# Mathematics Standards

**Mathematics
Standards**

*= Items with an asterisk are those expected of

students who plan to major in these fields of study

(mathematics, computer science, statistics).

**I. Computation**

**A. Successful students know basic
mathematical operations. They:**

A.1. apply arithmetic operations with

fractions and integers (e.g., add

and subtract by finding a

common denominator, multiply

and divide, reduce and perform

long division without a

calculator).

A.2. use exponents and scientific

notation.

A.3. use radicals correctly.

A.4. understand relative magnitude.

A.5. calculate using absolute value.

A.6. use the correct order of

arithmetic operations,

particularly demonstrating

facility with the Distributive Law.

A.7.* know terminology for complex

numbers, integers, rational

numbers, irrational numbers

and complex numbers.

**B. Successful students know and carefully
record symbolic manipulations. They:**

B.1. understand the uses of

mathematical symbols as well as

the limitations on their

appropriate uses (e.g., equal

signs, parentheses, superscripts

and subscripts).

**C. Successful students know and
demonstrate fluency with
mathematical notation and
computation. They:**

C.1. correctly perform addition,

subtraction, multiplication and

division that includes variables.

C.2. perform appropriate basic

operations on sets (e.g., union,

intersection, elements of,

subsets and complement).

C.3. use alternative symbolic

expressions, particularly

alternatives to x (e.g., letters of

the Greek alphabet that do not

already have specific scientific

or mathematical meanings).

## II. Algebra

**A. Successful students know and apply
basic algebraic concepts. They:**

A.1. use the distributive property to

multiply polynomials.

A.2. know how to compose and

decompose functions and how to

find inverses of basic functions.

A.3. simplify and perform basic

operations on rational

expressions, including finding

common denominators (e.g.,

add, subtract, multiply and

divide).

A.4. understand exponents, roots

and their properties [e.g.,

(x^{2})(x^{3})=x^{5} and (√x)^{3} = x^{3/2})].

A.5. know basic theorems of

exponents and roots.

A.6.* understand logarithms (to bases

2, 10 and e) and their properties.

A.7.* divide low degree polynomials

(e.g., long division).

A.8.* know basic theorems of

logarithms.

A.9.* factor polynomials (e.g.,

difference of squares, perfect

square trinomials, difference of

two cubes and trinomials such

as x^{2} + 3x + 2).

**B. Successful students use various
appropriate techniques to solve
basic equations and inequalities.
They:**

B.1. solve linear equations and

absolute value equations.

B.2. solve linear inequalities and

absolute value inequalities.

B.3. solve systems of linear

equations and inequalities

using algebraic and graphical

methods (e.g., substitution,

elimination, addition and

graphing).

B.4. solve quadratic equations using

various appropriate methods

while recognizing real

solutions. This includes:

B.4a. factoring.

B.4b. completing the square.

B.4c. the quadratic formula.

**C. Successful students distinguish between
and among expressions, formulas,
equations and functions. They:**

C.1. know when it is possible to

simplify, solve, substitute or

evaluate equations and

expressions and when it is not

possible. For example, expand,

but do not solve, the expression

(x+3)(x+1); substitute a = 3, b =

4 into the formula a^{2} + b^{2} = c^{2};

solve the equation 0 =

(x+3)(x+1); or evaluate the

function f(x) = (x+3)(x+1) at x

= -1.

C.2. understand that the concept of

a function has a specific

definition beyond being a type

of algebraic expression.

C.3. represent functions, patterns

and relationships in different

ways (e.g., statements, formulas

and graphs).

C.4. understand the algebraic

language and notation for

functions (e.g., domain and

range).

C.5. understand a variety of functions

(e.g., polynomial, rational,

exponential, logarithmic and

trigonometric) and properties of

each.

**D. Successful students understand the
relationship between equations and
graphs. They:**

D.1. understand basic forms of the

equation of a straight line and

how to graph the line without

the aid of a calculator.

D.2. understand the basic shape of

a quadratic function and the

relationships between the roots

of the quadratic and zeroes of

the function.

D.3. know the basic shape of the

graph of exponential and log

functions, including

exponential decay.

**E. Successful students understand
algebra well enough to apply it
procedurally and conceptually to a
range of common problems. They:**

E.1. recognize which type of

expression best fits the context of

a basic application (e.g., linear

equation to solve distance/time

problems; quadratic equation to

explain the motion of a falling

object; or compound interest as

an exponential function).

**F. Successful students demonstrate the
ability to work with formulas and
symbols algebraically. They:**

F.1.* know formal notation (e.g.,

sigma notation and factorial

notation).

F.2.* know arithmetic and geometric

progressions and series.

## III. Trigonometry

**A. Successful students know and
understand basic trigonometric
principles. They:**

A.1. know the definitions of sine,

cosine and tangent using right

triangle geometry and

similarity relations.

A.2. understand the relationship

between a trigonometric function

in standard form and its

corresponding graph (e.g.,

domain, range, amplitude,

period, phase shift and vertical

shift).

A.3. understand periodicity and

recognize graphs of periodic

functions, especially the

trigonometric functions.

A.4.* know and use identities for sum

and difference of angles [e.g.,

sin (x ± y), cos (x ± y)] and use

double and half angle formulas.