GED and HiSET mathematics — exponents, polynomials and quadratics

The algebra on the GED Mathematical Reasoning test and the HiSET Mathematics test does not stop at linear equations. Both tests ask you to work with powers and roots, to add and multiply polynomials, to factor, and to solve quadratic equations. The GED formula sheet prints the standard form of a quadratic equation and the quadratic formula, but it does not tell you when factoring is faster, how to simplify the radical you end up with, or which of two roots makes sense in a real problem. This material practices exactly those decisions.

The twelve quiz questions move from exponents to quadratics. You apply the product rule, then combine the power and quotient rules on $\frac{(2a^3{)}^2}{a^2}$. You evaluate a zero exponent and a negative exponent together, place $\sqrt{50}$ between two whole numbers, write a very small measurement in scientific notation, and multiply two numbers in scientific notation to estimate a city's yearly water use. You subtract one polynomial from another, where the minus sign in front of the parentheses is the whole question, and multiply two binomials. Then you factor a trinomial with a negative constant, solve a quadratic by factoring, solve $x^2+4x-2=0$ with the quadratic formula and simplify the answer, and finally find the width of a 96-square-foot lot whose length is 4 feet more than its width, rejecting the negative root.

Every wrong option comes from a real mistake: multiplying exponents instead of adding them, forgetting to square the number in front, leaving 18 in front of a power of ten, changing the sign of only the first term of a subtracted polynomial, picking factors that multiply correctly but add to the wrong middle term, or giving the length when the question asks for the width. The explanation names the mistake behind each wrong option.

The flashcards hold the exponent laws, scientific notation, the FOIL pattern, the difference of squares, the method for factoring trinomials, the zero product property, the quadratic formula and what the discriminant says about the number of real solutions.

The written work asks for full solutions on paper, with each step shown: simplifying expressions with several exponent rules, converting and computing in scientific notation, subtracting and multiplying polynomials, factoring, and solving quadratic word problems. The oral exam asks one question at a time and expects you to say why each step is allowed.

The material is independent practice written by Zestly, based on the published content of the GED and HiSET mathematics tests; it is not produced or endorsed by GED Testing Service or ETS.

• Apply the product, quotient and power rules of exponents, including zero and negative exponents
• Estimate and simplify square roots
• Write numbers in scientific notation and multiply them
• Add, subtract and multiply polynomials, distributing signs correctly
• Factor trinomials of the form x^2 + bx + c and solve quadratics by factoring
• Solve quadratics with the quadratic formula and simplify the radical
• Set up a quadratic from a word problem and choose the root that fits the situation

Practice material written by Zestly, based on the published content of the GED Mathematical Reasoning test (algebraic problem solving: exponents, polynomials, factoring, quadratic equations; standard form and quadratic formula as printed on the GED Mathematics Formula Sheet, GED Testing Service, 2014 test) and the HiSET Mathematics test (algebraic concepts; number and operations).