Prepare for the PERT Math section by mastering the algebra skills that drive many placement questions, including linear equations, inequalities, slope, functions, systems, exponents, polynomials, factoring, and quadratics.
Quick Answer
PERT Math is heavily focused on algebraic reasoning.
You should be comfortable with:
- Simplifying algebraic expressions
- Solving linear equations
- Solving inequalities
- Working with ratios and proportions
- Understanding slope
- Writing and interpreting linear equations
- Evaluating functions
- Solving systems of equations
- Applying exponent rules
- Working with polynomials
- Factoring
- Solving quadratic equations
- Interpreting algebra in word problems
Florida currently describes the PERT as an untimed, computer-adaptive placement test.
Each subject area contains:
- 25 operational questions used for the placement score
- 5 field-test questions
for 30 questions per section.
The statewide Mathematics readiness standard is currently 114.
The PERT is not technically a pass/fail test—your score is used to help determine appropriate course placement.
Why Algebra Matters So Much on PERT Math
Many students prepare for PERT Math by reviewing random topics:
- Fractions
- Geometry
- Percentages
- Algebra
- Probability
That is better than no review, but it is inefficient.
A large portion of the skills needed for college-level math readiness depend on algebra.
If you can confidently:
- Manipulate expressions
- Solve equations
- Understand functions
- Read linear graphs
- Factor expressions
you can solve many seemingly different PERT questions.
Start With Algebraic Expressions
An algebraic expression contains:
- Numbers
- Variables
- Operations
Example:
4x + 7
This is an expression.
It does not contain an equals sign.
Expression vs. Equation
This distinction matters.
Expression
4x + 7
You may be asked to simplify it.
Equation
4x + 7 = 19
You may be asked to solve for x.
An equation states that two quantities are equal.
Combining Like Terms
Like terms have the same variable raised to the same power.
Example:
3x + 5x
These are like terms.
3x + 5x = 8x
But:
3x + 5x²
cannot be combined because x and x² are different terms.
Example
Simplify:
4x + 7 + 3x – 2
Combine x terms:
4x + 3x = 7x
Combine constants:
7 – 2 = 5
Answer:
7x + 5
Distributive Property
The distributive property is essential.
Formula:
a(b + c) = ab + ac
Example:
3(x + 4)
Distribute 3:
3x + 12
Negative Distribution Trap
Simplify:
-2(x – 5)
Multiply -2 by both terms:
-2x + 10
The second term becomes positive because:
-2 × -5 = +10
Solving Linear Equations
A linear equation often has the variable raised only to the first power.
Example:
5x – 15 = 20
The goal is to isolate x.
Add 15:
5x = 35
Divide by 5:
x = 7
The Balance Principle
Whatever you do to one side of an equation, do to the other.
Think of an equation as a balanced scale.
If you subtract 8 from one side, subtract 8 from the other.
Multi-Step Equation Example
Solve:
3(x + 2) = 18
Distribute:
3x + 6 = 18
Subtract 6:
3x = 12
Divide by 3:
x = 4
Variables on Both Sides
Solve:
5x + 3 = 2x + 18
Subtract 2x from both sides:
3x + 3 = 18
Subtract 3:
3x = 15
Divide:
x = 5
Check Your Answer
Substitute x = 5 into the original equation:
Left:
5(5) + 3 = 28
Right:
2(5) + 18 = 28
Both sides match.
Correct.
Solving Inequalities
An inequality compares quantities using:
- <
- ≥
- ≤
Example:
x + 4 > 10
Subtract 4:
x > 6
The Most Important Inequality Rule
When multiplying or dividing both sides by a negative number, reverse the inequality sign.
Example:
-2x > 8
Divide by -2:
x < -4
The sign changes from:
to:
<
This is one of the most common algebra mistakes.
Ratios and Proportions
A proportion states that two ratios are equal.
Example:
3/5 = x/20
Cross multiply:
5x = 60
x = 12
Ratio Word Problem
If 4 notebooks cost $10, how much would 10 notebooks cost at the same rate?
Set up:
4 / 10 = 10 / x
Or find unit rate:
$10 ÷ 4 = $2.50 each
10 × 2.50 = $25
Percent Problems
The relationship:
Percent × Whole = Part
Example:
What is 18% of 250?
0.18 × 250 = 45
Finding the Percent
45 is what percent of 180?
45 / 180 = 0.25
0.25 = 25%
Percent Increase
A price increases from $80 to $100.
Increase:
100 – 80 = 20
Divide by original:
20 / 80 = 0.25
Percent increase:
25%
Always divide the change by the original amount.
Coordinate Plane Basics
A point is written:
(x, y)
Example:
(3, -2)
means:
- Move 3 units right
- Move 2 units down
The x-coordinate comes first.
Slope
Slope measures the rate of change of a line.
Formula:
m = (y₂ – y₁) / (x₂ – x₁)
Slope Example
Find the slope through:
(2, 3)
and:
(6, 11)
m = (11 – 3) / (6 – 2)
m = 8 / 4
m = 2
Positive vs. Negative Slope
Positive slope
Line rises from left to right.
