PERT Math Exam Flashcards

Q: How many questions are on the PERT Math subtest?

The PERT Math subtest has 30 questions total: 25 are scored operational items that determine placement, and 5 are unscored field-test items embedded throughout. You cannot tell which questions are field-test items.

Q: What score do I need to place into college-level math?

A score of 114 or higher places you into college elective math (such as Intermediate Algebra). A score of 123 or higher qualifies you for college general-education math courses. Scores are on a 50-150 scale; below 114 results in developmental education placement.

Q: Is the PERT Math test timed?

No. The PERT is an untimed computer-adaptive test. Most students complete the math subtest in about 30 minutes, but you may take as long as you need.

Q: Can I use a calculator on the PERT Math test?

You may not bring a personal calculator. An on-screen calculator is provided within the testing software for certain items that require it, but it is not available on every question.

Q: How does the computer-adaptive format work?

The PERT is a computer-adaptive test (CAT). Your first question is medium difficulty. If you answer correctly, the next question is harder; if you answer incorrectly, the next is easier. This calibrates your placement score more efficiently than a fixed-form test.

Q: How many times can I retake the PERT?

Most Florida colleges allow students two attempts within a two-year period. A third attempt typically requires approval from a dean or testing director based on documented extenuating circumstances. Check with your specific institution for their retake policy.

Question 1

Inverse operations for one-step equations

Accepted Answer

Addition reverses subtraction and multiplication reverses division. To isolate the variable, apply the opposite operation to both sides, preserving the equality.

Question 2

Multi-step linear equation: solving order

Accepted Answer

Distribute first, combine like terms on each side, move variable terms to one side and constants to the other, then divide by the coefficient. Skipping the order leaves the variable hidden inside nested operations.

Question 3

Variables on both sides of an equation

Accepted Answer

Collect the variable terms on one side by adding or subtracting, then collect the constants on the other. Choose the side that keeps the variable's coefficient positive to avoid sign errors.

Question 4

When do you flip an inequality sign?

Accepted Answer

Flip the inequality only when multiplying or dividing both sides by a negative number. Adding, subtracting, and multiplying or dividing by a positive number leave the direction unchanged.

Question 5

Compound inequality with 'and'

Accepted Answer

An 'and' compound inequality such as -3 < x <= 5 requires both conditions to hold at once, so the solution is the overlap of the two number lines. Graph it as a connected segment between the two endpoints.

Question 6

Compound inequality with 'or'

Accepted Answer

An 'or' compound inequality is satisfied when either condition holds, so the solution is the union of two rays. Graph it as two arrows pointing outward from the two boundary points.

Question 7

Fractional coefficients in an equation

Accepted Answer

Clear fractions first by multiplying every term by the LCD of all denominators. This converts a fraction-heavy equation into an integer-coefficient equation and avoids messy fraction arithmetic.

Question 8

Checking a solution by substitution

Accepted Answer

Substitute the candidate value back into the original equation; if both sides are equal, the value is a solution. With fractions or radicals, checking catches extraneous solutions introduced by squaring or multiplying by a variable expression.

Question 9

Substitution method for systems

Accepted Answer

Solve one equation for one variable, then substitute that expression into the other equation. This collapses two equations in two unknowns into one equation in one unknown.

Question 10

Elimination method for systems

Accepted Answer

Stack the equations aligned by variable, multiply one or both by constants so a variable's coefficients are opposites, then add the equations to drop that variable. Choose the variable whose coefficients are easiest to match.

Question 11

Consistent vs inconsistent systems

Accepted Answer

A consistent system has at least one solution (one unique solution or infinitely many); an inconsistent system has none. Graphically, parallel distinct lines are inconsistent and overlapping lines give infinitely many solutions.

Question 12

Combining like terms

Accepted Answer

Only terms with the same variable raised to the same power can be combined by adding or subtracting their coefficients. 3x and 3x^2 are not like terms even though the variable letter matches.

Question 13

Distributive property

Accepted Answer

a(b + c) = ab + ac; multiply the outside factor by each inside term. With a negative outside factor, the sign flips on each inside term: -(2x - 5) = -2x + 5.

