ny cc hmd aga burger 2012 130215
The New York Common Core
Learning Standards for
Mathematics: High School
Algebra 1, Geometry,
& Algebra 2
© 2012
© Houghton Milin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A.
Holt McDougal Algebra 1, Geometry, Algebra 2
Common Core Edition © 2012
correlated to
The New York Common Core Learning Standards for High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
N-RN-1. Explain how the definition of the meaning of
rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for
radicals in terms of rational exponents.
SE: 392-393, 398-402
N-RN-2. Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
SE: 400-402
N-RN-3. Explain why the sum or product of two rational
numbers is rational; that the sum of a rational number and an
irrational number is irrational; and that the product of a
nonzero rational number and an irrational number is
irrational.
SE: 431-432
Geometry
Algebra 2
SE: 358-360, 395
SE: 358
SE: 358-365, 392, 394, 398
Page 1 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
N-Q-1. Use units as a way to understand problems and to
guide the solution of multi-step problems; choose and
interpret units consistently in formulas; choose and interpret
the scale and the origin in graphs and data displays.*
SE: 10, 26-30, 43-45, 53, 5658, 59, 61, 62-68, 70-74,
83, 85-86, 88, 93, 108,
110, 115, 118, 122-124,
144, 159, 176, 184-185,
189-191, 194, 202, 208209, 212, 213, 223, 265,
271-273, 279-281, 284,
488, 534, 536-537, 539542, 549-550, 553, 556558, 564-566, 572, 577578, 598, 603, 628, 639641
SE: 105, 108, 140, 186,
193-195, 197, 200, 211,
273, 445, 461, 528,
586, 593, 657, 671,
684-685, 695, 697-698,
703, 708, 713, 715,
727, 750, 753-756, 777,
786, 800, 865
SE: 12, 39, 90, 122, 229,
265, 293-294, 325, 340,
345-348, 363-364, 373,
381, 383, 437, 506, 650,
713, 732
N-Q-2. Define appropriate quantities for the purpose of
descriptive modeling.*
SE: 62-68, 75-81, 686-694,
695-701
N-Q-3. Choose a level of accuracy appropriate to limitations
on measurement when reporting quantities.*
SE: 75-81
N-CN-1. Know there is a complex number i such that i2 = –1,
and every complex number has the form a + bi with a and b
real.
SE: 94-95, 138
N-CN-2. Use the relation i2 = –1 and the commutative,
associative, and distributive properties to add, subtract, and
multiply complex numbers.
SE: 128-131, 139, 141, 477
Page 2 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
N-CN-3. (+) Find the conjugate of a complex number; use
conjugates to find moduli and quotients of complex numbers.
SE: 96-99, 126-133, 138,
145, 226
N-CN-4. (+) Represent complex numbers on the complex
plane in rectangular and polar form (including real and
imaginary numbers), and explain why the rectangular and
polar forms of a given complex number represent the same
number.
Opportunities to address this
standard can be found on the
following pages:
N-CN-5. (+) Represent addition, subtraction, multiplication,
and conjugation of complex numbers geometrically on the
complex plane; use properties of this representation for
computation.
Opportunities to address this
standard can be found on the
following pages:
N-CN-6. (+) Calculate the distance between numbers in the
complex plane as the modulus of the difference, and the
midpoint of a segment as the average of the numbers at its
endpoints.
SE: 126-128, 139
SE: 126-133
This standard is outside the Common Core college and career ready standards.
N-CN-7. Solve quadratic equations with real coefficients that
have complex solutions.
SE: 96-99, 101-107, 109,
138, 140, 190-195, 221
N-CN-8. (+) Extend polynomial identities to the complex
numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
SE: 189-195, 221
N-CN-9. (+) Know the Fundamental Theorem of Algebra;
show that it is true for quadratic polynomials.
SE: 189-195, 221, 222
Page 3 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
N-VM-1. (+) Recognize vector quantities as having both
magnitude and direction. Represent vector quantities by
directed line segments, and use appropriate symbols for
vectors and their magnitudes (e.g., v, |v|, ||v||, v).
SE: 577-585
N-VM-2. (+) Find the components of a vector by subtracting
the coordinates of an initial point from the coordinates of a
terminal point.
SE: 577
N-VM-3. (+) Solve problems involving velocity and other
quantities that can be represented by vectors.
SE: 577-585, 586, 587, 591,
592, 593, 595
N-VM-4. (+) Add and subtract vectors.
SE: 577-585, 586, 587, 591,
596, 785
a. Add vectors end-to-end, component-wise, and by the
parallelogram rule. Understand that the magnitude of a sum
of two vectors is typically not the sum of the magnitudes.
b. Given two vectors in magnitude and direction form,
determine the magnitude and direction of their sum.
c. Understand vector subtraction v – w as v + (–w), where –w
is the additive inverse of w, with the same magnitude as w
and pointing in the opposite direction. Represent vector
subtraction graphically by connecting the tips in the
appropriate order, and perform vector subtraction
component-wise.
Page 4 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
N-VM-5. (+) Multiply a vector by a scalar.
Geometry
Algebra 2
SE: 577-585
a. Represent scalar multiplication graphically by scaling
vectors and possibly reversing their direction; perform scalar
multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
b. Compute the magnitude of a scalar multiple cv using ||cv||
= |c|v. Compute the direction of cv knowing that when |c|v
0, the direction of cv is either along v (for c > 0) or against v
(for c < 0).
N-VM-6. (+) Use matrices to represent and manipulate data,
e.g., to represent payoffs or incidence relationships in a
network.
This standard is outside the Common Core college and career ready standards.
N-VM-7. (+) Multiply matrices by scalars to produce new
matrices, e.g., as when all of the payoffs in a game are
doubled.
This standard is outside the Common Core college and career ready standards.
SE: 144
N-VM-8. (+) Add, subtract, and multiply matrices of
appropriate dimensions.
N-VM-9. (+) Understand that, unlike multiplication of
numbers, matrix multiplication for square matrices is not a
commutative operation, but still satisfies the associative and
distributive properties.
This standard is outside the Common Core college and career ready standards.
Page 5 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
N-VM-10. (+) Understand that the zero and identity matrices
play a role in matrix addition and multiplication similar to the
role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a
multiplicative inverse.
This standard is outside the Common Core college and career ready standards.
N-VM-11. (+) Multiply a vector (regarded as a matrix with
one column) by a matrix of suitable dimensions to produce
another vector. Work with matrices as transformations of
vectors.
This standard is outside the Common Core college and career ready standards.
N-VM-12. (+) Work with 2
2 matrices as a
transformations of the plane, and interpret the absolute value
of the determinant in terms of area.
This standard is outside the Common Core college and career ready standards.
Page 6 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
SE: 10-11, 512, 514
SE: 36-41, 312-318, 689,
751, 757, 759
SE: 75, 234-240
A-SSE-2. Use the structure of an expression to identify ways
to rewrite it.
SE: 462, 463-469, 470-471,
472-479, 480-486, 487,
488, 489, 490-496, 498503, 504, 505, 507-509,
510, 511, 514-515, 739
SE: 13-19
SE: 75, 141, 174-179, 219
A-SSE-3. Choose and produce an equivalent form of an
expression to reveal and explain properties of the quantity
represented by the expression.
SE:
SE:
a. & b.) 470-471, 472-479,
480-486, 487, 488, 489,
490-496, 499-503, 504,
505, 508-509, 510, 511,
514, 739
a. & b.) 75, 76, 77-84, 86-93,
137, 307
A-SSE-1. Interpret expressions that represent a quantity in
terms of its context.*
a. Interpret parts of an expression, such as terms, factors, and
coefficients.
b. Interpret complicated expressions by viewing one or more
of their parts as a single entity.
a. Factor a quadratic expression to reveal the zeros of the
function it defines.
b. Complete the square in a quadratic expression to reveal the
maximum or minimum value of the function it defines.
a.)
c.)
239
562-563, 636-641
c. Use the properties of exponents to transform expressions
for exponential functions.
SE: 658, 660-661, 678, 680
A-SSE-4. Derive the formula for the sum of a finite
geometric series (when the common ratio is not 1), and use
the formula to solve problems..
Page 7 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
A-APR-1. Understand that polynomials form a system
analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
Geometry
SE: 414-419, 422-429, 433439
A-APR-2. Know and apply the Remainder Theorem: For a
polynomial p(x) and a number a, the remainder on division
by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of
p(x).
Algebra 2
SE: 150-156, 158-164, 181,
218, 219, 222, 223, 224,
227, 307, 309, 335-338,
399, 403, 751
SE: 166-172, 174-179, 189195, 220, 222
A-APR-3. Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to construct a
rough graph of the function defined by the polynomial.
SE: 562-567, 600-601
SE: 176-179, 181, 182-188,
219, 220, 223, 880
A-APR-4. Prove polynomial identities and use them to
describe numerical relationships.
