Correlations to the Secondary Mathematics Benchmarks

KEY:

Algebra

A.A.1 Variables and expressions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Interpret and compare the different uses of variables and describe patterns, properties of numbers, formulas, and equations using variables. C.1 B.1
b. Analyze and identify characteristics of algebraic expressions. C.2 B.2 O3.f J1, J3
c. Evaluate, interpret, and construct simple algebraic expressions. C.2 B.2 J1.6, J2.3
d. Identify and transform expressions into equivalent expressions. C.2 B.2 O3.f J1.1, J1.2*, J1.4 6, 9, 20
e. Determine whether two algebraic expressions are equivalent. C.2 B.2 O3.f 20
f. Apply the properties of exponents to transform variable expressions involving integral exponents. B.2 G.1 O3.c J1.1
g. Interpret rational exponents; translate between rational exponents and notation involving integral powers and roots. B.1 part, B.2 part C.1 part, G.1 part O3.a, O3.b J1.1, J1.2*

A.A.2 Functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Determine whether a relationship is or is not a function. D.1 C.1 J2.1
b. Represent and interpret functions using graphs, tables, words, and symbols. D.1 C.1 MR2 9, 12, 20, 28, 30

A.A.3 Linear functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Analyze and identify linear functions of one variable. D.2 C.2 18, 28
b. Know the definitions of x- and y-intercepts, know how to find them, and use them to solve problems. D.2 C.2 J4.1, J4.2, J4.5
c. Know the definition of slope, calculate it, and use slope to solve problems. D.2 C.2 J4.1, K10.1
d. Express a linear function in several different forms for different purposes. D.3 C.3 MR2, K10.2
e. Recognize contexts in which linear models are appropriate; determine and interpret linear models that describe linear phenomena. D.4 C.4 J5.1, L3.4 28

A.A.4 Proportional functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Recognize, graph, and use direct proportional relationships. D.5 part C.5 part B.1 E.1
b. Recognize, graph, and use reciprocal relationships. B.2 E.2
c. Distinguish among and apply linear, direct proportional, and reciprocal relationships. B.3 E.3
d. Explain and illustrate the effect of varying the parameters m and b in the family of linear functions and varying the parameter k in the families of directly proportional and reciprocal functions. B.5 E.4 J4.2

A.A.5 Equations and identities.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Distinguish among an equation, an expression, and a function. E.1 D.1
b. Solve linear and simple nonlinear equations involving several variables for one variable in terms of the others. B.6 F.1 E2.e J3.2
c. Interpret identities as a special type of equation and identify their key characteristics. E.1 D.1
d. Make regular fluent use of basic algebraic identities such as (a + b)2 = a2 + 2ab + b2; (a – b)2 = a2 – 2ab + b2; and (a + b)(a – b) = a2 – b2. B.3 H.7 J1.4
e. Create, interpret, and apply mathematical models to solve problems arising from contextual situations. B.4 part D.3 part F.5 part, H.4 part J5, J5.1, J5.2, J5.3, J5.4, J5.5, J5.6

A.A.6 Linear equations and inequalities.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Solve linear equations in one variable algebraically. E.2 D.2 J3.1
b. Solve and graph the solution of linear inequalities in one variable. E.2 D.2 J3.1, J4.4
c. Identify the relationship between linear functions of one variable and linear equations in two variables. E.3 D.3
d. Use graphs to help solve linear equations in one variable. E.3 D.3 J4, J4.1, J4.2 10
e. Represent any straight line in the coordinate plane by a linear equation in two variables. E.3 D.3 K10.2
f. Solve and graph the solution of a linear inequality in two variables. E.4 F.3 J4.4
g. Recognize and solve problems that can be modeled using linear equations or inequalities in one or two variables; interpret the solution(s) in terms of the context of the problem. E.3 part D.3 part E.7 part F.5 part E1.d J5.1 10
h. Solve equations and inequalities involving the absolute value of a linear expression in one variable. E.3 F.2 E1.a J3.1

A.B.1 Quadratic functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Identify quadratic functions expressed in multiple forms; identify the specific information each form clarifies. C.1 H.1 P1.a, P1.b MR2 18
b. Graph quadratic functions and use the graph to help locate zeros. C.3 H.2 part C.1 part P1.b J4.5
c. Recognize contexts in which quadratic models are appropriate; determine and interpret quadratic models that describe quadratic phenomena. D.3 H.3 P1.d J5.3 18, 26

A.B.2 Simple quadratic functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Solve quadratic equations that can be easily transformed into the form (x - a)(x - b) = 0 or (x + a)2 = b, for a and b integers. C.3 H.4 E2.a J3.5
b. Estimate the roots of a quadratic equation from the graph of the corresponding function. C.3 H.4 P1.b J4.5
c. Solve simple quadratic equations that arise in the context of practical problems and interpret their solutions in terms of the context. D.3 H.4 P1.d J5.3

A.B.3 Systems of linear equations and inequalities.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Solve systems of simultaneous linear equations in two variables using algebraic procedures. E.4 part D.4 part E.6 F.4 part J3.3 10, 26
b. Use graphs to help solve systems of simultaneous linear equations in two variables. E.4 D.4 J4.3 10
c. Solve systems of two or more linear inequalities in two variables and graph the solution set. E.5 A.1 E1.c 27
d. Solve systems of simultaneous linear equations in three variables using algebraic procedures. E.6 A.2 E1.b, E1.d J3.4*
e. Describe the possible arrangements of the graphs of three linear equations in three variables and relate these to the number of solutions of the corresponding system of equations. E.6 A.2 J3.4*
f. Recognize and solve problems that can be modeled using a system of linear equations or inequalities; interpret the solution(s) in terms of the context of the problem. E.4 part D.4 part E.7 F.5 part A.3 part E1.d J5.2 27