Question 14

FOIL method for multiplying binomials

Accepted Answer

First, Outer, Inner, Last: multiply two binomials term-by-term in this order, then combine like terms. For (x + 3)(x - 2), this gives x^2 - 2x + 3x - 6, which simplifies to x^2 + x - 6.

Question 15

Order of operations (PEMDAS)

Accepted Answer

Parentheses, Exponents, Multiplication and Division left to right, Addition and Subtraction left to right. Multiplication and division share the same priority, as do addition and subtraction.

Question 16

Greatest common factor (GCF) of a polynomial

Accepted Answer

Find the largest factor common to every term, including the smallest power of each shared variable, and pull it outside a parenthesis. For 6x^3 + 9x^2, the GCF is 3x^2, giving 3x^2(2x + 3). Always factor the GCF first.

Question 17

Difference of squares: a^2 - b^2

Accepted Answer

Factors as (a + b)(a - b), the sum and difference of the square roots. It only works when both terms are perfect squares and the operation between them is subtraction.

Question 18

Perfect square trinomial: a^2 + 2ab + b^2

Accepted Answer

Factors as (a + b)^2. Verify by checking that the middle term is exactly twice the product of the square roots of the first and last terms; otherwise the trinomial is not a perfect square.

Question 19

AC method for factoring trinomials

Accepted Answer

For ax^2 + bx + c, multiply a times c, find two numbers that multiply to ac and add to b, split the middle term using those numbers, then factor by grouping. The AC method rescues you when the leading coefficient is not 1.

Question 20

Factoring by grouping

Accepted Answer

Group terms in pairs, factor the GCF from each pair, then pull out the common binomial. It works whenever the two pairs share a binomial factor after the GCF is pulled from each.

Question 21

Zero product property

Accepted Answer

If the product of factors is zero, at least one factor is zero: if (x - 2)(x + 5) = 0, then x = 2 or x = -5. This is why factoring solves quadratics; set each factor equal to zero.

Question 22

Polynomial long division

Accepted Answer

Divide term-by-term from highest degree to lowest, subtract, and bring down the next term, exactly like numerical long division. If the remainder is zero, the divisor is a factor of the dividend.

Question 23

Standard form of a quadratic equation

Accepted Answer

ax^2 + bx + c = 0 with a not equal to zero. Setting the equation to zero is required before factoring or applying the quadratic formula; a non-zero right-hand side breaks both methods.

Question 24

Quadratic formula

Accepted Answer

x = (-b plus or minus the square root of (b^2 - 4ac)) divided by (2a). It solves any quadratic, even ones that do not factor over the integers. The expression under the root is the discriminant.

Question 25

Discriminant: b^2 - 4ac

Accepted Answer

Positive means two distinct real roots, zero means one repeated real root, and negative means two complex (non-real) roots. The sign tells you the shape of the x-intercepts before you solve.

Question 26

Square root method for quadratics

Accepted Answer

When a quadratic has the form x^2 = k, take the square root of both sides: x = plus or minus the square root of k. Use it on quadratics with no linear term; it is faster than the full quadratic formula for that shape.

Question 27

Solving a quadratic by factoring

Accepted Answer

Move everything to one side so the expression equals zero, factor, then apply the zero product property to each factor. If you cannot find integer factors, switch to the quadratic formula.

Question 28

Vertex form of a parabola

Accepted Answer

y = a(x - h)^2 + k has its vertex at (h, k). The sign of a controls whether the parabola opens upward (a > 0) or downward (a < 0).

Question 29

Simplifying a rational expression

Accepted Answer

Factor numerator and denominator completely, then cancel factors that appear in both. You can only cancel common factors, never common terms; (x + 2)/x is not simplified by canceling the 2s.

Question 30

Common denominator for adding rational expressions

Accepted Answer

Find the LCD of all denominators, rewrite each fraction with that LCD, then add numerators and keep the denominator. Multiplying denominators always gives a common denominator, but using the LCD keeps the arithmetic smaller.

Question 31

Multiplying rational expressions

Accepted Answer

Factor everything first, multiply numerators together and denominators together, then cancel common factors across the fraction bar. Always reduce before multiplying to avoid huge coefficients.