SE: 433-439, 490-496, 497
SE: 158-161, 174-179
A-APR-5. (+) Know and apply the Binomial Theorem for the
expansion of (x + y)n in powers of x and y for a positive
integer n, where x and y are any numbers, with coefficients
determined for example by Pascal’s Triangle. (The Binomial
Theorem can be proved by mathematical induction or by a
combinatorial argument.)
SE: 157, 158-164, 531, 532,
587, 590, 684
Page 8 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
SE: 682, 685
A-APR-6. Rewrite simple rational expressions in different
forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x),
b(x), q(x), and r(x) are polynomials with the degree of r(x)
less than the degree of b(x), using inspection, long division,
or, for the more complicated examples, a computer algebra
system.
A-APR-7. (+) Understand that rational expressions form a
system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a
nonzero rational expression; add, subtract, multiply, and
divide rational expressions.
A-CED-1. Create equations and inequalities in one variable
and use them to solve problems. Include equations arising
from linear and quadratic functions, and simple rational and
exponential functions.*
Algebra 2
SE: 166-172, 219, 222, 224,
537
SE: 321-326, 327-334, 335338, 357, 391, 394, 395,
881
SE: 19-22, 26-29, 34-38, 4246, 54-59, 100-105, 107111, 114-117, 118, 119,
122-125, 127-132, 144147, 148, 149, 150-153,
154, 156-157, 158-159,
562-567, 568-573, 575581, 582-589, 624-630
SE: 42, 46, 77-84, 85-92, 9499, 100-107, 110-117,
144, 182-188, 189-195,
266-272, 348-355, 376383, 474, 785-797
Page 9 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
A-CED-2. Create equations in two or more variables to
represent relationships between quantities; graph equations
on coordinate axes with labels and scales.*
SE: 179-185, 186-192, 230236, 237-242, 244-251,
254-259, 260-265, 268274, 275-282, 293-299,
301-307, 329-334, 336342, 343-349, 352-357,
538-543, 545-551, 554559, 582-589, 635-642,
649-655
A-CED-3. Represent constraints by equations or inequalities,
and by systems of equations and/or inequalities, and interpret
solutions as viable or nonviable options in a modeling
context..*
SE: 179-185, 230-236, 237242, 260-265, 268-274,
275-282, 301-307, 331334, 339-342, 346-349,
350-351, 354-356, 358,
359, 369-371, 374, 375,
376-378, 380, 381, 384385, 451, 538-543, 554559, 562-567, 568-573,
575-581, 582-589, 613,
635-642, 649-655
A-CED-4. Rearrange formulas to highlight a quantity of
interest, using the same reasoning as in solving equations..*
SE: 49-53, 59, 68, 85, 88,
161
Geometry
Algebra 2
SE: 182-187, 190-197, 201,
205, 206, 517
SE: 15-21, 24-30, 32-39, 44,
46, 59-66, 67-74, 118125, 150-156, 197-203,
204-209, 210-215, 226,
234-240, 242-248, 249255, 275-280, 281-288,
289-295, 313-320, 340347, 367-375, 422-429,
432-439, 442-448, 450456, 458-465, 536, 749,
754-761, 767
SE: 15-21, 24-30, 32-39, 5966, 67-74, 110-117, 118125, 150-156, 197-203,
204-209, 210-215, 234240, 242-248, 249-255,
275-280, 281-288, 289295, 313-320, 340-347,
367-375, 422-429, 432439, 442-448, 450-456,
458-465, 749, 754-761,
762-767
SE: 41, 673, 674, 676, 685
SE: 449
Page 10 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
A-REI-1. Explain each step in solving a simple equation as
following from the equality of numbers asserted at the
previous step, starting from the assumption that the original
equation has a solution. Construct a viable argument to
justify a solution method.
SE: 17-22, 24-30, 32-38, 4046, 54-59, 61, 84-85
SE: 104-109, 127, 132, 134
SE: 77-84, 85-92, 100-107,
182-188, 266-272, 348355, 376-383
A-REI-2. Solve simple rational and radical equations in one
variable, and give examples showing how extraneous
solutions may arise.
SE: 669, 673, 674
SE: 466-471, 482-489, 493,
495-501, 520
SE: 348-355, 357, 376-383,
388, 389, 392, 393, 394,
395, 398, 399, 476, 809
A-REI-3. Solve linear equations and inequalities in one
variable, including equations with coefficients represented by
letters.
SE: 16, 17-22, 24-30, 31, 3238, 39, 40-46, 53, 59, 60,
61, 68, 84-85, 88, 89,
92-93, 97, 106-111, 112117, 118, 119, 120-125,
126-132, 140, 147, 148,
149, 151-152, 154, 155,
158-159, 161, 169, 185,
192, 203, 211, 222, 223,
236, 274, 299, 325, 334,
397, 403, 419, 450, 469,
519, 612, 623, 630, 679,
701, 721, 760
SE: 43, 46, 47, 48
Page 11 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
A-REI-4. Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any
quadratic equation in x into an equation of the form (x – p)2 =
q that has the same solutions. Derive the quadratic formula
from this form.
Algebra 1
Geometry
Algebra 2
SE: 554-559, 560-561, 562567, 568-573, 576-581,
582-583, 585-589, 598,
599, 606-607, 608, 609,
613, 655
SE: 27, 45, 47-48, 55, 59,
63, 243, 245, 289, 338,
361-367, 377, 381, 382,
400, 427, 442, 444-446,
508, 798, 842, 844-846
SE: 77-84, 85-92, 96-99,
100-107, 108, 109, 137,
140, 143, 145, 307, 309,
684, 749
b. Solve quadratic equations by inspection (e.g., for x2 = 49),
taking square roots, completing the square, the quadratic
formula and factoring, as appropriate to the initial form of the
equation. Recognize when the quadratic formula gives
complex solutions and write them as a ± bi for real numbers
a and b.
A-REI-5. Prove that, given a system of two equations in two
variables, replacing one equation by the sum of that equation
and a multiple of the other produces a system with the same
solutions.
SE: 343-349
A-REI-6. Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs of linear
equations in two variables.
SE: 329-334, 336-342, 343349, 350-351, 352-357,
358, 359, 376-378, 380,
381, 383, 384
SE: 152-153, 158-160, 161,
176, 194, 195, 328,
329-330
SE: 684
A-REI-7. Solve a simple system consisting of a linear
equation and a quadratic equation in two variables
algebraically and graphically.
SE: 590-597
SE: 853
SE: 809, 862-869, 871, 872,
876, 877
Page 12 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
A-REI-8. (+) Represent a system of linear equations as a
single matrix equation in a vector variable.
This standard is outside the Common Core college and career ready standards.
A-REI-9. (+) Find the inverse of a matrix if it exists and use
it to solve systems of linear equations (using technology for
matrices of dimension 3 ! 3 or greater).
This standard is outside the Common Core college and career ready standards.
A-REI-10. Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the coordinate
plane, often forming a curve (which could be a line).
SE: 186-192, 193, 216
SE: 43, 46
A-REI-11. Explain why the x-coordinates of the points where
the graphs of the equations y = f(x) and y = g(x) intersect are
the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions,
make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic
functions.*
SE: 47-48, 554-559, 560561, 628, 629
SE: 79-80, 182-186, 191192, 268-269, 351-352,
384-387
A-REI-12. Graph the solutions to a linear inequality in two
variables as a half-plane (excluding the boundary in the case
of a strict inequality), and graph the solution set to a system
of linear inequalities in two variables as the intersection of
the corresponding half-planes.
SE: 360-366, 368-372, 373,
374, 375, 379, 380, 381,
486
SE: 44, 46, 47, 50, 307, 880
Page 13 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
F-IF-1. Understand that a function from one set (called the
domain) to another set (called the range) assigns to each
element of the domain exactly one element of the range. If f
is a function and x is an element of its domain, then f(x)
denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation y = f(x).
SE: 170-176, 177, 179-186,
187-192, 193, 195, 215,
219, 222
F-IF-2. Use function notation, evaluate functions for inputs in
their domains, and interpret statements that use function
notation in terms of a context.
F-IF-3. Recognize that sequences are functions, some-times
defined recursively, whose domain is a subset of the integers.
