Maths Problems, Questions and Online Tests

Free online maths problems, questions and self tests on precalculus topics. Answers and detailed solutions are provided.

Maths Tests Practice

• Free ACT Maths Test Practice Questions with Answers. 60 Maths questions, with answers, similar to the questions in the ACT maths test. The answers are at the bottom of the page.
• Free SAT Maths Test Practice Questions with Answers - sample 1. A set of 25 Maths questions, with answers, similar to the questions in the SAT maths test. The answers are at the bottom of the page.

Maths Problems and Questions

• Solve maths problems (1) and the Solutions are provided.
• Numerical, Graphical and Analytical Maths Problem Solving (1). The problem of maximizing the area of a rectangular garden is examined using three approaches: numerical, graphical and analytical. A discussion to compare the three methods is also presented.
• Linear Functions Problems with Solutions A set of problems involving linear functions, along with detailed solutions, are presented. The problems are designed with emphasis on the meaning of the slope and the y intercept.
• Maths Problems and Solutions on Integers. Problems related to integer numbers are presented along with their solutions.
• Mixture Problems With Solutions. Mixture problems and their solutions are presented along with their solutions. Percentages are also used to solve these types of problems.
• Polynomial Problems with Solutions. Polynomial problems with detailed solutions.
• Write Rational Functions - Problems With Solutions. Write rational functions given their characteristics such as vertical asymptotes, horizontal asymptote, x intercepts, hole.
• Rate, Time Distance Problems With Solutions. The relationship between distance, rate (speed) and time Distance = time * rate is used to solve uniform motion problems. Detailed solutions to the problems are provided.
• Work Rate Problems with Solutions. A set of problems related to work and rate of work is presented with detailed solutions.
• Projectile Problems with Solutions. A tutorial on solving projectile problems. Detailed solutions to the problems are provided.
• Maths Questions With Answers (1) and detailed explanations and solutions of these questions are also provided.
• Maths Questions With Answers (2) and Solutions and explanations. A set of multiple choice maths questions and their answers are presented. These questions have been designed to test for deep understanding of maths concepts.
• Maths Questions With Answers (3). Maths questions on logarithmic and exponential expressions and equations, with answers.
• Maths Questions With Answers (4). Maths questions on solving equations and inequalities with absolute value. Equations with complex solutions are also included.
• Maths Questions With Answers (5). Maths questions on circles and distance between two points.
• Maths Questions With Answers (6). Maths questions on slopes and equations of lines.
• Maths Questions With Answers (7). Maths questions on how to find the domain of a function.
• Maths Questions With Answers (8). Maths questions on simplifying polynomials.
• Maths Questions With Answers (9). Maths questions on synthetic division of polynomials.
• Maths Questions With Answers (10). Maths questions on degree and multiplicity of zeros of polynomials.
• Maths Questions With Answers (11). Maths questions on factoring polynomials.
• Maths Questions With Answers (12). Maths questions on decomposition into partial fractions.
• Maths Questions With Answers (13): Quadratic Functions. Maths Questions with answers on finding maximum and minimum values, vertex, axis of symmetry, interval of increase and decrease and the range of quadratic functions.
• Percent Maths Problems Several word problems on percentage with detailed solutions are presented.
• Percent Maths Questions Several questions on percentages, with detailed solutions are presented.
• Solve Slope Problems and the Solutions are provided.
• Equations of Lines: Problems with Solutions
• Solve Exponential and Logarithm Problems and the Solutions are provided.
• Solve Distance Problems with detailed solutions included provided.
• Questions on Functions with Solutions.
• Mathematical Induction - Problems With Solutions. Several problems, with detailed solutions, on mathematical induction are presented.

Vectors

• Vector Addition and Scalar Multiplication. A tutorial on how to find components of a vector , add two vectors, multiply a vector by a scalar. Examples, solutions, exercises and answers are included.
• Dot Product of Two Vectors and Applications. A tutorial on the dot product of two vectors and how it is applied to find angle between two vectors. Find magnitude and direction of vectors.