A.C.1 Elementary functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Identify key characteristics of absolute value, step, and other piecewise-linear functions and graph them. D.1 E.5 F3.a, F3.b J4, J5 11, 12
b. Graph and analyze exponential functions and identify their key characteristics. D.2 G.2 part F.1 part, F.4 part X1.a, X1.b, X1.c J4.7 18
c. Analyze power functions and identify their key characteristics. E.1 D.1 P2.a 18
d. Transform the algebraic expression of power functions using properties of exponents and roots. E.2 D.1 O3.a J1.1, J1.2
e. Differentiate the graphs of simple exponential and power functions by their key characteristics. E.1 F.2 P2.a, P2.c, P2.d, X1.b J4.7 18
f. Recognize and solve problems that can be modeled using exponential and power functions; interpret the solution(s) in terms of the context of the problem. E.4 G.3 part D.4 part E2.a, P2.e, X1.d J5.4 3, 18
g. Explain, illustrate, and identify the effect of simple coordinate transformations on the graph of a function. E.5 F.4 X1.c J4.2, J4.5, J4.6, J4.8 12

A.C.2 Polynomial functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Transform quadratic functions and interpret their graphical forms. C.2 H.5 part C.2 part P1.a, P1.c K6
b. Analyze polynomial functions and identify their key characteristics. E.3 D.2 P2.b J4.5
c. Use key characteristics to identify the graphs of simple polynomial functions. E.4 D.3 P2.b, P2.c
d. Recognize and solve problems that can be modeled using simple polynomial functions; interpret the solution(s) in terms of the context of the problem. E.5 D.4 P1.d, P2.f 26

A.C.3 Polynomial and rational expressions and equations.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Solve and graph quadratic equations having real solutions using a variety of methods. C.3 part, D.3 part H.6 E2.a J4.5
b. Relate the coefficients a, b and c of the quadratic equation ax2 + bx + c = 0 to its roots. D.2 C.1 E2.a, E2.c J4.5
c. Distinguish among linear, exponential, polynomial, rational, and power expressions, equations, and functions by their symbolic form. E.2 F.3 MR2
d. Perform operations on polynomial expressions. E.6 D.5 O3.d J1.3, J1.4
e. Know and use the binomial expansion theorem. B.4 D.5 J6*
f. Use factoring to reduce rational expressions that consist of the quotient of two simple polynomials. E.7 E.1 O3.e J1.3, J1.4
g. Perform operations on simple rational expressions. E.8 E.2 O3.e, O3.f J1.5

A.D.1 General quadratic equations and inequalities.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Solve and graph quadratic equations having complex solutions. D.2 C.1 E2.a, E2.b J3.5
b. Solve and graph quadratic inequalities in one or two variables. D.4 C.3 E2.b, E2.d 17
c. Manipulate simple quadratic equations to extract information. D.5 C.2 E2.c, E2.e C1.b

A.D.2 Rational and radical equations and functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Solve simple rational and radical equations in one variable. E.3 E.3 E2.a 30
b. Graph simple rational and radical functions in two variables. E.1 part, E.2 part, E.5 part E.4 P2.d, P2.e 30

A.E.1 Trigonometric functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Relate sine and cosine functions to a central angle of the unit circle. T1.b K12.1*
b. Define and graph trigonometric functions over the real numbers. T1.c, T1.d, T1.e, T1.f K12.3*
c. Analyze periodic functions and identify their key characteristics. T1.a, T1.g K12.3*
d. Recognize and solve problems that can be modeled using equations and inequalities involving trigonometric functions. T1.g
e. Derive and use basic trigonometric identities. D3 K12.2*
f. Solve geometric problems using the sine and cosine functions. T1.g K11, K11.2, K11.3, K12*, K12.4*

A.E.2 Matrices and linear equations.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know and use matrix notation for rows, columns, and entries of cells. M1.a
b. Compute the determinant of a 2x2 or 3x3 matrix. M2.b
c. Know and perform addition, subtraction, and scalar multiplication of matrices. M1.a
d. Know and perform matrix multiplication. M1.b
e. Relate vector and matrix operations to transformations in the coordinate plane. M3.a
f. Apply the concept of inverse to matrix multiplication. M2.b, M2.d
g. Write and solve systems of 2x2 and 3x3 linear equations in matrix form. M2.c

A.E.3 Operations on functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Compare and contrast properties of different types (families) of functions. H.3 opt P2.a L2.a, L2.b, L2.d
b. Analyze the transformations of a function from its graph, formula, or verbal description. F.3 part/opt, G.1 part/opt L2.b, L2.c
c. Compute the sum, difference, product, and quotient of two functions. G.1 opt F1.a J2.4*
d. Determine the composition of simple functions, including any necessary restrictions on the domain. D.4 opt G.1 opt F1.b J2.4*

A.E.4 Inverse functions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Analyze characteristics of inverse functions. D.5 opt G.2 opt F2.a J2.5*
b. Determine the inverse of linear and simple non-linear functions, including any necessary restrictions on the domain. D.5 part/opt, D.6 part/opt G.3 opt F2.b J2.5*
c. Apply properties of logarithms to solve problems and prove theorems. D.6 opt G.4 opt L1.a, L1.b, L2.d J2.6*

A.E.5 Relations.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know the definition of a relation and distinguish non-function relations from functions. J2.1
b. Determine whether a function has the characteristics of reflexivity, symmetry, and transitivity; know that relations exhibiting these characteristics are members of a special class of relations called equivalence relations.
c. Explain how some geometric concepts, such as equality, parallelism, and similarity, can be defined as equivalence relations.