F-IF-4. For a function that models a relationship between two
quantities, interpret key features of graphs and tables in terms
of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. Key features
include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and
periodicity.*
SE: 180-185, 192, 195, 216,
218, 219, 223, 322, 397,
629
SE: 50
SE: 206-211, 618-623
SE: 626-632
SE: 165, 167-168, 195, 214,
230, 234-235, 237-238,
240-242, 266, 267, 271273, 309, 310-313, 315,
318, 531-532, 535-537,
541-543, 545-551, 552,
553, 554-559, 600-601,
603, 604-605, 608, 613,
630, 641, 644-647, 649655, 565-659
SE: 7-14, 24-30, 43, 59-66,
67-74, 77-84, 109, 137,
140, 153-156, 183-188,
197-203, 204-209, 218,
220, 221, 222, 223, 236240, 251-255, 275-280,
281-288, 313-320, 340347, 367-375, 399, 406413, 422-429, 432-439,
457, 476, 754-761, 762767
Page 14 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-IF-5. Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it
describes..*
SE: 170-176, 182-184, 186192, 194, 195, 218, 223,
233-235, 241, 260-265,
310-311, 313, 314, 323,
486, 525-529, 542-543,
545-551, 553, 600-601,
603, 669, 672, 674, 675
F-IF-6. Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a
specified interval. Estimate the rate of change from a graph.*
SE: 244-245, 248-251, 254259, 267, 268-274, 308,
315, 318, 323, 469, 656659, 660-667, 739
Geometry
SE: 401, 685
Algebra 2
SE: 14, 19-21, 65, 70, 72-73,
134, 172, 196, 226, 240,
241, 242, 245, 247, 253,
263, 280, 285-286, 288,
299, 302, 341, 345, 367368, 371-372, 375, 388,
389, 392-393, 394, 413,
428-429, 439, 441, 453454, 467, 470, 472, 685,
713, 719, 749, 754-761,
767, 851
SE: 44, 210-215, 408-413,
414-421, 468
Page 15 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-IF-7. Graph functions expressed symbolically and show
key features of the graph, by hand in simple cases and using
technology for more complicated cases.*
a. Graph linear and quadratic functions and show intercepts,
maxima, and minima.
b. Graph square root, cube root, and piecewise-defined
functions, including step functions and absolute value
functions.
c. Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end
behavior.
d. (+) Graph rational functions, identifying zeros and
asymptotes when suitable factorizations are available, and
showing end behavior.
Geometry
Algebra 2
SE:
SE:
a.) 186-192, 193, 195, 216,
218, 219, 220, 230-236,
237-242, 260-265, 266,
267, 268-274, 275-282,
283, 301-307, 309, 314317, 318, 320, 321, 522529, 531-537, 538-543,
553, 554-559, 605, 608,
609, 649-655
a.)
24-30, 43, 46, 59-66,
67-74, 76, 77-84, 109,
137, 140, 144, 226, 476
b.)
45, 46, 367-375, 388,
389, 393, 394, 398,
422-429, 430-431, 441,
469, 685
c.)
153-156, 182-188, 196,
197-203, 204-209, 218,
220, 221
d.)
339, 340-347, 357, 392,
395, 399
e.)
234-240, 251-255, 275280, 297, 298, 302,
754-755, 762-767, 768,
769, 800, 801, 804, 807
b.) 310-313
c.) 544, 545-551, 600-603
e.) 624-630
e. Graph exponential and logarithmic functions, showing
intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude.
Page 16 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-IF-8. Write a function defined by an expression in different
but equivalent forms to reveal and explain different
properties of the function.
Geometry
SE: 530, 533-534, 536-537,
541, 543, 553, 605, 608,
Algebra 2
SE:
a.)
624-630
a. Use the process of factoring and completing the square in a
quadratic function to show zeros, extreme values, and
symmetry of the graph, and interpret these in terms of a
context.
67-74, 77-84, 85-92, 109,
881
b.)
234-240, 265, 302, 684
b. Use the properties of exponents to interpret expressions for
exponential functions.
F-IF-9. Compare properties of two functions each represented
in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions).
SE: 230-236, 310-313, 531-
F-BF-1. Write a function that describes a relationship
between two quantities.*
SE: 179-185, 230-236, 268274, 275-282, 545-551,
568-573, 635-642, 644647, 649-655
SE: 32-39, 118-125, 159163, 169-171, 180, 181,
206-209, 210-215, 219,
221, 222, 278, 289-295,
425-429, 434-438, 442448, 450-456, 458-465,
470, 472, 475, 476, 881
SE: 206-210, 622-623, 644647
SE: 626-632, 647-650, 653,
654-663, 676, 677, 678,
680, 681, 684, 685, 749
a. Determine an explicit expression, a recursive process, or
steps for calculation from a context.
537, 538-543, 600-601,
624-630, 660-667
b. Combine standard function types using arithmetic
operations.
c. (+) Compose functions.
F-BF-2. Write arithmetic and geometric sequences both
recursively and with an explicit formula, use them to model
situations, and translate between the two forms.*
SE: 414-421
Page 17 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-BF-3. Identify the effect on the graph of replacing f(x) by
f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing
even and odd functions from their graphs and algebraic
expressions for them.
SE: 300, 301-307, 309, 310313, 317, 318, 544, 545551, 553, 559, 606, 608,
732, 747
F-BF-4. Find inverse functions.
Geometry
Algebra 2
SE: 101, 374, 618, 638,
640, 748
SE: 7-14, 15-21, 22, 23, 2430, 44, 46, 51, 59-66,
109, 136, 204-209, 221,
222, 223, 225, 227, 281288, 301, 302, 306, 368375, 388, 389, 432-439,
469, 472, 473, 684, 748,
756-761, 762-767
SE: 551, 558
SE:
a. Solve an equation of the form f(x) = c for a simple function
f that has an inverse and write an expression for the inverse.
a-c). 241, 242-248, 251-255,
265, 299, 302, 303, 306,
450-456, 470, 472, 473,
684, 881
b. (+) Verify by composition that one function is the inverse
of another.
c.)
c. (+) Read values of an inverse function from a graph or a
table, given that the function has an inverse.
367
d. (+) Produce an invertible function from a non-invertible
function by restricting the domain.
F-BF-5. (+) Understand the inverse relationship between
exponents and logarithms and use this relationship to solve
problems involving logarithms and exponents.
SE: 249-255, 256-263, 264,
265, 266-272, 275-280,
297, 300, 302, 303, 306,
399, 881
Page 18 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-LE-1. Distinguish between situations that can be modeled
with linear functions and with exponential functions.*
Geometry
SE: 625-628, 649-655
Algebra 2
SE:
a.)
a. Prove that linear functions grow by equal differences over
equal intervals, and that exponential functions grow by equal
factors over equal intervals.
210-215, 406-413, 458465
b.)
406-413, 441, 458-465,
471, 472
b. Recognize situations in which one quantity changes at a
constant rate per unit interval relative to another.
c.)
234-240, 458-465, 471,
472
c. Recognize situations in which a quantity grows or decays
by a constant percent rate per unit interval relative to another.
F-LE-2. Construct linear and exponential functions, including
arithmetic and geometric sequences, given a graph, a
description of a relationship, or two input-output pairs
(include reading these from a table).*
SE: 206-211, 213, 216-217,
218, 219, 220, 230-236,
237-242, 260-265, 268274, 275-282, 309, 314317, 318, 320, 321, 618623, 633, 635-642, 644647, 649-655
SE: 44, 46, 234-240, 305,
398, 406-413, 441, 458465, 468, 471, 472, 537,
643-651, 654-753, 880
F-LE-3. Observe using graphs and tables that a quantity
increasing exponentially eventually exceeds a quantity
increasing linearly, quadratically, or (more generally) as a
polynomial function.*
SE: 630, 660-667
SE: 234-240, 458-465
F-LE-4. For exponential models, express as a logarithm the
solution to abct = d where a, c, and d are numbers and the
base b is 2, 10, or e; evaluate the logarithm using
technology.*
SE: 249-255, 268-272, 274,
275-280
Page 19 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-LE-5. Interpret the parameters in a linear or exponential
function in terms of a context.*
Geometry
SE: 268-274, 635-642
Algebra 2
SE: 234-240, 299
F-TF-1. Understand radian measure of an angle as the length
of the arc on the unit circle subtended by the angle.
SE: 707-713
F-TF-2. Explain how the unit circle in the coordinate plane
enables the extension of trigonometric functions to all real
numbers, interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
SE: 700-702, 706-709
F-TF-3. (+) Use special triangles to determine geometrically
the values of sine, cosine, tangent for π/3, π/4 and π/6, and
use the unit circle to express the values of sine, cosines, and
tangent for x, π + x, and 2π – x in terms of their values for x,
where x is any real number.
SE: 693-699, 706-713, 721,
741, 744, 745
F-TF-4. (+) Use the unit circle to explain symmetry (odd and
even) and periodicity of trigonometric functions.
Opportunities to address this
standard can be found on the
following pages:
SE: 707-713, 754-761
SE: 756-760, 762-767
F-TF-5. Choose trigonometric functions to model periodic
phenomena with specified amplitude, frequency, and
midline.*
Page 20 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
SE: 714-719
F-TF-6. (+) Understand that restricting a trigonometric
function to a domain on which it is always increasing or
always decreasing allows its inverse to be constructed.
SE: 551, 552-559
F-TF-7. (+) Use inverse functions to solve trigonometric
equations that arise in modeling contexts; evaluate the
solutions using technology, and interpret them in terms of the
context.*
SE: 716-719, 721, 742, 744,
745, 748, 791-797
F-TF-8. Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1
and use it to calculate trigonometric ratios.
SE: 772-777, 801, 804, 807
F-TF-9. (+) Prove the addition and subtraction formulas for
sine, cosine, and tangent and use them to solve problems.
