PERT Math Expressions Questions: Arithmetic, Exponents and Polynomials
PERT expression questions ask you to evaluate, simplify, expand, factor or divide an expression and pick the equivalent form from the choices. They run from signed numbers, fractions and exponents through polynomials, factoring and rational expressions. The method is to work one operation at a time in the right order, keep track of every sign, and check that your answer and the original agree at a simple value. This guide covers each family, the traps in the answer choices and two worked examples.
Updated November 5, 2026
PERT Math Expressions Questions: Arithmetic, Exponents and Polynomials at a glance
Detail
What to know
Subject
PERT Mathematics, scored from 50 to 150
Questions in the subject
30: 25 scored and 5 field-test; you won’t be told which 5 are unscored, so treat every question as if it counts
Timing
Untimed; testing centers keep their own hours
Navigation
Computer-adaptive; you answer each question to move on and cannot go back
Answer format
Multiple choice; the public study-guide samples show four choices, A to D
Calculator
On-screen four-function calculator on some questions only; no personal calculator unless an approved disability accommodation allows one
Topics in our practice set
Signed numbers, fractions, exponents, substitution, polynomials, factoring, polynomial division and rational expressions
PERT Mathematics has 30 multiple-choice questions. Twenty-five produce your score and five are field-test questions used to build the question bank. You won’t be told which 5 are unscored, so treat every question as if it counts. The test is computer-adaptive: each question is chosen from your answers to earlier ones, you must answer to move on, and you cannot go back once you submit.
Expression questions are short. Most are a single instruction, Evaluate, Simplify, Expand or Factor, followed by an expression, and the four choices in our bank are numbers, fractions or equivalent-looking expressions. A few add a one-line setting, such as a temperature that changes or a length cut into equal parts, or a condition, such as for x ≠ 0. The choices differ in small ways, often a single sign or exponent, because each wrong one comes from a particular slip: squaring a negative the wrong way, subtracting only the first term of a polynomial, or leaving out the middle term of a product.
This page does not cover slope or equations of lines. In our practice bank those questions belong to the algebra question type, and its guide is linked below. The skills here still feed into them: a slope is a fraction of two signed differences, and turning 5x − 2y = 6 into y = (5/2)x − 3 is distribution and sign work.
You can’t bring your own calculator unless an approved disability accommodation allows one; an on-screen calculator appears only on some math questions. The study guide describes it as a standard four-function calculator that performs operations in the order you enter them. That matters on this question type: on a calculator that works in the order you enter the keys, 2 + 3 × 4 gives 20, not 14. Order of operations, signs and fractions stay your job.
What they test
Every question here tests whether two forms of a number or expression truly mean the same thing. Our 50 practice questions cover:
Signed numbers and order of operations, including a negative sign outside a power versus inside parentheses, and division and multiplication from left to right
Fractions: common denominators, dividing by a fraction, mixed numbers and complex fractions
Exponent rules, negative exponents, fractional exponents and scientific notation
Substituting values, including negatives, fractions and function notation
Distributing, combining like terms, and adding or subtracting polynomials
Multiplying monomials and binomials, including squares and the difference of squares
Factoring by common factor, trinomials, grouping and the difference of squares
Dividing polynomials and simplifying rational expressions while keeping excluded values
How to answer PERT expression questions
Signed numbers: mark the grouping, then go one level at a time
Before you calculate, mark what is grouped: parentheses and brackets first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. In −5 + 2(1 − 6), the parentheses give −5, the multiplication gives −10, and −5 + (−10) = −15. Adding 5 to −10 instead gives −5, a typical trap choice.
Watch what an exponent touches. In −5², only the 5 is squared and the minus sign waits outside, so −5² = −25. In (−5)², the sign is inside the parentheses and gets squared too, so (−5)² = 25. An expression that contains both, such as −5² + (−5)², comes out to 0, not 50.
