Algebra Practice Quizzes





Order of Operation Algebra Problems

Problems with evaluations of expressions using the correct order of operations.
Order of Operation Algebra Practice


Basic Rules of Exponents

- Multiplication of two terms with the same base.
- Exponents expressions raised to a power.
Exponents: Basic Rules Practice


Polynomials Problems

This quiz has problems with evaluation, addition and subtraction of monomials and polynomials.
Polynomials Practice


Polynomials Multiplication Problems

- Problems with multiplications of polynomials.
- Evaluations of products of polynomials.
Polynomials Multiplication Practice


Graphs of Linear Equations Problems

The problems of this quiz present you with a linear graph and ask you to construct the correct linear function.
Graphs of Linear Equations Practice


Graphs of Radical Functions Problems

The problems of this quiz present you with a graph of a radical function and ask you to construct the correct radical function.
Graphs of Radical Functions Practice


X-intercepts and Y-intercepts Problems

- an x-intercept is a point on the graph where y is zero, and
- a y-intercept is a point on the graph where x is zero.
X-intercepts and Y-intercepts Quiz


Midpoint Formula Problems

The midpoint of two points, (xa, ya) and (xb, yb) is the point M with the following coordinates:


Midpoint Formula Practice


Operation with Radicals

- Problems with radicals simplification,
- Problems with addition and subtraction of radicals,
- Problems with multiplication and division of expressions with radicals.
Operation with Radicals Practice


Factoring Polynomials Problems

Factor polynomials by:
- applying the difference of squares formula,
- applying the square of a sum formula,
- applying the square of a difference formula,
- applying the distributive property.
Factoring Polynomials Practice


Slope of a Straight Line Practice

- Problems with the slope of a line given in graphical form,
- Problems with the slope of a line given in analytical form.
Slope of a Straight Line Practice


Equations with Absolute Value Practice

Steps to solve equations with absolute values:
1: Isolate the absolute value expression,
2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation,
3:Solve for the unknown in both equations.
Equations with Absolute Value Problems


Negative Exponents Problems

Problems with operations of expressions with negative exponents.
Negative Exponents Practice


Linear Equations Problems

Problems with linear inequalities.
- Simplify the expressions on each side of the equation, if necessary,
- Get all variable terms on one side and all numbers on the other side,
- Isolate the variable term to find the solution of the equation,
- Check your solution by substituting the value of the variable in the original equation.
Linear Equations Practice


Literal Equations Problems

A literal equation is an equation where variables represent known values. Literal equations allow use to represent things like distance, time, interest, and slope as variables in an equation.
Literal Equations Practice


Equations with Radicals Problems

Steps to solve an equation with radicals:
1. Isolate the radical expression involving the variable on one side of the equation. If more than one radical expression involves the variable, then isolate one of them.
2. Raise both sides of the equation to the index of the radical.
3. If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.
Equations with Radicals Practice


Solving Inequalities Problems

Problems with linear inequalities.
Solving Inequalities Practice


Circle Equations Problems

- Problems that ask you to find the equation of a circle given its radius and its center.
- Problems that ask you to find the radius and center of a circle defined by a specific equation.
- Problems that ask you to find the intersection points of two circles.
Circle Equations Practice


Domains and Ranges of Functions Problems

The domain of a function is the complete set of possible values of the independent variable.
The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.
Domains and Ranges of Functions Practice


Absolute Value Inequalities Problems

1. Isolate the absolute value expression on the left side of the inequality.
2. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.
3. Remove the absolute value operators by setting up a compound inequality. The type of inequality sign in the problem will tell us the way we set up the compound inequality.
4. Solve the inequalities.
Absolute Value Inequalities Practice


Factoring Quadratic Expressions Problems

A trinomial in the form x2 + ax + b can be factored to equal (x + m)(x + n) when the product of m and n equals b and the sum of m + n equals a.
1: Common factor if you can.
2: Find two integers m and n, that their product is equal to b and their sum is equal to a.
Step 3: Substitute the numbers m and n directly into the expression (x + m)(x + n).
Factoring Quadratic Expressions Practice