SE: 778-783, 799, 802, 804,
805, 808
Page 21 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
G-CO-1. Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment, based on
the undefined notions of point, line, distance along a line, and
distance around a circular arc.
SE: 6-11, 20-27, 35, 64, 68,
69, 146-151, 688-693
G-CO-2. Represent transformations in the plane using, e.g.,
transparencies and geometry software; describe
transformations as functions that take points in the plane as
inputs and give other points as outputs. Compare
transformations that preserve distance and angle to those that
do not (e.g., translation versus horizontal stretch).
SE: 50-55, 56-57, 509-514,
523, 529, 596, 604-610,
611-617, 619-625, 626631, 633, 650-657, 660663, 664, 668, 669, 785
G-CO-3. Given a rectangle, parallelogram, trapezoid, or
regular polygon, describe the rotations and reflections that
carry it onto itself.
SE: 604-610, 611-617, 619625, 626-631, 633, 634640, 660-663, 664, 665
G-CO-4. Develop definitions of rotations, reflections, and
translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
SE: 50-55, 604-610, 611617, 619-625, 633, 660,
661, 664
G-CO-5. Given a geometric figure and a rotation, reflection,
or translation, draw the transformed figure using, e.g., graph
paper, tracing paper, or geometry software. Specify a
sequence of transformations that will carry a given figure
onto another.
SE: 50-55, 56-57, 59, 63,
64, 604-610, 611-617,
619-625, 626-631, 633,
660-663, 664, 665, 668,
669, 785
Algebra 2
SE: 700-705, 707-713
Page 22 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
G-CO-6. Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid
motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motions to decide if
they are congruent.
G-CO-7. Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and only
if corresponding pairs of sides and corresponding pairs of
angles are congruent.
Geometry
SE: 220-223, 258-267, 274277, 293, 298, 300,
604-610, 611-617, 619625
SE: 69-74
SE: 220-223, 268-273, 274277, 293, 294-295, 298,
300
G-CO-8. Explain how the criteria for triangle congruence
(ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
SE: 248-249, 250-257, 260267, 293, 297, 300,
302, 304, 387
G-CO-9. Prove geometric theorems about lines and angles.
Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are congruent;
points on a perpendicular bisector of a line segment are
exactly those equidistant from the segment's endpoints.
SE: 118-125, 155-159, 162,
169, 181, 203-204, 206,
312-318
Page 23 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
G-CO-10. Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; base
angles of isosceles triangles are congruent; the segment
joining midpoints of two sides of a triangle is parallel to the
third side and half the length; the medians of a triangle meet
at a point.
G-CO-11. Prove theorems about parallelograms. Theorems
include: opposite sides are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles
are parallelograms with congruent diagonals.
Geometry
SE: 231-238, 247, 285-291,
293, 296, 299, 300,
326-331, 334-339, 341,
379, 380
SE: 294, 297, 299
SE: 403-404, 419, 420-427,
451, 454
G-CO-12. Make formal geometric constructions with a
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometry
software, etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a
line segment; and constructing a line parallel to a given line
through a point not on the line.
SE: 14, 16, 17-18, 22-27,
35, 61, 170-171, 172,
177, 179
G-CO-13. Construct an equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
SE: 392-393, 826
Page 24 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
G-SRT-1. Verify experimentally the properties of dilations
given by a center and a scale factor:
Geometry
SE: 472-479, 509-514, 650657, 659, 663, 664
a. A dilation takes a line not passing through the center of the
dilation to a parallel line, and leaves a line passing through
the center unchanged.
b. The dilation of a line segment is longer or shorter in the
ratio given by the scale factor.
G-SRT-2. Given two figures, use the definition of similarity
in terms of similarity transformations to decide if they are
similar; explain using similarity transformations the meaning
of similarity for triangles as the equality of all corresponding
angles and the proportionality of all corresponding pairs of
sides.
SE: 466-471, 472-479, 480481, 482-489, 493, 495501, 519, 521, 524,
525, 526, 527, 531, 597
G-SRT-3. Use the properties of similarity transformations to
establish the AA criterion for two triangles to be similar.
SE: 482-489, 521, 524
G-SRT-4. Prove theorems about triangles. Theorems include:
a line parallel to one side of a triangle divides the other two
proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.
SE: 69-70, 72-74, 83, 86, 88,
89, 185, 236, 323
SE: 312-318, 341, 359, 360367, 377, 378, 490-491,
495, 501, 522, 696
Page 25 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
G-SRT-5. Use congruence and similarity criteria for triangles
to solve problems and prove relationships in geometric
figures.
SE: 250-257, 258-267, 268273, 293, 297-298, 300,
302, 304, 482-489, 493,
495-501, 519, 521, 524
G-SRT-6. Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading
to definitions of trigonometric ratios for acute angles.
SE: 534-539, 540, 541-548,
561, 588, 589, 592
G-SRT-7. Explain and use the relationship between the sine
and cosine of complementary angles.
SE: 549-550
G-SRT-8. Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.
SE: 360-371, 377, 381, 382,
383, 385, 552-559, 560,
561, 562-567, 568, 587,
589, 590, 592, 594,
596, 865
SE: 689, 693-699, 721, 740,
744, 745, 749, 809
G-SRT-9. (+) Derive the formula A = 1/2 ab sin(C) for the
area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
SE: 701
SE: 722
G-SRT-10. (+) Prove the Laws of Sines and Cosines and use
them to solve problems.
SE: 569-576, 587, 590, 592,
593
SE: 722-729, 730-737, 739,
742-743, 744, 745, 748
SE: 693
Page 26 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
G-SRT-11. (+) Understand and apply the Law of Sines and
the Law of Cosines to find unknown measurements in right
and non-right triangles (e.g., surveying problems, resultant
forces).
SE: 569-576, 587, 590, 592,
593
SE: 725-729, 733-737, 739,
742-743, 744
G-C-1. Prove that all circles are similar.
SE: 472-479
G-C-2. Identify and describe relationships among inscribed
angles, radii, and chords. Include the relationship between
central, inscribed, and circumscribed angles; inscribed
angles on a diameter are right angles; the radius of a circle
is perpendicular to the tangent where the radius intersects
the circle.
SE: 820-827, 830-837, 840846, 855, 856, 860,
863, 864
G-C-3. Construct the inscribed and circumscribed circles of a
triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
SE: 319, 325, 823-827, 855,
858, 865
G-C-4. (+) Construct a tangent line from a point outside a
given circle to the circle.
SE: 827
G-C-5. Derive using similarity the fact that the length of the
arc intercepted by an angle is proportional to the radius, and
define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
SE: 810-815, 816-817
SE: 707-713
Page 27 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
SE: 847-853, 859, 860
G-GPE-1. Derive the equation of a circle of given center and
radius using the Pythagorean Theorem; complete the square
to find the center and radius of a circle given by an equation.
Algebra 2
SE: 823-828, 858-860, 870,
871
G-GPE-2. Derive the equation of a parabola given a focus
and directrix.
SE: 845-851, 853, 871, 874,
876, 880
G-GPE-3. (+) Derive the equations of ellipses and hyperbolas
given foci and directrices.
SE: 748, 830-836, 837, 838844, 852, 853, 871, 873874, 876, 881
SE: 279-284
G-GPE-4. Use coordinates to prove simple geometric
theorems algebraically.
G-GPE.5. Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric problems
(e.g., find the equation of line parallel or perpendicular to a
given line that passes through a given point).
SE: 293-299, 307, 309, 317,
318, 323, 384, 450, 573,
761
SE: 190-197, 216-219, 412417, 419, 426-427, 452,
454, 669
G-GPE-6. Find the point on a directed line segment between
two given points that partitions the segment in a given ratio.
SE: 267, 316
SE: 515-516, 704-709
G-GPE-7. Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g., using the
distance formula.*
SE: 820, 821
SE: 704-705, 706-709, 727,
730, 732, 737
Page 28 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
G-GMD-1. Give an informal argument for the formulas for
the circumference of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri's principle, and informal limit arguments.
SE: 688-693, 749-751, 757
G-GMD-2. (+) Give an informal argument using Cavalieri’s
principle for the formulas for the volume of a sphere and
other solid figures.
SE: 749-756, 757-763, 765772
G-GMD-3. Use volume formulas for cylinders, pyramids,
cones, and spheres to solve problems.*
SE: 402-403, 429, 430, 503,
573, 631
SE: 172, 191-192, 325, 366,
816, 829
SE: 742-748, 778
G-GMD-4. Identify the shapes of two-dimensional crosssections of three-dimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
G-MG-1. Use geometric shapes, their measures, and their
properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).*
SE: 668, 749-756, 757-764,
766-773, 777, 779, 781,
784, 785, 864
Algebra 2
SE: 365, 410
Learning Standards for
Mathematics: High School
Algebra 1, Geometry,
& Algebra 2
© 2012
© Houghton Milin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A.
