High School: Algebra
HSA.SSE.A2
Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ – y⁴ as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
October 1, 2018HSA.SSE.B3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*
October 1, 2018HSA.SSE.B3a
Factor a quadratic expression to reveal the zeros of the function it defines.
October 1, 2018HSA.SSE.B3b
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
October 1, 2018HSA.SSE.B3c
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
October 1, 2018HSA.APR.A1
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.
October 1, 2018HSA.REI.B4b
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.
October 1, 2018HSA.APR.B2
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).
October 1, 2018HSA.APR.B3
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.
October 1, 2018HSA.APR.C4
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagorean triples.
October 1, 2018HSA.APR.C5
(+) 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.1
October 1, 2018HSA.APR.D6
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.
October 1, 2018