Question 32

Dividing rational expressions

Accepted Answer

Keep the first fraction, change division to multiplication, and flip the second fraction (take its reciprocal). Then multiply and simplify as usual.

Question 33

Excluded values in a rational expression

Accepted Answer

Any value that makes a denominator zero is excluded from the domain, even if it would cancel from the numerator. State these restrictions before simplifying, since canceling can hide them.

Question 34

Solving a rational equation

Accepted Answer

Multiply both sides by the LCD of all denominators to clear the fractions, then solve the resulting polynomial equation. Always check for extraneous solutions that make an original denominator zero.

Question 35

Product rule for exponents

Accepted Answer

a^m times a^n equals a^(m + n); add exponents when multiplying like bases. The bases must match; do not add exponents across different bases.

Question 36

Quotient rule for exponents

Accepted Answer

a^m divided by a^n equals a^(m - n); subtract exponents when dividing like bases. A negative result signals the answer belongs in the denominator as a positive exponent.

Question 37

Power of a power: (a^m)^n

Accepted Answer

Multiply the exponents: (a^m)^n equals a^(mn). This differs from the product rule, which adds exponents of like bases being multiplied together.

Question 38

Negative exponent

Accepted Answer

a^(-n) equals 1 / a^n. A negative exponent signals a reciprocal, not a negative number; 2^(-3) equals 1/8, not -8.

Question 39

Fractional exponent: a^(1/n)

Accepted Answer

a^(1/n) equals the n-th root of a; the denominator of the exponent becomes the index of the root. More generally, a^(m/n) equals the m-th power of the n-th root of a.

Question 40

Simplifying a radical with perfect-square factors

Accepted Answer

Factor out the largest perfect square from the radicand. The square root of 72 becomes the square root of (36 times 2), which equals 6 times the square root of 2. Stop only when the remaining radicand has no perfect-square factor.

Question 41

Rationalizing a denominator

Accepted Answer

Multiply numerator and denominator by the radical in the denominator to remove it from the bottom: 5 over the square root of 3 becomes (5 times the square root of 3) over 3. Use conjugate pairs when the denominator is a sum or difference of radicals.

Question 42

Slope-intercept form

Accepted Answer

y = mx + b, where m is the slope and b is the y-intercept. Reading the form directly tells you the line's steepness and where it crosses the y-axis.

Question 43

Slope formula from two points

Accepted Answer

m = (y2 - y1) / (x2 - x1). Keep the point order consistent in numerator and denominator; swapping the order of one point but not the other flips the sign of the slope.

Question 44

Parallel vs perpendicular slopes

Accepted Answer

Parallel lines have equal slopes. Perpendicular lines have negative reciprocal slopes: m1 times m2 equals -1, so a line with slope 2 is perpendicular to a line with slope -1/2.

Question 45

Distance formula

Accepted Answer

d equals the square root of ((x2 - x1)^2 + (y2 - y1)^2). It is the Pythagorean theorem applied to the horizontal and vertical legs between two points on the plane.

Question 46

Midpoint formula

Accepted Answer

Midpoint equals ((x1 + x2)/2, (y1 + y2)/2). It averages the x-coordinates and the y-coordinates separately to find the point exactly halfway between two endpoints.

Question 47

Pythagorean theorem

Accepted Answer

For a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2. It underpins the distance formula and only applies when the triangle has a 90-degree angle.

Question 48

Percent change: increase and decrease

Accepted Answer

Percent change equals (new - old) divided by the absolute value of old, times 100. The denominator is always the original amount, not the new amount; confusing the two is the most common percent error.

Question 49

Translating a word problem into an equation

Accepted Answer

Identify what x represents, write the relationship in English first, then translate keywords: 'of' means multiply, 'is' means equals, 'per' means divide, and 'less than' reverses the subtraction order.

Question 50

Direct variation: y = kx

Accepted Answer

When y varies directly with x, the ratio y/x is a constant k. Doubling x doubles y, tripling x triples y. The graph is a straight line through the origin with slope k.

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