t he skills of successful learning at a dist ance, as well as giving a
good grounding in m at erial relevant t o MU123. On successful com plet ion of a final
assignm ent you gain 10 point s at Level 1, which m ay be count ed t owards a degree.
Your Regional Cent re m ay be able t o give you furt her advice on ot her access or
preparat ory courses.
M ST1 2 1 Qu iz
MST121 will assum e t hat you can do m ost of t he following quest ions before you st art t he
course. Ther e is a preparat ory package t o help you prepare for MST121 but it s m ain aim is
t o help you t o revise exist ing skills.
Try t o answer t he following quest ions. Do t hem in any order and t ake as m uch t im e as you
like. I f need be, use a calculat or t o help you wit h Quest ions 1, 2, 3, 5, 8 and 10.
MST121 quiz
Question 1
The mean height of a sample of sunflowers was 1 m. The grower then tried
a new fertiliser which claimed to increase the average height of a plant by
at least 10%. The heights that the sunflowers reached (in metres) were:
1.12
1.26
1.34
1.25
0.96
1.04
0.95
1.21
1.11
1.24
1.02
0.99
0.87
1.27
1.28
0.98
1.29
1.22
Calculate the mean (average) height of the sunflowers, and say whether it
is consistent with the claim given for the fertiliser or not.
Question 2
Straight in front of me is Fred at a distance of 100 m. Directly to my right
is Gillian at a distance of 200 m. How far apart are Fred and Gillian?
Question 3
The mass, m, of the Earth, in kilograms, can be calculated by using the
gR2
, where g = 9.8 ms−2 , R = 6.37 × 106 m and
formula m =
G
G = 6.67 × 10−11 m3 s−2 kg−1 .
Find the Earth’s mass in scientific notation, correct to 3 significant figures.
Question 4
(a) Factorise x2 − 8x + 15.
(b) Expand (3y − 2)(2y + 4) by multiplying out the brackets.
(c) These two pieces of metal have the same area. What are the actual
dimensions of each piece?
( y + 12) cm
( y + 5) cm
y cm
( y + 5) cm
Question 5
The road sign below shows that the road rises 1 m for every 10 m along the
road. Calculate the angle between the road and the horizontal.
10%
Question 6
Make s the subject of the formula
p=
100(s − c)
.
c
Question 7
(a) Sketch the two lines represented by the equations
y = 5 − x and y = 2x + 14.
(b) Using algebra, find the coordinates of the point where the two lines
meet.
Question 8
(a) Sketch the graph of y = sin(2x).
(b) Give the values of cos x when x = 0.5 radians and when x = 23â—¦.
Question 9
Solve each of the following.
(a) 5t + 4 = 3t
(b) 3y + 2 ≥ 5
(c) 2(x − 1) < 3
Question 10
Solve, using the quadratic equation formula, each of the following
equations.
(a) x2 − 5x + 2 = 0
(b) 3x2 + 4x − 5 = 0
The quadratic formula is x =
−b ±
√
b2 − 4ac
.
2a
[END OF QUESTIONS]
MST121 answers
Answer 1
20.4
= 1.1333 . . . = 1.13 m (to three significant figures).
18
Previous mean height was 1 m so there has been an increase in mean
height of 0.13 m. 10% of 1 m is 0.10 m. This result supports the claim.
Mean =
Answer 2
Since the triangle formed by Fred, Gillian and me is right-angled,
Pythagoras’ Theorem can be applied. 1002 + 2002 = 50 000. Taking the
square root of this value gives 223.6068 so the distance is 223.6 m (to one
decimal place).
Answer 3
5.96 × 1024 kg (to three significant figures).
Answer 4
(a) x2 − 8x + 15 = (x − 3)(x − 5).
(b) (3y − 2)(2y + 4) = 6y 2 + 12y − 4y − 8 = 6y 2 + 8y − 8.
(c) Since the areas are equal,
y(y + 12) = (y + 5)(y + 5)
y 2 + 12y = y 2 + 10y + 25
12y = 10y + 25
2y = 25
y = 12.5
Dimensions are 12.5 cm by 24.5 cm and 17.5 cm by 17.5 cm.
Answer 5
10
1
Let x be the angle between the road and the horizontal.
Then sin x =
figures).
1
10
= 0.1; thus x = 5.74â—¦ (or 0.10 radians) (to three significant
Answer 6
100(s − c)
.
c
pc = 100(s − c)
pc
=s−c
100
pc
+c=s
100
p
pc
So s =
+c=c
+1 .