Factoring Formulas Problems

Difference of squares formula: x2 - y2 = (x - y)(x + y).
Difference of cubes formula: x3 - y3 = (x - y)(x2 + xy + y2).
Sum of cubes formula: x3 + y3 = (x + y)(x2 - xy + y2).
Factoring Formulas Practice


Functions Translations and Reflections Problems

Translations of graphs:
Translate a graph m (m > 0) units to the right, by replacing x with x - m.
Translate a graph m (m > 0) units to the left, by replacing x with x + m.
Translate a graph m (m > 0) units up, by replacing y with y - m.
Translate a graph m (m > 0) units down, by replacing y with y + m.

Reflections of graphs:
Reflect a graph in the y axis by replacing x with -x.
Reflect a graph in the x axis by replacing y with -y.
Reflect a graph in the x = y line by replacing x with y and y with x.
Functions Translations and Reflections Practice


Quadratic Formula

The Quadratic Formula:
For , the values of x which are the solutions of the equation are given by:

Quadratic Formula Practice


Quadratic Inequalities

1. Solve the inequality as though it were an equation. The real solutions to the equation are boundary points for the solution to the inequality.
2. Test points from each of the regions created by the boundary points.
3. If a test point satisfies the original inequality, then the specific region is part of the solution.
4. Represent the solution in graphic form and in solution set form.
Quadratic Inequalities Practice


The Remainder Theorem

The remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r). In particular, x-r is a divisor of f(x) if and only if f(r)=0.
The Remainder Theorem Practice


Sequences Quiz

- arithmetic sequences.
- geometric sequences.
- problems to find specific terms of different sequences.
Sequences Practice


Series Problems

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.


Geometric series:
For and r different than 1, the sum of the first n terms of a geometric series is:

Series Practice


Systems of Non-Linear Equations Problems

Find the points of intersection between different curves like lines, parabolae, circles, ellipses. Also solve symmetrical non-linear systems.
Systems of Non-Linear Equations Practice


Quadratic Vertex Problems

The vertex of a quadratic equation is the highest or lowest point of the graph of that equation.
If you want to find the vertex of a quadratic equation, you can either use the vertex formula, or complete the square.
Quadratic Vertex Practice








Complex Numbers Quiz

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. No real number satisfies this equation, so i is called an imaginary number.
The following quiz has problems that require knowledge of complex numbers operations.
Complex Numbers Quiz


Determinants Quiz

In algebra, the determinant is a scalar value that can be calculated from the elements of a square matrix and encodes properties of the linear transformation described by the matrix.
Determinants Practice


Complex Fractions Quiz

A complex fraction is a fraction where the numerator, denominator, or both contain a fraction.
Complex Fractions Quiz


Logarithms Quiz

Properties of logarithms and exponents:






Logarithms Quiz


Logarithms Equations Problems

Equations involving logarithms and exponentials.
Logarithms Equations Practice


Addition and Subtraction of Matrices

Two matrices must have an equal number of rows and columns to be added. The sum of two matrices A and B will be a matrix which has the same number of rows and columns as do A and B. The sum of A and B, denoted A + B, is computed by adding corresponding elements of A and B.
Addition and Subtraction of Matrices Practice


Multiplication of Matrices Problems

This quiz has problems that require knowledge of matrix multiplication.
Multiplication of Matrices Practice


Asymptotes Problems

- Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.
- Horizontal asymptotes are horizontal lines the graph approaches.
- A slant asymptote is a slanted line, i.e. neither vertical nor horizontal. A rational function has a slant asymptote if the degree of a numerator polynomial is 1 more than the degree of the denominator polynomial.
Asymptotes of Functions Practice


Partial Decomposition Problems

The partial fraction decomposition or partial fraction expansion of a rational function is an operation that consists of expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator.
Partial Decomposition Practice


Systems of Linear Equations Problems

In mathematics, a system of linear equations is a collection of one or more linear equations involving the same set of variables.
Systems of Linear Equations Practice