Holt McDougal Algebra 1, Geometry, Algebra 2
Common Core Edition © 2012
correlated to
The New York Common Core Learning Standards for High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
N-RN-1. Explain how the definition of the meaning of
rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for
radicals in terms of rational exponents.
SE: 392-393, 398-402
N-RN-2. Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
SE: 400-402
N-RN-3. Explain why the sum or product of two rational
numbers is rational; that the sum of a rational number and an
irrational number is irrational; and that the product of a
nonzero rational number and an irrational number is
irrational.
SE: 431-432
Geometry
Algebra 2
SE: 358-360, 395
SE: 358
SE: 358-365, 392, 394, 398
Page 1 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
N-Q-1. Use units as a way to understand problems and to
guide the solution of multi-step problems; choose and
interpret units consistently in formulas; choose and interpret
the scale and the origin in graphs and data displays.*
SE: 10, 26-30, 43-45, 53, 5658, 59, 61, 62-68, 70-74,
83, 85-86, 88, 93, 108,
110, 115, 118, 122-124,
144, 159, 176, 184-185,
189-191, 194, 202, 208209, 212, 213, 223, 265,
271-273, 279-281, 284,
488, 534, 536-537, 539542, 549-550, 553, 556558, 564-566, 572, 577578, 598, 603, 628, 639641
SE: 105, 108, 140, 186,
193-195, 197, 200, 211,
273, 445, 461, 528,
586, 593, 657, 671,
684-685, 695, 697-698,
703, 708, 713, 715,
727, 750, 753-756, 777,
786, 800, 865
SE: 12, 39, 90, 122, 229,
265, 293-294, 325, 340,
345-348, 363-364, 373,
381, 383, 437, 506, 650,
713, 732
N-Q-2. Define appropriate quantities for the purpose of
descriptive modeling.*
SE: 62-68, 75-81, 686-694,
695-701
N-Q-3. Choose a level of accuracy appropriate to limitations
on measurement when reporting quantities.*
SE: 75-81
N-CN-1. Know there is a complex number i such that i2 = –1,
and every complex number has the form a + bi with a and b
real.
SE: 94-95, 138
N-CN-2. Use the relation i2 = –1 and the commutative,
associative, and distributive properties to add, subtract, and
multiply complex numbers.
SE: 128-131, 139, 141, 477
Page 2 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
N-CN-3. (+) Find the conjugate of a complex number; use
conjugates to find moduli and quotients of complex numbers.
SE: 96-99, 126-133, 138,
145, 226
N-CN-4. (+) Represent complex numbers on the complex
plane in rectangular and polar form (including real and
imaginary numbers), and explain why the rectangular and
polar forms of a given complex number represent the same
number.
Opportunities to address this
standard can be found on the
following pages:
N-CN-5. (+) Represent addition, subtraction, multiplication,
and conjugation of complex numbers geometrically on the
complex plane; use properties of this representation for
computation.
Opportunities to address this
standard can be found on the
following pages:
N-CN-6. (+) Calculate the distance between numbers in the
complex plane as the modulus of the difference, and the
midpoint of a segment as the average of the numbers at its
endpoints.
SE: 126-128, 139
SE: 126-133
This standard is outside the Common Core college and career ready standards.
N-CN-7. Solve quadratic equations with real coefficients that
have complex solutions.
SE: 96-99, 101-107, 109,
138, 140, 190-195, 221
N-CN-8. (+) Extend polynomial identities to the complex
numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
SE: 189-195, 221
N-CN-9. (+) Know the Fundamental Theorem of Algebra;
show that it is true for quadratic polynomials.
SE: 189-195, 221, 222
Page 3 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
N-VM-1. (+) Recognize vector quantities as having both
magnitude and direction. Represent vector quantities by
directed line segments, and use appropriate symbols for
vectors and their magnitudes (e.g., v, |v|, ||v||, v).
SE: 577-585
N-VM-2. (+) Find the components of a vector by subtracting
the coordinates of an initial point from the coordinates of a
terminal point.
SE: 577
N-VM-3. (+) Solve problems involving velocity and other
quantities that can be represented by vectors.
SE: 577-585, 586, 587, 591,
592, 593, 595
N-VM-4. (+) Add and subtract vectors.
SE: 577-585, 586, 587, 591,
596, 785
a. Add vectors end-to-end, component-wise, and by the
parallelogram rule. Understand that the magnitude of a sum
of two vectors is typically not the sum of the magnitudes.
b. Given two vectors in magnitude and direction form,
determine the magnitude and direction of their sum.
c. Understand vector subtraction v – w as v + (–w), where –w
is the additive inverse of w, with the same magnitude as w
and pointing in the opposite direction. Represent vector
subtraction graphically by connecting the tips in the
appropriate order, and perform vector subtraction
component-wise.
Page 4 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
N-VM-5. (+) Multiply a vector by a scalar.
Geometry
Algebra 2
SE: 577-585
a. Represent scalar multiplication graphically by scaling
vectors and possibly reversing their direction; perform scalar
multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
b. Compute the magnitude of a scalar multiple cv using ||cv||
= |c|v. Compute the direction of cv knowing that when |c|v
0, the direction of cv is either along v (for c > 0) or against v
(for c < 0).
N-VM-6. (+) Use matrices to represent and manipulate data,
e.g., to represent payoffs or incidence relationships in a
network.
This standard is outside the Common Core college and career ready standards.
N-VM-7. (+) Multiply matrices by scalars to produce new
matrices, e.g., as when all of the payoffs in a game are
doubled.
This standard is outside the Common Core college and career ready standards.
SE: 144
N-VM-8. (+) Add, subtract, and multiply matrices of
appropriate dimensions.
N-VM-9. (+) Understand that, unlike multiplication of
numbers, matrix multiplication for square matrices is not a
commutative operation, but still satisfies the associative and
distributive properties.
This standard is outside the Common Core college and career ready standards.
Page 5 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Number and Quantity Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
N-VM-10. (+) Understand that the zero and identity matrices
play a role in matrix addition and multiplication similar to the
role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a
multiplicative inverse.
This standard is outside the Common Core college and career ready standards.
N-VM-11. (+) Multiply a vector (regarded as a matrix with
one column) by a matrix of suitable dimensions to produce
another vector. Work with matrices as transformations of
vectors.
This standard is outside the Common Core college and career ready standards.
N-VM-12. (+) Work with 2
2 matrices as a
transformations of the plane, and interpret the absolute value
of the determinant in terms of area.
This standard is outside the Common Core college and career ready standards.
Page 6 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
SE: 10-11, 512, 514
SE: 36-41, 312-318, 689,
751, 757, 759
SE: 75, 234-240
A-SSE-2. Use the structure of an expression to identify ways
to rewrite it.
SE: 462, 463-469, 470-471,
472-479, 480-486, 487,
488, 489, 490-496, 498503, 504, 505, 507-509,
510, 511, 514-515, 739
SE: 13-19
SE: 75, 141, 174-179, 219
A-SSE-3. Choose and produce an equivalent form of an
expression to reveal and explain properties of the quantity
represented by the expression.
SE:
SE:
a. & b.) 470-471, 472-479,
480-486, 487, 488, 489,
490-496, 499-503, 504,
505, 508-509, 510, 511,
514, 739
a. & b.) 75, 76, 77-84, 86-93,
137, 307
A-SSE-1. Interpret expressions that represent a quantity in
terms of its context.*
a. Interpret parts of an expression, such as terms, factors, and
coefficients.
b. Interpret complicated expressions by viewing one or more
of their parts as a single entity.
a. Factor a quadratic expression to reveal the zeros of the
function it defines.
b. Complete the square in a quadratic expression to reveal the
maximum or minimum value of the function it defines.
a.)
c.)
239
562-563, 636-641
c. Use the properties of exponents to transform expressions
for exponential functions.
SE: 658, 660-661, 678, 680
A-SSE-4. Derive the formula for the sum of a finite
geometric series (when the common ratio is not 1), and use
the formula to solve problems..
Page 7 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
A-APR-1. Understand that polynomials form a system
analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
Geometry
SE: 414-419, 422-429, 433439
A-APR-2. Know and apply the Remainder Theorem: For a
polynomial p(x) and a number a, the remainder on division
by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of
p(x).
Algebra 2
SE: 150-156, 158-164, 181,
218, 219, 222, 223, 224,
227, 307, 309, 335-338,
399, 403, 751
SE: 166-172, 174-179, 189195, 220, 222
A-APR-3. Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to construct a
rough graph of the function defined by the polynomial.
SE: 562-567, 600-601
SE: 176-179, 181, 182-188,
219, 220, 223, 880
A-APR-4. Prove polynomial identities and use them to
describe numerical relationships.
SE: 433-439, 490-496, 497
SE: 158-161, 174-179
A-APR-5. (+) Know and apply the Binomial Theorem for the
expansion of (x + y)n in powers of x and y for a positive
integer n, where x and y are any numbers, with coefficients
determined for example by Pascal’s Triangle. (The Binomial
Theorem can be proved by mathematical induction or by a
combinatorial argument.)