Multiplication and division share a level, so work them from left to right as written. In 24 ÷ 4 × (−3) − (−8), divide first to get 6, multiply to get −18, and subtracting −8 adds 8, so the value is −10. Reading 4 × (−3) as a denominator would invent parentheses that are not there. For a setting with signed changes, keep the start separate from each change: a thermometer that reads −8°F at dawn, climbs 15°F by noon and drops 11°F by evening ends at −8 + 15 − 11 = −4°F.
Fractions: decide the operation, then the method
Adding and subtracting need a common denominator. For 7/8 − 2/3, rewrite both in twenty-fourths, 21/24 − 16/24, to get 5/24. Subtracting tops and bottoms separately gives 5/5, which treats eighths and thirds as the same size. Multiplying needs no common denominator, and dividing means multiplying by the reciprocal: (−5/6) ÷ (10/3) becomes (−5/6) × (3/10), and cancelling leaves −1/4. Settle the sign first; a negative divided by a positive stays negative.
Read word settings for what each fraction is a fraction of. A jug that is 5/6 full, after you pour out an amount equal to 1/3 of the whole jug, holds 5/6 − 1/3 = 1/2 of the jug, because both fractions refer to the same whole. Multiplying 5/6 by 2/3 answers a different question, about pouring out a third of what was in the jug. To count equal parts, divide: a 4 1/2-foot board cut into 3/4-foot lengths gives (9/2) × (4/3) = 6 lengths.
For a fraction inside a fraction, simplify the inside first. In 1/(3 + 1/2), the denominator is 7/2, so the value is its reciprocal, 2/7. A choice of 7/2 stops one step early. If the on-screen calculator appears, it will give decimals such as 0.5 or 0.2857…, so be ready to turn a decimal back into the fraction the choices use.
Exponents and monomials: name the rule before you use it
Most exponent errors come from using the right rule in the wrong place. Multiplying powers of the same base adds exponents. Dividing subtracts them: x⁷/x³ = x⁴. Raising a power to a power multiplies them, and an outside power applies to every factor, including the sign: (−3a²b³)² = 9a⁴b⁶. Fractional exponents follow the same rules for a positive base: x^(1/3) · x^(5/3) = x², since 1/3 + 5/3 = 2.
A negative exponent makes a reciprocal, not a negative number. So 3⁻² + 3⁻¹ is 1/9 + 1/3, which is 4/9. The exponent rules do not apply here at all, because the outer operation is addition. In scientific notation, handle the numbers and the powers of 10 separately: (8 × 10⁶)/(2 × 10²) is 4 × 10⁴, or 40,000.
For monomials, split the work into coefficients and variables. In (−2a³b)(5ab²), the coefficients multiply to −10, the a exponents add to 4 and the b exponents add to 3, giving −10a⁴b³. In (14a⁵b²)/(21a²b⁵), the coefficients reduce to 2/3, three factors of a stay on top and three factors of b stay on the bottom: 2a³/(3b³). To divide a polynomial by a monomial, divide every term: (18x⁴ − 12x³ + 6x)/(6x) = 3x³ − 2x² + 1. The last term is 1, because 6x divided by 6x is 1.
Substitution: replace every copy, in parentheses
Write the expression again with each value in parentheses before you do any arithmetic. For 3x² − 4y with x = −3 and y = 2, that is 3(−3)² − 4(2) = 27 − 8 = 19. Skipping the parentheses invites −3² = −9, which leads to −35. Count how many times each letter appears and make sure every copy is replaced.
Fractions and function notation follow the same routine. With p = 1/2 and q = −3/2, (p + q)/(p − q) has numerator −1 and denominator 2, so it equals −1/2. For g(t) = t² + 3t, g(2) = 10 and g(−3) = 9 − 9 = 0, so g(2) − g(−3) = 10. Put each result in parentheses before subtracting so the whole second value is removed.
Polynomials: distribute to every term and line up like terms
A minus sign in front of parentheses changes every sign inside. In 5x − (3x − 8) + 2, the group becomes −3x + 8, so the total is 2x + 10. Read subtract A from B as B − A: subtracting (3x² − 2x − 4) from (7x² + x − 1) gives 7x² + x − 1 − 3x² + 2x + 4, which is 4x² + 3x + 3. Only like terms combine. An x² term and an x term stay separate, and a missing term, such as the x² term in 4x³ − x + 6, simply has a coefficient of 0.
