Algebra II End-of-Course Exam Content Standards—Core: Operations on Numbers and Expressions (Priority: 15%)
Successful students will be able to perform operations with rational, real, and complex numbers, using both numeric and algebraic expressions, including expressions involving exponents and roots. There are a variety of types of test items including some that cut across the objectives in this standard and require students to make connections and, where appropriate, solve contextual problems.
O1. Real numbers
a. Convert between and among radical and exponential forms of numerical expressions.
- Convert between expressions involving rational exponents and those involving roots and integral powers.
b. Simplify and perform operations on numerical expressions containing radicals.
- Convert radicals to alternate forms and use the understanding of
this conversion to perform calculations with numbers in radical form.
c. Apply the laws of exponents to numerical expressions with rational and negative exponents to order and rewrite them in alternative forms.
O2. Complex numbers
a. Represent complex numbers in the form a + bi, where a and b are real; simplify powers of pure imaginary numbers.
- Every real number, a, is a complex number because it can be
expressed as a + 0i.
- Represent the square root of a negative number in the form bi, where b is real; simplify powers of pure imaginary numbers.
Example: i5 = -i
b. Perform operations on the set of complex numbers.
O3. Algebraic expressions
a. Convert between and among radical and exponential forms of algebraic expressions.
b. Simplify and perform operations on radical algebraic expressions.
c. Apply the laws of exponents to algebraic expressions, including those involving rational and negative exponents, to order and rewrite them in alternative forms.
Example: a4 · a3 = a(4+3) = a7, = a(4-3) = a, (a4)3 = a(4·3) = a12
Example: , (a3b5)2 = a6b10
d. Perform operations on polynomial expressions.
- Limit to at most multiplication of a binomial by a trinomial.
- For division limit the divisor to a linear or factorable quadratic polynomial.
- Division may be performed using factoring.
e. Perform operations on rational expressions, including complex fractions.
- These expressions should be limited to linear and factorable
- Complex fractions should be limited to simple fractions in
numerators and denominators.
f. Identify or write equivalent algebraic expressions in one or more variables to extract information.
Example: The expression, C + 0.07C, represents the cost of an item plus sales tax, while 1.07C is an equivalent expression that can be used to simplify calculations of the total cost.
Example: can be rewritten as