SE: 157, 158-164, 531, 532,
587, 590, 684
Page 8 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
SE: 682, 685
A-APR-6. Rewrite simple rational expressions in different
forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x),
b(x), q(x), and r(x) are polynomials with the degree of r(x)
less than the degree of b(x), using inspection, long division,
or, for the more complicated examples, a computer algebra
system.
A-APR-7. (+) Understand that rational expressions form a
system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a
nonzero rational expression; add, subtract, multiply, and
divide rational expressions.
A-CED-1. Create equations and inequalities in one variable
and use them to solve problems. Include equations arising
from linear and quadratic functions, and simple rational and
exponential functions.*
Algebra 2
SE: 166-172, 219, 222, 224,
537
SE: 321-326, 327-334, 335338, 357, 391, 394, 395,
881
SE: 19-22, 26-29, 34-38, 4246, 54-59, 100-105, 107111, 114-117, 118, 119,
122-125, 127-132, 144147, 148, 149, 150-153,
154, 156-157, 158-159,
562-567, 568-573, 575581, 582-589, 624-630
SE: 42, 46, 77-84, 85-92, 9499, 100-107, 110-117,
144, 182-188, 189-195,
266-272, 348-355, 376383, 474, 785-797
Page 9 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
A-CED-2. Create equations in two or more variables to
represent relationships between quantities; graph equations
on coordinate axes with labels and scales.*
SE: 179-185, 186-192, 230236, 237-242, 244-251,
254-259, 260-265, 268274, 275-282, 293-299,
301-307, 329-334, 336342, 343-349, 352-357,
538-543, 545-551, 554559, 582-589, 635-642,
649-655
A-CED-3. Represent constraints by equations or inequalities,
and by systems of equations and/or inequalities, and interpret
solutions as viable or nonviable options in a modeling
context..*
SE: 179-185, 230-236, 237242, 260-265, 268-274,
275-282, 301-307, 331334, 339-342, 346-349,
350-351, 354-356, 358,
359, 369-371, 374, 375,
376-378, 380, 381, 384385, 451, 538-543, 554559, 562-567, 568-573,
575-581, 582-589, 613,
635-642, 649-655
A-CED-4. Rearrange formulas to highlight a quantity of
interest, using the same reasoning as in solving equations..*
SE: 49-53, 59, 68, 85, 88,
161
Geometry
Algebra 2
SE: 182-187, 190-197, 201,
205, 206, 517
SE: 15-21, 24-30, 32-39, 44,
46, 59-66, 67-74, 118125, 150-156, 197-203,
204-209, 210-215, 226,
234-240, 242-248, 249255, 275-280, 281-288,
289-295, 313-320, 340347, 367-375, 422-429,
432-439, 442-448, 450456, 458-465, 536, 749,
754-761, 767
SE: 15-21, 24-30, 32-39, 5966, 67-74, 110-117, 118125, 150-156, 197-203,
204-209, 210-215, 234240, 242-248, 249-255,
275-280, 281-288, 289295, 313-320, 340-347,
367-375, 422-429, 432439, 442-448, 450-456,
458-465, 749, 754-761,
762-767
SE: 41, 673, 674, 676, 685
SE: 449
Page 10 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
A-REI-1. Explain each step in solving a simple equation as
following from the equality of numbers asserted at the
previous step, starting from the assumption that the original
equation has a solution. Construct a viable argument to
justify a solution method.
SE: 17-22, 24-30, 32-38, 4046, 54-59, 61, 84-85
SE: 104-109, 127, 132, 134
SE: 77-84, 85-92, 100-107,
182-188, 266-272, 348355, 376-383
A-REI-2. Solve simple rational and radical equations in one
variable, and give examples showing how extraneous
solutions may arise.
SE: 669, 673, 674
SE: 466-471, 482-489, 493,
495-501, 520
SE: 348-355, 357, 376-383,
388, 389, 392, 393, 394,
395, 398, 399, 476, 809
A-REI-3. Solve linear equations and inequalities in one
variable, including equations with coefficients represented by
letters.
SE: 16, 17-22, 24-30, 31, 3238, 39, 40-46, 53, 59, 60,
61, 68, 84-85, 88, 89,
92-93, 97, 106-111, 112117, 118, 119, 120-125,
126-132, 140, 147, 148,
149, 151-152, 154, 155,
158-159, 161, 169, 185,
192, 203, 211, 222, 223,
236, 274, 299, 325, 334,
397, 403, 419, 450, 469,
519, 612, 623, 630, 679,
701, 721, 760
SE: 43, 46, 47, 48
Page 11 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
A-REI-4. Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any
quadratic equation in x into an equation of the form (x – p)2 =
q that has the same solutions. Derive the quadratic formula
from this form.
Algebra 1
Geometry
Algebra 2
SE: 554-559, 560-561, 562567, 568-573, 576-581,
582-583, 585-589, 598,
599, 606-607, 608, 609,
613, 655
SE: 27, 45, 47-48, 55, 59,
63, 243, 245, 289, 338,
361-367, 377, 381, 382,
400, 427, 442, 444-446,
508, 798, 842, 844-846
SE: 77-84, 85-92, 96-99,
100-107, 108, 109, 137,
140, 143, 145, 307, 309,
684, 749
b. Solve quadratic equations by inspection (e.g., for x2 = 49),
taking square roots, completing the square, the quadratic
formula and factoring, as appropriate to the initial form of the
equation. Recognize when the quadratic formula gives
complex solutions and write them as a ± bi for real numbers
a and b.
A-REI-5. Prove that, given a system of two equations in two
variables, replacing one equation by the sum of that equation
and a multiple of the other produces a system with the same
solutions.
SE: 343-349
A-REI-6. Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs of linear
equations in two variables.
SE: 329-334, 336-342, 343349, 350-351, 352-357,
358, 359, 376-378, 380,
381, 383, 384
SE: 152-153, 158-160, 161,
176, 194, 195, 328,
329-330
SE: 684
A-REI-7. Solve a simple system consisting of a linear
equation and a quadratic equation in two variables
algebraically and graphically.
SE: 590-597
SE: 853
SE: 809, 862-869, 871, 872,
876, 877
Page 12 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Algebra Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
A-REI-8. (+) Represent a system of linear equations as a
single matrix equation in a vector variable.
This standard is outside the Common Core college and career ready standards.
A-REI-9. (+) Find the inverse of a matrix if it exists and use
it to solve systems of linear equations (using technology for
matrices of dimension 3 ! 3 or greater).
This standard is outside the Common Core college and career ready standards.
A-REI-10. Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the coordinate
plane, often forming a curve (which could be a line).
SE: 186-192, 193, 216
SE: 43, 46
A-REI-11. Explain why the x-coordinates of the points where
the graphs of the equations y = f(x) and y = g(x) intersect are
the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions,
make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic
functions.*
SE: 47-48, 554-559, 560561, 628, 629
SE: 79-80, 182-186, 191192, 268-269, 351-352,
384-387
A-REI-12. Graph the solutions to a linear inequality in two
variables as a half-plane (excluding the boundary in the case
of a strict inequality), and graph the solution set to a system
of linear inequalities in two variables as the intersection of
the corresponding half-planes.
SE: 360-366, 368-372, 373,
374, 375, 379, 380, 381,
486
SE: 44, 46, 47, 50, 307, 880
Page 13 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
F-IF-1. Understand that a function from one set (called the
domain) to another set (called the range) assigns to each
element of the domain exactly one element of the range. If f
is a function and x is an element of its domain, then f(x)
denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation y = f(x).
SE: 170-176, 177, 179-186,
187-192, 193, 195, 215,
219, 222
F-IF-2. Use function notation, evaluate functions for inputs in
their domains, and interpret statements that use function
notation in terms of a context.
F-IF-3. Recognize that sequences are functions, some-times
defined recursively, whose domain is a subset of the integers.