Negative slope
Line falls from left to right.
Zero slope
Horizontal line.
Undefined slope
Vertical line.
Slope-Intercept Form
One of the most useful algebra forms is:
y = mx + b
where:
- m = slope
- b = y-intercept
Example
Equation:
y = 3x – 5
Slope:
3
Y-intercept:
-5
Finding the Y-Intercept
Suppose:
y = 2x + 7
Set x = 0:
y = 7
The y-intercept is:
(0, 7)
Writing an Equation From Slope and Intercept
Slope:
4
Y-intercept:
-3
Use:
y = mx + b
Answer:
y = 4x – 3
Finding an Equation From a Point and Slope
Suppose a line has slope 2 and passes through:
(1, 5)
Start with:
y = 2x + b
Substitute:
5 = 2(1) + b
5 = 2 + b
b = 3
Equation:
y = 2x + 3
Parallel Lines
Parallel lines have:
The same slope
Example:
y = 3x + 2
and:
y = 3x – 7
These are parallel.
Perpendicular Lines
Perpendicular lines have slopes that are negative reciprocals.
Example:
Slope = 2
Perpendicular slope:
-1/2
What Is a Function?
A function assigns each input exactly one output.
Function notation:
f(x)
does not mean:
f × x
It means:
“the output of function f when the input is x.”
Evaluating a Function
Suppose:
f(x) = 2x + 5
Find:
f(4)
Substitute x = 4:
f(4) = 2(4) + 5
= 8 + 5
= 13
Function Table
Suppose:
f(x) = 3x – 1
| x | f(x) |
|---|---|
| 0 | -1 |
| 1 | 2 |
| 2 | 5 |
| 3 | 8 |
Notice the output increases by 3 every time x increases by 1.
That rate of change is the slope.
Linear vs. Nonlinear Functions
A linear function has a constant rate of change.
Example:
y = 2x + 1
A nonlinear function does not have constant slope across its graph.
Example:
y = x²
Systems of Equations
A system contains two or more equations.
The solution is the point that satisfies all equations.
Example:
x + y = 10
x – y = 4
Add equations:
2x = 14
x = 7
Substitute:
7 + y = 10
y = 3
Solution:
(7, 3)
Graphical Meaning of a System
When two lines intersect:
The intersection point is the solution.
One intersection
One solution.
Parallel lines
No solution.
Same line
Infinitely many solutions.
Exponent Rules
These are high-value algebra skills.
Product Rule
When multiplying powers with the same base:
xᵃ × xᵇ = xᵃ⁺ᵇ
Example:
x³ × x⁴ = x⁷
Quotient Rule
When dividing powers with the same base:
xᵃ / xᵇ = xᵃ⁻ᵇ
Example:
x⁷ / x³ = x⁴
Power Rule
(xᵃ)ᵇ = xᵃᵇ
Example:
(x³)² = x⁶
Do not add the exponents here.
Multiply them.
Zero Exponent
For nonzero x:
x⁰ = 1
Example:
7⁰ = 1
Negative Exponents
x⁻² = 1/x²
A negative exponent does not make the value automatically negative.
It indicates a reciprocal.
Polynomials
A polynomial may contain several terms.
Example:
3x² + 5x – 7
Terms:
- 3x²
- 5x
- -7
Multiplying Monomials
Example:
(3x²)(4x³)
Multiply coefficients:
3 × 4 = 12
Add exponents:
x² × x³ = x⁵
Answer:
12x⁵
Multiplying Binomials
Example:
(x + 3)(x + 5)
Multiply:
x² + 5x + 3x + 15
Combine:
x² + 8x + 15
Factoring
Factoring reverses multiplication.
Example:
x² + 8x + 15
Find two numbers that:
Multiply to 15
and add to 8.
Those numbers are:
3 and 5
So:
(x + 3)(x + 5)
Difference of Squares
Memorize:
a² – b² = (a – b)(a + b)
Example:
x² – 25
= x² – 5²
= (x – 5)(x + 5)
Quadratic Equations
A quadratic usually contains x².
Example:
x² – 5x + 6 = 0
Factor:
(x – 2)(x – 3) = 0
Therefore:
x = 2 or 3
Zero Product Property
If:
ab = 0
then:
a = 0
or:
b = 0
That is why factoring solves many quadratics.
Quadratic Formula
For:
ax² + bx + c = 0
the quadratic formula is:
x = (-b ± √(b² – 4ac)) / 2a
This becomes especially useful when the quadratic does not factor easily.
Order of Operations
Use:
PEMDAS
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
Remember:
Multiplication and division have the same priority.
Work left to right.
Addition and subtraction also have the same priority.
Example
Evaluate:
4 + 3(2²)
Exponent first:
2² = 4
Multiply:
3 × 4 = 12
Add:
4 + 12 = 16
Rational Expressions
A rational expression contains a polynomial in a denominator.
Example:
(x + 2)/(x – 3)
The denominator cannot equal zero.
