Pre-Calculus Practice Test PDF (Free Printable 2026)

Pre-Calculus Practice Test PDF (Free Printable 2026)

Pre-calculus bridges the gap between algebra and calculus, covering the functions, trigonometry, and analytic geometry concepts you need to succeed in Calculus I and beyond. This free printable PDF is designed for students preparing for course exams, college placement tests, and standardized assessments such as the CLEP College Algebra and CLEP Pre-Calculus exams.

Print the PDF and work through problems offline, annotate formulas, and use the included answer explanations to identify weak areas before your exam date.

What Pre-Calculus Tests Cover

Functions and Graphs

The foundation of pre-calculus is a deep understanding of functions. You need to find domain and range, interpret function notation f(x), and identify even and odd functions from graphs and equations. Composition of functions f∘g and finding inverse functions f⁻¹(x) are tested both procedurally and conceptually. Transformations — vertical and horizontal shifts, reflections across axes, and stretches or compressions — apply to every function family. Piecewise functions and absolute value functions round out this foundational topic.

Polynomial and Rational Functions

Factoring is a core skill: you should master GCF factoring, difference of squares, sum and difference of cubes, and factoring by grouping. The Rational Root Theorem and synthetic division let you find zeros of higher-degree polynomials efficiently, and the Remainder and Factor Theorems connect division to root-finding. Understanding end behavior and the effect of zero multiplicity on graphs is essential.

Rational functions introduce asymptotes: vertical asymptotes occur where the denominator equals zero, horizontal asymptotes depend on comparing the degrees of numerator and denominator, and oblique asymptotes arise when the numerator's degree exceeds the denominator's by exactly one (found via polynomial division). Holes appear at common factors that cancel. Partial fraction decomposition is introduced as a precursor to calculus integration techniques.

Exponential and Logarithmic Functions

Exponential growth and decay models underpin many real-world applications. You need fluency with logarithm properties — the product rule, quotient rule, and power rule — as well as the change-of-base formula for evaluating logs in any base. Solving exponential equations by taking logarithms of both sides is a standard exam task. The natural logarithm ln and Euler's number e are central to compound interest: the standard formula A = P(1 + r/n)^(nt) and the continuous compounding formula A = Pe^(rt) both appear regularly.

Trigonometry

Trigonometry is typically the largest portion of a pre-calculus course. The unit circle — including exact values at 0°, 30°, 45°, 60°, and 90° and their equivalents in radians — must be memorized. SOHCAHTOA applies to right triangle problems, and the reciprocal identities (csc, sec, cot) and Pythagorean identities connect the six trig functions. Solving trig equations requires knowledge of reference angles and periodicity.

Graphing sine and cosine means understanding amplitude, period (2π/b), phase shift, and vertical shift from the general form y = a·sin(bx + c) + d. The Law of Sines and Law of Cosines handle oblique triangles, and the area formula A = ½ab·sin C appears in both geometry and trig contexts. Inverse trig functions (arcsin, arccos, arctan) complete the trigonometry unit.

Conic Sections

Each conic has a standard form you need to know cold. Parabolas in vertex form y = a(x – h)² + k reveal the vertex, and focus-directrix form connects geometry to the definition. Circles are defined by (x – h)² + (y – k)² = r². Ellipses have major and minor axes and two foci; hyperbolas have a transverse axis and asymptotes with slopes ±b/a. Completing the square is the key technique for converting general-form equations into standard form.

Systems and Matrices

Solving systems of equations by substitution and elimination is reviewed from algebra. Matrix operations — addition, scalar multiplication, and matrix multiplication — build toward solving linear systems. The determinant of a 2×2 matrix (ad – bc) and its 3×3 extension enable Cramer's Rule. The identity matrix and matrix inverse are introduced, with the inverse used to solve AX = B style systems.

Sequences, Series, and the Binomial Theorem

Arithmetic sequences have a constant difference d, with nth term a_n = a_1 + (n – 1)d and sum S_n = n(a_1 + a_n)/2. Geometric sequences have a constant ratio r, with nth term a_n = a_1 · r^(n–1) and sum S_n = a_1(1 – r^n)/(1 – r). An infinite geometric series converges to a_1/(1 – r) only when |r| < 1. Sigma notation compactly represents series. The Binomial Theorem and Pascal's triangle allow efficient expansion of (a + b)^n without multiplying out each factor.

Free Pre-Calculus Practice Tests Online

Printed PDF study and online practice complement each other well. Interactive practice tests give you immediate feedback on each answer and help you build the problem-solving speed required for timed exams.

Visit our pre-calculus practice test page for free online questions covering all major pre-calculus topics including functions, trigonometry, conics, and more.