F-IF-4. For a function that models a relationship between two
quantities, interpret key features of graphs and tables in terms
of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. Key features
include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and
periodicity.*
SE: 180-185, 192, 195, 216,
218, 219, 223, 322, 397,
629
SE: 50
SE: 206-211, 618-623
SE: 626-632
SE: 165, 167-168, 195, 214,
230, 234-235, 237-238,
240-242, 266, 267, 271273, 309, 310-313, 315,
318, 531-532, 535-537,
541-543, 545-551, 552,
553, 554-559, 600-601,
603, 604-605, 608, 613,
630, 641, 644-647, 649655, 565-659
SE: 7-14, 24-30, 43, 59-66,
67-74, 77-84, 109, 137,
140, 153-156, 183-188,
197-203, 204-209, 218,
220, 221, 222, 223, 236240, 251-255, 275-280,
281-288, 313-320, 340347, 367-375, 399, 406413, 422-429, 432-439,
457, 476, 754-761, 762767
Page 14 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-IF-5. Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it
describes..*
SE: 170-176, 182-184, 186192, 194, 195, 218, 223,
233-235, 241, 260-265,
310-311, 313, 314, 323,
486, 525-529, 542-543,
545-551, 553, 600-601,
603, 669, 672, 674, 675
F-IF-6. Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a
specified interval. Estimate the rate of change from a graph.*
SE: 244-245, 248-251, 254259, 267, 268-274, 308,
315, 318, 323, 469, 656659, 660-667, 739
Geometry
SE: 401, 685
Algebra 2
SE: 14, 19-21, 65, 70, 72-73,
134, 172, 196, 226, 240,
241, 242, 245, 247, 253,
263, 280, 285-286, 288,
299, 302, 341, 345, 367368, 371-372, 375, 388,
389, 392-393, 394, 413,
428-429, 439, 441, 453454, 467, 470, 472, 685,
713, 719, 749, 754-761,
767, 851
SE: 44, 210-215, 408-413,
414-421, 468
Page 15 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-IF-7. Graph functions expressed symbolically and show
key features of the graph, by hand in simple cases and using
technology for more complicated cases.*
a. Graph linear and quadratic functions and show intercepts,
maxima, and minima.
b. Graph square root, cube root, and piecewise-defined
functions, including step functions and absolute value
functions.
c. Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end
behavior.
d. (+) Graph rational functions, identifying zeros and
asymptotes when suitable factorizations are available, and
showing end behavior.
Geometry
Algebra 2
SE:
SE:
a.) 186-192, 193, 195, 216,
218, 219, 220, 230-236,
237-242, 260-265, 266,
267, 268-274, 275-282,
283, 301-307, 309, 314317, 318, 320, 321, 522529, 531-537, 538-543,
553, 554-559, 605, 608,
609, 649-655
a.)
24-30, 43, 46, 59-66,
67-74, 76, 77-84, 109,
137, 140, 144, 226, 476
b.)
45, 46, 367-375, 388,
389, 393, 394, 398,
422-429, 430-431, 441,
469, 685
c.)
153-156, 182-188, 196,
197-203, 204-209, 218,
220, 221
d.)
339, 340-347, 357, 392,
395, 399
e.)
234-240, 251-255, 275280, 297, 298, 302,
754-755, 762-767, 768,
769, 800, 801, 804, 807
b.) 310-313
c.) 544, 545-551, 600-603
e.) 624-630
e. Graph exponential and logarithmic functions, showing
intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude.
Page 16 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-IF-8. Write a function defined by an expression in different
but equivalent forms to reveal and explain different
properties of the function.
Geometry
SE: 530, 533-534, 536-537,
541, 543, 553, 605, 608,
Algebra 2
SE:
a.)
624-630
a. Use the process of factoring and completing the square in a
quadratic function to show zeros, extreme values, and
symmetry of the graph, and interpret these in terms of a
context.
67-74, 77-84, 85-92, 109,
881
b.)
234-240, 265, 302, 684
b. Use the properties of exponents to interpret expressions for
exponential functions.
F-IF-9. Compare properties of two functions each represented
in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions).
SE: 230-236, 310-313, 531-
F-BF-1. Write a function that describes a relationship
between two quantities.*
SE: 179-185, 230-236, 268274, 275-282, 545-551,
568-573, 635-642, 644647, 649-655
SE: 32-39, 118-125, 159163, 169-171, 180, 181,
206-209, 210-215, 219,
221, 222, 278, 289-295,
425-429, 434-438, 442448, 450-456, 458-465,
470, 472, 475, 476, 881
SE: 206-210, 622-623, 644647
SE: 626-632, 647-650, 653,
654-663, 676, 677, 678,
680, 681, 684, 685, 749
a. Determine an explicit expression, a recursive process, or
steps for calculation from a context.
537, 538-543, 600-601,
624-630, 660-667
b. Combine standard function types using arithmetic
operations.
c. (+) Compose functions.
F-BF-2. Write arithmetic and geometric sequences both
recursively and with an explicit formula, use them to model
situations, and translate between the two forms.*
SE: 414-421
Page 17 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-BF-3. Identify the effect on the graph of replacing f(x) by
f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing
even and odd functions from their graphs and algebraic
expressions for them.
SE: 300, 301-307, 309, 310313, 317, 318, 544, 545551, 553, 559, 606, 608,
732, 747
F-BF-4. Find inverse functions.
Geometry
Algebra 2
SE: 101, 374, 618, 638,
640, 748
SE: 7-14, 15-21, 22, 23, 2430, 44, 46, 51, 59-66,
109, 136, 204-209, 221,
222, 223, 225, 227, 281288, 301, 302, 306, 368375, 388, 389, 432-439,
469, 472, 473, 684, 748,
756-761, 762-767
SE: 551, 558
SE:
a. Solve an equation of the form f(x) = c for a simple function
f that has an inverse and write an expression for the inverse.
a-c). 241, 242-248, 251-255,
265, 299, 302, 303, 306,
450-456, 470, 472, 473,
684, 881
b. (+) Verify by composition that one function is the inverse
of another.
c.)
c. (+) Read values of an inverse function from a graph or a
table, given that the function has an inverse.
367
d. (+) Produce an invertible function from a non-invertible
function by restricting the domain.
F-BF-5. (+) Understand the inverse relationship between
exponents and logarithms and use this relationship to solve
problems involving logarithms and exponents.
SE: 249-255, 256-263, 264,
265, 266-272, 275-280,
297, 300, 302, 303, 306,
399, 881
Page 18 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-LE-1. Distinguish between situations that can be modeled
with linear functions and with exponential functions.*
Geometry
SE: 625-628, 649-655
Algebra 2
SE:
a.)
a. Prove that linear functions grow by equal differences over
equal intervals, and that exponential functions grow by equal
factors over equal intervals.
210-215, 406-413, 458465
b.)
406-413, 441, 458-465,
471, 472
b. Recognize situations in which one quantity changes at a
constant rate per unit interval relative to another.
c.)
234-240, 458-465, 471,
472
c. Recognize situations in which a quantity grows or decays
by a constant percent rate per unit interval relative to another.
F-LE-2. Construct linear and exponential functions, including
arithmetic and geometric sequences, given a graph, a
description of a relationship, or two input-output pairs
(include reading these from a table).*
SE: 206-211, 213, 216-217,
218, 219, 220, 230-236,
237-242, 260-265, 268274, 275-282, 309, 314317, 318, 320, 321, 618623, 633, 635-642, 644647, 649-655
SE: 44, 46, 234-240, 305,
398, 406-413, 441, 458465, 468, 471, 472, 537,
643-651, 654-753, 880
F-LE-3. Observe using graphs and tables that a quantity
increasing exponentially eventually exceeds a quantity
increasing linearly, quadratically, or (more generally) as a
polynomial function.*
SE: 630, 660-667
SE: 234-240, 458-465
F-LE-4. For exponential models, express as a logarithm the
solution to abct = d where a, c, and d are numbers and the
base b is 2, 10, or e; evaluate the logarithm using
technology.*
SE: 249-255, 268-272, 274,
275-280
Page 19 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
F-LE-5. Interpret the parameters in a linear or exponential
function in terms of a context.*
Geometry
SE: 268-274, 635-642
Algebra 2
SE: 234-240, 299
F-TF-1. Understand radian measure of an angle as the length
of the arc on the unit circle subtended by the angle.
SE: 707-713
F-TF-2. Explain how the unit circle in the coordinate plane
enables the extension of trigonometric functions to all real
numbers, interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
SE: 700-702, 706-709
F-TF-3. (+) Use special triangles to determine geometrically
the values of sine, cosine, tangent for π/3, π/4 and π/6, and
use the unit circle to express the values of sine, cosines, and
tangent for x, π + x, and 2π – x in terms of their values for x,
where x is any real number.
SE: 693-699, 706-713, 721,
741, 744, 745
F-TF-4. (+) Use the unit circle to explain symmetry (odd and
even) and periodicity of trigonometric functions.
Opportunities to address this
standard can be found on the
following pages:
SE: 707-713, 754-761
SE: 756-760, 762-767
F-TF-5. Choose trigonometric functions to model periodic
phenomena with specified amplitude, frequency, and
midline.*
Page 20 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Functions Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
SE: 714-719
F-TF-6. (+) Understand that restricting a trigonometric
function to a domain on which it is always increasing or
always decreasing allows its inverse to be constructed.
SE: 551, 552-559
F-TF-7. (+) Use inverse functions to solve trigonometric
equations that arise in modeling contexts; evaluate the
solutions using technology, and interpret them in terms of the
context.*
SE: 716-719, 721, 742, 744,
745, 748, 791-797
F-TF-8. Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1
and use it to calculate trigonometric ratios.
SE: 772-777, 801, 804, 807
F-TF-9. (+) Prove the addition and subtraction formulas for
sine, cosine, and tangent and use them to solve problems.
SE: 778-783, 799, 802, 804,
805, 808
Page 21 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
G-CO-1. Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment, based on
the undefined notions of point, line, distance along a line, and
distance around a circular arc.
