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TexasMaths

Number and Algebraic Methods

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you identify terms of arithmetic and geometric sequences in recursive form, and write a formula for the nth term?

Identify terms of arithmetic and geometric sequences when given in recursive form, and write a formula for the $n$ th term of arithmetic and geometric sequences given several of their terms (TEKS A.12C, A.12D).
A STAAR Algebra I answer on arithmetic and geometric sequences (TEKS A.12C, A.12D), recursive versus explicit form, finding the common difference or ratio, and the nth-term formulas you must memorize off the reference sheet.
9 min answer →

How do you divide a polynomial of degree one or two by a polynomial of degree one, and when can you simplify by factoring instead?

Determine the quotient of a polynomial of degree one or two divided by a polynomial of degree one when the degree of the divisor does not exceed the degree of the dividend (TEKS A.10C).
A STAAR Algebra I answer on dividing a degree-one or degree-two polynomial by a degree-one polynomial (TEKS A.10C), using factor-and-cancel and long division, and handling remainders.
9 min answer →

How do you simplify expressions with the laws of exponents, including negative and rational exponents, and simplify numerical square-root radicals?

Simplify numerical radical expressions involving square roots, and simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents (TEKS A.11A, A.11B).
A STAAR Algebra I answer on the laws of exponents (product, quotient, power, negative, and rational exponents) and simplifying numerical square-root radicals (TEKS A.11A, A.11B), all keyed to the reference-sheet identities.
10 min answer →

How do you factor trinomials and binomials on STAAR, including the GCF, the difference of two squares, and perfect-square trinomials?

Factor, if possible, trinomials with real factors in the form $ax^2 + bx + c$ , including perfect-square trinomials, and decide if a binomial is a difference of two squares and rewrite it (TEKS A.10E, A.10F).
A STAAR Algebra I answer on factoring trinomials of the form ax squared plus bx plus c, perfect-square trinomials, and the difference of two squares (TEKS A.10E, A.10F), the GCF-first routine, and the reference-sheet identities.
10 min answer →

How do you add, subtract, and multiply polynomials of degree one and two, and where does the STAAR test reward the structure of the work?

Add and subtract polynomials of degree one and degree two, and multiply polynomials of degree one and degree two, writing the result in standard form (TEKS A.10A, A.10B).
A STAAR Algebra I answer on adding, subtracting, and multiplying polynomials of degree one and two (TEKS A.10A, A.10B), distributing the subtraction sign, the FOIL and box methods, and writing answers in standard form for the equation editor.
9 min answer →

How do you solve simple-interest and compound-interest problems on STAAR, and why is compound interest an exponential model?

Solve problems involving the simple interest formula $I = Prt$ and compound interest (TEKS A.12E).
A STAAR Algebra I answer on simple interest I equals Prt and compound interest (TEKS A.12E), the formulas you must memorize off the reference sheet, and why compound interest is an exponential growth model.
9 min answer →