Sequences

• Geometric Sequences Problems with Solutions. Problems and exercises involving geometric sequences, along with detailed solutions and answers, are presented.
• Arithmetic Sequences Problems with Solutions. Problems and exercises involving arithmetic sequences, along with detailed solutions and answers.

Algebra, Equations and Inequalities

• Algebra Problems and their detailed solutions: You have the choice between a set of questions with their answers or a set of 50 questions in the applet to self test you background on algebra.
• Solve Quadratic Equations With Rational Expressions - Problems and detailed solutions provided. Solve a set of problems related to quadratic and rational equations. You have the choice between a set of 10 problems and 50 questions from an applet.
• Solving Linear Equations - Questions. Multiple choice questions on solving linear equations. Answers included.
• Absolute Value Equations And Inequalities questions with detailed solutions and explanations.
• Polynomial and Rational Inequalities, questions and their answers: Questions on solving Polynomial and Rational Inequalities are presented. These may be used as a self test.

Functions, Domain, Composition and Inverse

• Find the Domain of a Function - Problems with detailed solutions: A set of 10 problems, on finding the domain of a function, with their solutions are presented.
• Composition of Functions Questions with Solutions.
• Find Inverse Functions - Questions and their detailed solutions. Questions on how to find the inverse of linear, quadratic with restricted domain, logarithmic, exponential and rational, together with detailed solutions, are presented.
• Questions on one to one Functions. Several questions with detailed solutions as well as exercises with answers on how to prove that a given function is a one to one function.

Logarithms

• Solve Exponential and Logarithmic Equations, examples with detailed solutions and explanations.

Graphs of Functions

• Graphs of Functions - Questions and their answers: Given the equation of a function, identify a possible graph (among 4) corresponding to the given function. Algebraic functions including linear, square root, quadratic and absolute value functions are included.
• Graphs of Polynomial Functions - Questions with answers: Questions and their answers on graphs of polynomial functions are presented. These questions may be used as a self self test.
• Graphs of Rational Functions - Questions with answers: Questions, and their answers, on identifying graphs of rational functions are presented.
• Graphs of Logarithmic and Exponential Functions - Questions with answers: Questions, and their answers, on the graphs of Logarithmic and Exponential functions are presented. These may be used as a self test.

Trigonometry

• Solve Trigonometric Equations - Problems with answers: 10 problems, with their answers, on solving trigonometric equations are presented here and more in the applet below.
• Graphs Trigonometric Functions - Questions with answers: A set of questions, with their answers, on identifying the graphs of trigonometric functions sin(x), cos(x), tan(x), sec(x), csc(x), cot(x) are presented. These may be used as a self test on the graphs of trigonometric functions.
• Find Values Of Trigonometric Functions - Questions with answers. A set of questions, with their answers, on finding exact values of trigonometric functions sin(x), cos(x), tan(x), sec(x), csc(x), cot(x) are presented.

Unit Converion

• Convert Units of Lengths. A set of questions on how to convert from one unit of length to another: meters, kilometers, millimeters, centimeters, decimeters, feet, inches, yards, miles, nanometers and micrometers. Both metric and imperial units are used.
• Convert Units of Velocity. Questions, with answers, on how to convert from one unit of velocity (speed) to another. For the lengths, both metric and imperial units are used.

Complex Numbers

• Questions on Complex Numbers with answers. The questions are about adding, multiplying and dividing complex as well as finding the complex conjugate.
• Complex Numbers in Exponential Form. Examples and questions with detailed solutions.
• Complex Numbers in Polar Form. Examples and questions with detailed solutions.
• De Moivre's Theorem Power and Root. Examples and questions with detailed solutions on using De Moivre's theorem to find powers and roots of complex numbers. .
• Free Practice for SAT, ACT Maths tests
• Free Practice for GAMT Maths tests
• Free GRE Quantitative for Practice