To multiply two binomials, pair every term in the first with every term in the second. (x + 5)(x − 3) gives x², −3x, 5x and −15, so x² + 2x − 15. A square is a product of two copies: (2x − 5)² = (2x − 5)(2x − 5) = 4x² − 20x + 25, with two cross-products of −10x each. Only a difference of squares loses its middle term, because the cross-products are opposites: (3x + 4)(3x − 4) = 9x² − 16.
When you are unsure, test a value. Put a small number into the original expression and into your answer; if they disagree, something went wrong. For (x + 6)(x − 2) = x² + 4x − 12, x = 3 gives 9 × 1 = 9 on the left and 9 + 12 − 12 = 9 on the right. A match at one value does not prove the forms are equal, but a mismatch proves they are not.
Factoring, division and rational expressions: undo multiplication and keep the restrictions
Factor in a fixed order. Take out the greatest common factor first: 10x² + 15x = 5x(2x + 3). For x² + bx + c, find two numbers that multiply to c and add to b: for x² − 2x − 24 those are −6 and 4, so (x − 6)(x + 4). With four terms, try grouping: x³ + 2x² − 9x − 18 = x²(x + 2) − 9(x + 2) = (x + 2)(x² − 9), and x² − 9 = (x − 3)(x + 3). Then expand your answer to check it. The near-miss choices usually match the first and last terms and differ only in the middle.
Long division of polynomials repeats one cycle: divide the leading terms, multiply the whole divisor, subtract the whole product, bring down. For x³ − 27 divided by x − 3, write the missing terms as 0x² and 0x so the columns line up; the quotient is x² + 3x + 9. A remainder stays in the answer. Dividing 3x³ + 2x² − x + 4 by x + 1 gives 3x² − x with a remainder of 4, so the result is 3x² − x + 4/(x + 1). For a remainder alone, evaluate at the divisor’s zero: dividing x² − 3x + 7 by x − 2 leaves 2² − 3(2) + 7 = 5.
A rational expression is a fraction of polynomials, and it is undefined wherever its original denominator is 0. Factor before cancelling, because only common factors cancel: (x² − 16)/(x − 4) = (x − 4)(x + 4)/(x − 4) = x + 4, but only for x ≠ 4. To find where an expression is undefined, factor the denominator and set each factor to 0: (x − 5)/(x² + x − 12) has denominator (x + 4)(x − 3), so it is undefined at −4 and 3. The numerator’s zero, 5, is a place where the expression equals 0, which is a different thing.
Common mistakes
Six slips that the answer choices in this question type are built to catch, and the habit that prevents each one.
Mistake: Evaluating −5² as 25.
Better: Square only what the exponent touches: −5² = −25, while (−5)² = 25.
Why: Without parentheses the minus sign is applied after the squaring. Writing a substituted negative in parentheses keeps the two cases apart.
Why: A squared binomial has two cross-products. Only a difference of squares, with opposite signs, loses its middle term.
Mistake: Cancelling the 4s in (x² − 16)/(x − 4) or dropping the restriction after simplifying.
Better: Factor first, cancel the common factor x − 4, and keep x ≠ 4: the result is x + 4.
Why: Only factors cancel, never terms joined by + or −. The simpler form does not make x = 4 allowed, because the original denominator is still 0 there.
Working without a clock
No PERT subject has an official time limit. In 2015, FDOE reported that the Mathematics subtest took about 30 minutes on average, and colleges’ own estimates range from about two hours to more than three for all three subjects, and our PERT test dates and registration guide lists them by college.
Expression questions are where unhurried checking pays off, because the wrong choices differ by a single sign. Before you submit, run one quick check that fits the question: put a small value into the original and your simplified answer and see that they match, expand a factorization, or confirm the sign you predicted before calculating. If you pick a test value, avoid any value the expression excludes. Miami Dade College notes that you can change an answer before moving on, but once you submit, the question is closed. One good check, then move on.