100
100
p=
Answer 7
(a)
y
(0,14)
(0,5)
(5,0)
(–7,0)
y = 2x + 14
x
y=5–x
(b) At the point (x, y) where the two lines meet, both y = 5 − x and
y = 2x + 14 hold, so that
5 − x = 2x + 14
5 − 14 = 3x
−9 = 3x.
So x = −3.
When x = −3, y = 5 − (−3) = 8.
So the lines meet at the point (−3, 8).
Answer 8
(a)
y = sin 2x
1
–90°
0
90°
180°
270°
360°
–1
(b) cos 0.5 = 0.878 (to three decimal places);
cos 23â—¦ = 0.921 (to three decimal places).
Answer 9
(a) t = −2
(b) y ≥ 1
(c) x < 2.5
Answer 10
√
5 ± 25 − 8
(a) x =
2
which gives 0.438 and 4.562 (to three decimal places).
√
16 + 60
6
which gives −2.120 and 0.786 (to three decimal places).
(b) x =
−4 ±
[END OF ANSWERS]
x
I f you m anaged t o get m ost ly correct answers, or at least t he m et hod of solut ion given
here m akes sense t o you, t hen consider st art ing wit h MST121.
I f you are planning t o st udy MST121 t hen you m ight like t o consider t aking MS221 at t he
sam e t im e. I f you haven't already done so, t ry t he quiz for t he com bined courses. You
should be ready t o st udy MS221 if you can answer 'yes' t o t he following quest ions.
1.
Do you feel t hat you will be able t o devot e no less t han 16 hours t o your st udies
each week?
2.
Does your m at hem at ical background include an A- Level or Higher in m at hs or an
HNC/ D in an engineering subj ect , or have you obt ained t his level of knowledge
som e ot her way?
3.
When you st udy m at hem at ics, do you like t o underst and t he principles behind
what you are doing rat her t han j ust learn how t o do it ?
I f you decide t o st art your st udies wit h MST121, you will be sent a preparat or y pack t o
work t hrough before t he course begins. However, you can do som e addit ional preparat ion
by working t hrough one or m ore of t he books recom m ended for MST121 in t he Are you
ready? sect ion.
I f you found t he MST121 quiz quest ions quit e challenging t hen you m ight be able t o do
MST121 aft er a considerable am ount of preparat ion. However you m ay need t o st art wit h
MU123 inst ead, so have a look at t he MU123 quiz. Ot herwise you should consult your
Regional Cent re for furt her advice on access or preparat ory courses.
M ST1 2 1 / M S2 2 1 com bine d Qu iz
I f you are considering doing MST121 and MS221 t oget her at t he sam e t im e, t hen you will
need t o be m ore confident wit h algebra and t rigonom et ry t han if you were t aking MST121
alone. You should t herefore be able t o do m ost of t he following quest ions before you
em bark on t he t wo courses at t he sam e t im e. There is a preparat ory package t o help you
revise exist ing skills for MST121, but t here is no separat e pr eparat ory pack for MS221.
Try t o answer t he following quest ions. Do t hem in any order and t ake as m uch t im e as you
like. You should at t em pt t he quest ions wit hout use of a calculat or.
MST121/MS221 combined
quiz
Question 1
Given that ap × aq = ap+q , a−p =
1
and (ap )q = apq simplify.
ap
(a) 93/2
(b) a2 ÷ a−7 × a−12 ÷ a−4
Question 2
Find the area of the triangle.
5
4
Question 3
Fill in the two correct numbers in the places denoted by (∗):
(x + (∗))2 − (∗) = x2 + 8x + 13.
Question 4
Change the subject of the equation to the letter given in brackets.
l
(l)
(a) T = 2Ï€
g
x+a
(x)
(b) m =
b−x
Question 5
Find the coordinates of the points of intersection of the line y = 2 − x and
the parabola y = x2 − 4.
Question 6
By multiplying out the brackets, simplify
√
5+
√ √
√
2
5− 2 .
1
Question 7
Find tan θ (as an exact fraction) from the following triangle.
Ö13
q
3
[END OF QUESTIONS]
2
MST121/MS221 combined
answers
Answer 1
3
(a) 93/2 = 91/2 = 33 = 27.
(b) a2 ÷ a−7 × a−12 ÷ a−4 = a2 × a7 × a−12 × a4 = a(2+7−12+4) = a1 = a.
Answer 2
The base of the triangle is
1
2
× base × height =
1
2
√
52 − 42 = 3, so the area of the triangle is:
× 3 × 4 = 6 square units.
Answer 3
(x + (4))2 − (3) = x2 + 8x + 16 − 3 = x2 + 8x + 13.
Hence the two numbers required are 4 and 3.
Answer 4
l
(a) T = 2Ï