SE: 6-11, 20-27, 35, 64, 68,
69, 146-151, 688-693
G-CO-2. Represent transformations in the plane using, e.g.,
transparencies and geometry software; describe
transformations as functions that take points in the plane as
inputs and give other points as outputs. Compare
transformations that preserve distance and angle to those that
do not (e.g., translation versus horizontal stretch).
SE: 50-55, 56-57, 509-514,
523, 529, 596, 604-610,
611-617, 619-625, 626631, 633, 650-657, 660663, 664, 668, 669, 785
G-CO-3. Given a rectangle, parallelogram, trapezoid, or
regular polygon, describe the rotations and reflections that
carry it onto itself.
SE: 604-610, 611-617, 619625, 626-631, 633, 634640, 660-663, 664, 665
G-CO-4. Develop definitions of rotations, reflections, and
translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
SE: 50-55, 604-610, 611617, 619-625, 633, 660,
661, 664
G-CO-5. Given a geometric figure and a rotation, reflection,
or translation, draw the transformed figure using, e.g., graph
paper, tracing paper, or geometry software. Specify a
sequence of transformations that will carry a given figure
onto another.
SE: 50-55, 56-57, 59, 63,
64, 604-610, 611-617,
619-625, 626-631, 633,
660-663, 664, 665, 668,
669, 785
Algebra 2
SE: 700-705, 707-713
Page 22 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
G-CO-6. Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid
motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motions to decide if
they are congruent.
G-CO-7. Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and only
if corresponding pairs of sides and corresponding pairs of
angles are congruent.
Geometry
SE: 220-223, 258-267, 274277, 293, 298, 300,
604-610, 611-617, 619625
SE: 69-74
SE: 220-223, 268-273, 274277, 293, 294-295, 298,
300
G-CO-8. Explain how the criteria for triangle congruence
(ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
SE: 248-249, 250-257, 260267, 293, 297, 300,
302, 304, 387
G-CO-9. Prove geometric theorems about lines and angles.
Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are congruent;
points on a perpendicular bisector of a line segment are
exactly those equidistant from the segment's endpoints.
SE: 118-125, 155-159, 162,
169, 181, 203-204, 206,
312-318
Page 23 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
G-CO-10. Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; base
angles of isosceles triangles are congruent; the segment
joining midpoints of two sides of a triangle is parallel to the
third side and half the length; the medians of a triangle meet
at a point.
G-CO-11. Prove theorems about parallelograms. Theorems
include: opposite sides are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles
are parallelograms with congruent diagonals.
Geometry
SE: 231-238, 247, 285-291,
293, 296, 299, 300,
326-331, 334-339, 341,
379, 380
SE: 294, 297, 299
SE: 403-404, 419, 420-427,
451, 454
G-CO-12. Make formal geometric constructions with a
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometry
software, etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a
line segment; and constructing a line parallel to a given line
through a point not on the line.
SE: 14, 16, 17-18, 22-27,
35, 61, 170-171, 172,
177, 179
G-CO-13. Construct an equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
SE: 392-393, 826
Page 24 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
G-SRT-1. Verify experimentally the properties of dilations
given by a center and a scale factor:
Geometry
SE: 472-479, 509-514, 650657, 659, 663, 664
a. A dilation takes a line not passing through the center of the
dilation to a parallel line, and leaves a line passing through
the center unchanged.
b. The dilation of a line segment is longer or shorter in the
ratio given by the scale factor.
G-SRT-2. Given two figures, use the definition of similarity
in terms of similarity transformations to decide if they are
similar; explain using similarity transformations the meaning
of similarity for triangles as the equality of all corresponding
angles and the proportionality of all corresponding pairs of
sides.
SE: 466-471, 472-479, 480481, 482-489, 493, 495501, 519, 521, 524,
525, 526, 527, 531, 597
G-SRT-3. Use the properties of similarity transformations to
establish the AA criterion for two triangles to be similar.
SE: 482-489, 521, 524
G-SRT-4. Prove theorems about triangles. Theorems include:
a line parallel to one side of a triangle divides the other two
proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.
SE: 69-70, 72-74, 83, 86, 88,
89, 185, 236, 323
SE: 312-318, 341, 359, 360367, 377, 378, 490-491,
495, 501, 522, 696
Page 25 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Algebra 2
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
G-SRT-5. Use congruence and similarity criteria for triangles
to solve problems and prove relationships in geometric
figures.
SE: 250-257, 258-267, 268273, 293, 297-298, 300,
302, 304, 482-489, 493,
495-501, 519, 521, 524
G-SRT-6. Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading
to definitions of trigonometric ratios for acute angles.
SE: 534-539, 540, 541-548,
561, 588, 589, 592
G-SRT-7. Explain and use the relationship between the sine
and cosine of complementary angles.
SE: 549-550
G-SRT-8. Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.
SE: 360-371, 377, 381, 382,
383, 385, 552-559, 560,
561, 562-567, 568, 587,
589, 590, 592, 594,
596, 865
SE: 689, 693-699, 721, 740,
744, 745, 749, 809
G-SRT-9. (+) Derive the formula A = 1/2 ab sin(C) for the
area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
SE: 701
SE: 722
G-SRT-10. (+) Prove the Laws of Sines and Cosines and use
them to solve problems.
SE: 569-576, 587, 590, 592,
593
SE: 722-729, 730-737, 739,
742-743, 744, 745, 748
SE: 693
Page 26 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
Algebra 2
G-SRT-11. (+) Understand and apply the Law of Sines and
the Law of Cosines to find unknown measurements in right
and non-right triangles (e.g., surveying problems, resultant
forces).
SE: 569-576, 587, 590, 592,
593
SE: 725-729, 733-737, 739,
742-743, 744
G-C-1. Prove that all circles are similar.
SE: 472-479
G-C-2. Identify and describe relationships among inscribed
angles, radii, and chords. Include the relationship between
central, inscribed, and circumscribed angles; inscribed
angles on a diameter are right angles; the radius of a circle
is perpendicular to the tangent where the radius intersects
the circle.
SE: 820-827, 830-837, 840846, 855, 856, 860,
863, 864
G-C-3. Construct the inscribed and circumscribed circles of a
triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
SE: 319, 325, 823-827, 855,
858, 865
G-C-4. (+) Construct a tangent line from a point outside a
given circle to the circle.
SE: 827
G-C-5. Derive using similarity the fact that the length of the
arc intercepted by an angle is proportional to the radius, and
define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
SE: 810-815, 816-817
SE: 707-713
Page 27 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
SE: 847-853, 859, 860
G-GPE-1. Derive the equation of a circle of given center and
radius using the Pythagorean Theorem; complete the square
to find the center and radius of a circle given by an equation.
Algebra 2
SE: 823-828, 858-860, 870,
871
G-GPE-2. Derive the equation of a parabola given a focus
and directrix.
SE: 845-851, 853, 871, 874,
876, 880
G-GPE-3. (+) Derive the equations of ellipses and hyperbolas
given foci and directrices.
SE: 748, 830-836, 837, 838844, 852, 853, 871, 873874, 876, 881
SE: 279-284
G-GPE-4. Use coordinates to prove simple geometric
theorems algebraically.
G-GPE.5. Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric problems
(e.g., find the equation of line parallel or perpendicular to a
given line that passes through a given point).
SE: 293-299, 307, 309, 317,
318, 323, 384, 450, 573,
761
SE: 190-197, 216-219, 412417, 419, 426-427, 452,
454, 669
G-GPE-6. Find the point on a directed line segment between
two given points that partitions the segment in a given ratio.
SE: 267, 316
SE: 515-516, 704-709
G-GPE-7. Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g., using the
distance formula.*
SE: 820, 821
SE: 704-705, 706-709, 727,
730, 732, 737
Page 28 of 36
Common Core State Standards for Mathematics© Copyright 2010.
National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved
Holt McDougal Algebra 1, Geometry, Algebra 2 – Common Core Edition ©2012 correlated to the
New York Common Core Learning Standards for Mathematics: High School
Geometry Strand
(+ = advanced; * = also a Modeling Standard)
Algebra 1
Geometry
G-GMD-1. Give an informal argument for the formulas for
the circumference of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri's principle, and informal limit arguments.
SE: 688-693, 749-751, 757
G-GMD-2. (+) Give an informal argument using Cavalieri’s
principle for the formulas for the volume of a sphere and
other solid figures.
SE: 749-756, 757-763, 765772
G-GMD-3. Use volume formulas for cylinders, pyramids,
cones, and spheres to solve problems.*
SE: 402-403, 429, 430, 503,
573, 631
SE: 172, 191-192, 325, 366,
816, 829
SE: 742-748, 778
G-GMD-4. Identify the shapes of two-dimensional crosssections of three-dimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
G-MG-1. Use geometric shapes, their measures, and their
properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).*
SE: 668, 749-756, 757-764,
766-773, 777, 779, 781,
784, 785, 864
Algebra 2
SE: 365, 410