5165 · Syllabus & Exam Outline 2026
Praxis (5165): Mathematics
In short
The Praxis (5165) Mathematics exam has 66 selected-response questions in 180 minutes, with passing scores that vary by state (commonly around 159). It covers number and quantity and algebra, functions and calculus, geometry, and statistics and probability. An on-screen graphing calculator is provided. Free practice questions and a full study plan are below.
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- Questions
- 66 selected-response questions
- Time limit
- 180 minutes
- Cost
- $130
- Format
- selected-response · numeric entry
- Delivery
- Computer-delivered (at an authorized Praxis testing center or at home)
- Calculator
- On-screen graphing calculator
- Prep time
- ~90 hours
Exam overview
The Praxis Mathematics (5165) exam is designed to assess the mathematical knowledge and competencies required of a beginning secondary school math teacher. The test goes beyond basic calculation, evaluating a candidate's deep understanding of mathematical concepts and their ability to apply this knowledge in instructional settings. Approximately one-quarter of the test questions explicitly measure how well you can navigate the 'Tasks of Teaching Mathematics,' which includes evaluating student work, validating mathematical models, and diagnosing common misconceptions. The curriculum is spread across four primary domains: Number & Quantity and Algebra, Functions and Calculus, Geometry, and Statistics & Probability. To streamline your preparation, Only Ever maps every domain to 15-minute study topics, helping you master everything from complex plane transformations to probability distributions efficiently and effectively.
Exam domains & weighting
Each domain's share of the exam — study deepest where the weight is highest. Open one for how to study it and its objectives.
How to study this domain
Focus on building a strong foundation in real, rational, and complex number systems. Practice factoring polynomials, solving quadratic equations, and working with radicals. Ensure you can seamlessly transition between different forms of algebraic equations and inequalities.
Key objectives
- Structure of the Real Number System
- Ratios, Rates, and Percents
- Radicals and Rational Exponents
- Quantitative Reasoning and Units
- Complex Number System
- Algebraic Expressions and Polynomials
- Creating Equations and Inequalities
- Solving Linear Equations and Inequalities
- Solving Quadratic Equations
- Solving Systems of Equations
- Polynomial Functions and Zeros
- Rational and Radical Equations
Readiness self-check
Tick off everything you can confidently explain. Anything left unchecked is your study list — tap “Review” to jump straight into that domain.
Quick reference
Provided Mathematical Notation
Standard notation conventions provided on the official test reference screen.
gcd(m, n)
Greatest common divisor of two integers m and n
lcm(m, n)
Least common multiple of two integers m and n
[x]
Greatest integer m such that m is less than or equal to x
m ≡ k (mod n)
m and k are congruent modulo n (they have the same remainder when divided by n)
f^-1
Inverse of an invertible function f (not to be read as 1/f)
On-Screen Reference Formulas: Trigonometry & Calculus
Select formulas available to candidates during the test.
Law of Sines
(sin A) / a = (sin B) / b = (sin C) / c
Law of Cosines
c² = a² + b² - 2ab(cos C)
Differentiation Product Rule
(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)
Differentiation Chain Rule
(f(g(x)))' = f'(g(x))g'(x)
Differentiation Quotient Rule
(f(x)/g(x))' = [f'(x)g(x) - f(x)g'(x)] / (g(x))²
On-Screen Reference Formulas: Geometry Volume & Surface Area
Volume and surface area formulas provided to candidates.
Volume of a Sphere
V = (4/3)πr³
Volume of a Right Circular Cone
V = (1/3)πr²h
Volume of a Pyramid
V = (1/3)Bh
Surface Area of a Sphere
A = 4πr²
Surface Area of a Right Circular Cone
A = πrs + πr²
Frequently asked questions
Good to know
- An on-screen graphing calculator is provided for the computer-delivered test. Candidates should download the trial version from ETS and become familiar with its functionality prior to test day.
- A reference sheet containing specific mathematical notations, definitions, and formulas is directly accessible via the test's Help screen.
- Approximately 25% of the selected-response questions explicitly evaluate 'Tasks of Teaching Mathematics'—assessing content knowledge within grading, student interaction, and instructional design scenarios.
- The exam may contain pretest questions that are unscored and do not count toward your final grade.
Reading isn’t remembering.
Most Praxis math prep either drills mechanics without the teaching frame or scatters topics so you cannot see how the exam weights algebra, geometry, and stats.
We translate the official ETS syllabus into a full learning map with topic-sized notes, consistent coverage of instructional scenarios, and retention-focused structure.