Reading Material - English for Basic Mathematics
Unit 6
Equations and formulae
Section 1 Equations
If we wish to solve an equation, we must find the value of the letter (usually x ) which
statisfies the equation .When the equation is solved,the answer must be checked, by
substituting it for x in the original.
Example :
x + 9 = 23
Here we subtract 9 from each side ;
x + 9 – 9 = 23 – 9
Therefore x = 14
We can check by substituting 14 for x
Equation which we solve at the same time in order to find two unknown values are
called simultaneous equations.
An expression which contains a square as the highest power or any letter ( x 2 ,y 2 ,etc )
is called a quadratic.If we say that such an expression is equal to some value, the
resulting equation is known as quadratic equation.
Example :
Solve x 2 - 5x +6 = 0
By factorising we get
( x -2 ) ( x – 3 ) = 0
Therefore either x – 2 = 0
so
x = 2 or x – 3 = 0
so
x=3
x = 2 or 3
The values for x are the roots of the equation
Practice 1.
1) Find the number when seven times
2) Find
the number is four less than sixty seven.
the number when twenty-eight is one more than three quarters of the
number.
3) Find the number when five , plus three times the number.equals
fourty.
4) Three consecutive odd numbers add up to twenty-seven what are they?
5) Two consecutive even numbers
add up to thirty.What are they ?
Section 2 Formulae
When we have solved particular problem, we can often reduce the method of
solving it to a fixed pattern,and write down this pattern as a formula which can be
used for similar problems.
For example , the statement Average speed is equal to distance covered divided by
the total time taken, can be written as the formula :
S=
D
T
Often we will need to change the subject of a formula.
For example, from Boyle's law , we have the formula
P=
k
v
We can change the subject of the formula to v, and the result is
V=
k
p
Practice 2
Read out the following formulae :
1) C =
d
2) 2S = U + V
3)
x = an - b2
4 ) V = u + at
5) I =
PRT
100
6)F=
9
C + 32))
5
2
7) V= r h
8)F=
9 ) E = mc 2
10) A = r 2
Change the subjects of the a bove formulae as follows :
1) d =
3) b =
2) V =
4)u=
5) P =
7)h=
6) C =
8)R=
9) m =
10) =
Practice 3
Solve the following :
1) b plus eight equals eleven.
2) Seven b equals forty-two.
3) Two x equals one.
4) Three y plus nine equals twenty –seven.
5) Four y minus eleven equals y plus one.
6) Seven b equals sixteen minus three.
MV 2
R
7) Five c plus six equals two c plus twenty-four.
8) Twelve plus four a equals seven a minus twenty one.
9) Twelve minus two b equals four b plus thirty-six.
10) Three x plus five equals two x.
Vocabulary practice
Fill in the blank spaces in the following sentences :
1) When we have ------- an equation,we should ------ our answer.
2) The answer is cheked by ------ for the letter in the original equation.
3) If our answer ------- the equation , it is correct.
4) We can use one equation to help us solve another equation.These are called -----equations.
5) ---------- are fixed equations which can be applied in certain regular situations.
Equations and formulae
Section 1 Equations
If we wish to solve an equation, we must find the value of the letter (usually x ) which
statisfies the equation .When the equation is solved,the answer must be checked, by
substituting it for x in the original.
Example :
x + 9 = 23
Here we subtract 9 from each side ;
x + 9 – 9 = 23 – 9
Therefore x = 14
We can check by substituting 14 for x
Equation which we solve at the same time in order to find two unknown values are
called simultaneous equations.
An expression which contains a square as the highest power or any letter ( x 2 ,y 2 ,etc )
is called a quadratic.If we say that such an expression is equal to some value, the
resulting equation is known as quadratic equation.
Example :
Solve x 2 - 5x +6 = 0
By factorising we get
( x -2 ) ( x – 3 ) = 0
Therefore either x – 2 = 0
so
x = 2 or x – 3 = 0
so
x=3
x = 2 or 3
The values for x are the roots of the equation
Practice 1.
1) Find the number when seven times
2) Find
the number is four less than sixty seven.
the number when twenty-eight is one more than three quarters of the
number.
3) Find the number when five , plus three times the number.equals
fourty.
4) Three consecutive odd numbers add up to twenty-seven what are they?
5) Two consecutive even numbers
add up to thirty.What are they ?
Section 2 Formulae
When we have solved particular problem, we can often reduce the method of
solving it to a fixed pattern,and write down this pattern as a formula which can be
used for similar problems.
For example , the statement Average speed is equal to distance covered divided by
the total time taken, can be written as the formula :
S=
D
T
Often we will need to change the subject of a formula.
For example, from Boyle's law , we have the formula
P=
k
v
We can change the subject of the formula to v, and the result is
V=
k
p
Practice 2
Read out the following formulae :
1) C =
d
2) 2S = U + V
3)
x = an - b2
4 ) V = u + at
5) I =
PRT
100
6)F=
9
C + 32))
5
2
7) V= r h
8)F=
9 ) E = mc 2
10) A = r 2
Change the subjects of the a bove formulae as follows :
1) d =
3) b =
2) V =
4)u=
5) P =
7)h=
6) C =
8)R=
9) m =
10) =
Practice 3
Solve the following :
1) b plus eight equals eleven.
2) Seven b equals forty-two.
3) Two x equals one.
4) Three y plus nine equals twenty –seven.
5) Four y minus eleven equals y plus one.
6) Seven b equals sixteen minus three.
MV 2
R
7) Five c plus six equals two c plus twenty-four.
8) Twelve plus four a equals seven a minus twenty one.
9) Twelve minus two b equals four b plus thirty-six.
10) Three x plus five equals two x.
Vocabulary practice
Fill in the blank spaces in the following sentences :
1) When we have ------- an equation,we should ------ our answer.
2) The answer is cheked by ------ for the letter in the original equation.
3) If our answer ------- the equation , it is correct.
4) We can use one equation to help us solve another equation.These are called -----equations.
5) ---------- are fixed equations which can be applied in certain regular situations.