Practice without a countdown too. Our practice sets are untimed, and the explanations appear after you submit the set. When you miss a question, write down which slip caused it. The same few slips, signs, exponents and subtraction of a group, account for most misses in this question type.
Two questions from our practice bank: an order-of-operations question built around the negative-square trap, and a factoring question where three choices look almost right.
Example 1 · Medium · Signed numbers and order of operations
Evaluate −3² + (−3)² + 8 ÷ (−2).
A.−4
B.0
C.4
D.14
Answer: A (−4)
How to solve it
Mark what each exponent touches. In −3², only the 3 is squared, so the term is −9. In (−3)², the parentheses put the sign inside, so the term is 9.
Do the division next: 8 ÷ (−2) = −4.
Add from left to right: −9 + 9 + (−4) = −4, choice A.
D, 14, is what you get by treating both powers as 9: 9 + 9 − 4. C, 4, comes from dropping the sign of the quotient.
Why it works: The first power is −9; the parenthesized power is 9. They cancel. The remaining quotient is −4. Treating both powers as 9 would give 14.
Example 2 · Medium · Factoring polynomials
Which product is a complete factorization over the integers of 6x² − x − 2?
A.(2x + 1)(3x − 2)
B.(x + 1)(6x − 2)
C.(2x + 2)(3x − 1)
D.(2x − 1)(3x + 2)
Answer: A ((2x + 1)(3x − 2))
How to solve it
Look for a common factor first. The terms 6x², −x and −2 share none, so the answer must be two binomials whose first terms multiply to 6x² and last terms multiply to −2.
Check the middle term of each choice by expanding. For A, (2x + 1)(3x − 2), the cross-products are −4x and 3x, which add to −x. The full product is 6x² − x − 2, a match.
D swaps the signs: (2x − 1)(3x + 2) gives cross-products 4x and −3x, so its middle term is +x.
B and C both expand to 6x² + 4x − 2, so their middle term is wrong, and each also contains a factor with a common 2, so neither is complete over the integers. The answer is A.
Why it works: The leading coefficients must multiply to 6 and constants to −2. The product (3x − 2)(2x + 1) has cross-terms 3x − 4x = −x, matching the middle coefficient. The near-match (3x + 2)(2x − 1) produces +x instead.
Practice expressions, polynomials and factoring questions
Here are 20 more expressions, polynomials and factoring questions from our practice bank. The set is untimed. Submit it when you are done to see the answer and a full explanation for every question. Unlike the real PERT, this practice set lets you move back and forth between questions. For mixed sets from every part of the test, use the question bank.
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Lessons on this question type
Each lesson teaches one idea with a worked example, then gives you a question to try.
Algebra and mathematical models: An equation expresses a relationship that stays true for the unknown quantity. PERT preparation should connect a verbal condition to linear or quadratic equations, inequalities, literal formulas and simultaneous equations. The goal is to find values that satisfy every original condition, including units and denominator restrictions.
The study guide’s Mathematics outline lists evaluating expressions, polynomials and dividing by monomials and binomials alongside equations and coordinate work. Our expression practice covers signed numbers and order of operations, fractions, exponents, substitution, polynomial arithmetic, factoring, polynomial division and rational expressions.
No. Coordinate work is part of PERT Mathematics, but in our practice bank slope and line questions belong to the algebra question type. Its guide is linked below under Other Mathematics question types as Algebra and mathematical models.
You can’t bring your own calculator unless an approved disability accommodation allows one; an on-screen calculator appears only on some math questions. The study guide describes it as a four-function calculator that works in the order you enter operations, so it will not apply order of operations or keep fractions exact for you.
For expression questions, know the order of operations, the exponent rules, how to multiply binomials, the difference of squares and how to factor a trinomial. These are rules you apply, and our practice questions use each of them.
Florida’s college-ready (standard) score for PERT Mathematics is 114 on the 50 to 150 scale, set by State Board of Education Rule 6A-10.0315. Our practice results cannot be converted into a PERT score, because no official conversion from correct answers to a PERT score is published.