So:
x ≠ 3
Simplifying Rational Expressions
Example:
(x² – 9)/(x – 3)
Factor numerator:
(x – 3)(x + 3)
Cancel common factor:
Answer:
x + 3
with restriction:
x ≠ 3
That restriction still matters because the original expression was undefined at x = 3.
Algebra Word Problems
Many placement questions hide algebra inside real situations.
Use this process:
Step 1
Identify the unknown.
Step 2
Choose a variable.
Step 3
Translate the relationships into an equation.
Step 4
Solve.
Step 5
Check whether the result answers the actual question.
Word Problem Example
A gym charges a $25 registration fee plus $15 per month.
Total cost after x months:
C = 15x + 25
What does 15 represent?
Monthly rate
What does 25 represent?
Starting/registration fee
This is the same structure as:
y = mx + b
PERT Math Common Mistakes
Mistake 1: Combining Unlike Terms
3x + 4x² cannot become 7x³.
Mistake 2: Forgetting to Distribute a Negative
-2(x – 3) = -2x + 6
Mistake 3: Not Reversing an Inequality
Divide by a negative → reverse the sign.
Mistake 4: Confusing Slope With Y-Intercept
In y = mx + b:
m = slope
b = y-intercept
Mistake 5: Treating f(x) Like Multiplication
f(4) means substitute 4 into the function.
Mistake 6: Adding Exponents During a Power Rule
(x³)² = x⁶, not x⁵.
Mistake 7: Forgetting Both Quadratic Solutions
A factored quadratic can produce two values.
Mistake 8: Ignoring Denominator Restrictions
Never allow a denominator to equal zero.
A Reliable PERT Math Strategy
Because PERT is untimed, accuracy matters more than rushing. Florida describes the test as computer-adaptive, meaning your responses are used to select questions appropriate to your demonstrated skill level.
Use this sequence:
1. Identify the Algebra Topic
Equation?
Function?
Slope?
Factoring?
Exponent?
2. Write the Rule You Need
Do not mentally juggle several operations.
3. Work One Step at a Time
Especially with negative numbers and fractions.
4. Substitute Back When Possible
Check equations.
5. Estimate
Does the answer make sense?
6. Avoid Changing Correct Work
Do not second-guess yourself without a mathematical reason.
What Score Do You Need on PERT Math?
Florida’s current statewide college-readiness standard for PERT Mathematics is:
114
The current standards listed by the Florida Department of Education are:
- Reading: 106
- Writing: 103
- Mathematics: 114
However, specific course placement can depend on the institution and program.
For example, some colleges distinguish between the score needed for general readiness and a higher score used for placement into College Algebra or another particular course.
Always check the current placement table at the college you plan to attend.
Is the PERT Pass or Fail?
Technically:
No.
Florida describes PERT as a placement test rather than a pass/fail exam.
Your score helps determine whether your skills demonstrate readiness for particular college coursework or whether additional preparation may be recommended.
That said, students commonly use the word “pass” when they mean:
“Reach the score I need for my intended placement.”
Frequently Asked Questions
What math should I study for the PERT?
Prioritize algebraic skills including equations, inequalities, expressions, slope, linear functions, systems, exponents, polynomials, factoring, and quadratics, along with quantitative and applied problem-solving skills.
How many questions are on PERT Math?
Florida states that the PERT contains 25 operational questions used for scoring plus five field-test questions in each subject area, for 30 questions per section.
Is the PERT timed?
No. The Florida Department of Education describes PERT as untimed.
What PERT Math score shows college readiness?
The current statewide Mathematics readiness standard is 114.
Is PERT Math adaptive?
Yes. PERT is a computer-adaptive test.
What’s the most important algebra formula for PERT?
There is no single formula that covers everything, but students should be especially comfortable with slope, slope-intercept form, exponent rules, proportions, and the quadratic formula.
Do I need to know quadratics for PERT Math?
Quadratic expressions, factoring, and related algebra skills are appropriate topics to review when preparing for college-level mathematics placement.
Key Takeaways
- PERT Math is strongly algebra-focused.
- Know how to simplify expressions and solve linear equations.
- Reverse an inequality when multiplying or dividing by a negative.
- Slope formula: (y₂ – y₁)/(x₂ – x₁).
- Slope-intercept form: y = mx + b.
- Be able to evaluate functions.
- Understand systems of equations.
- Memorize core exponent rules.
- Learn factoring patterns such as difference of squares.
- Know how to solve basic quadratics.
- Translate word problems into equations rather than guessing.
- PERT is untimed and adaptive.
- Florida’s current statewide Mathematics readiness standard is 114.
Test Your PERT Math Skills
The fastest way to improve your PERT Math placement is to stop treating algebra as dozens of disconnected rules.
Most questions reduce to a few core skills:
Simplify → Translate → Solve → Check
Once those become automatic, unfamiliar questions become much easier.
Take our full PERT Math Practice Test to practice equations, functions, slope, factoring, quadratics, geometry, quantitative reasoning, and realistic PERT-style problem solving.
