Algebra Practice Questions: Test Your Knowledge | LearnByTeaching.ai
These 40 algebra practice questions cover linear equations, quadratic equations, polynomials, and systems of equations. They range from foundational skills to challenging applications, helping you identify areas that need more practice before your next exam.
40 questions total
Linear Equations and Inequalities
Covers solving linear equations, graphing lines, slope-intercept form, and linear inequalities.
Solve for x: 3x - 7 = 14
What is the slope of the line passing through points (2, 5) and (6, 13)?
Which equation represents a line with slope -3 and y-intercept 5?
Solve for x: 2(x + 3) - 4 = 3x + 1
Solve the inequality: -2x + 5 > 11
A line passes through (1, 4) and is parallel to y = 2x - 3. What is its equation?
If |2x - 3| = 7, what are the values of x?
Which graph represents the solution to y <= -x + 4?
The sum of three consecutive integers is 84. What is the largest integer?
Solve for x: (x/3) + (x/4) = 7
Quadratic Equations
Covers factoring, the quadratic formula, completing the square, and interpreting parabolas.
Factor: x^2 + 5x + 6
What are the solutions to x^2 - 9 = 0?
Using the quadratic formula, solve 2x^2 + 3x - 2 = 0.
The vertex of the parabola y = x^2 - 6x + 8 is at:
The discriminant of a quadratic equation is negative. This means the equation has:
A ball is thrown upward with height h(t) = -16t^2 + 64t + 5 feet after t seconds. When does it reach maximum height?
Complete the square for x^2 + 8x + 3 = 0 to solve for x.
For which value of k does the equation x^2 + kx + 9 = 0 have exactly one real solution?
If the roots of a quadratic equation are x = -3 and x = 5, which could be the equation?
Which of the following quadratic equations has no real solutions?
Polynomials and Exponents
Covers polynomial operations, exponent rules, factoring techniques, and the behavior of polynomial functions.
Simplify: (3x^2)(4x^3)
Simplify: x^(-3)
Expand: (2x - 3)^2
Factor completely: 2x^3 - 8x
What is the degree of the polynomial 5x^4 - 3x^2 + 7x - 1?
Divide (x^3 + 2x^2 - 5x - 6) by (x + 3). What is the quotient?
Simplify: (2x^3y^2)^3
If f(x) = x^3 - 4x and f(a) = 0, which of the following could be a value of a?
What is the remainder when x^4 + 3x^2 - 5 is divided by (x - 1)?
The end behavior of f(x) = -2x^5 + x^3 - 7 is:
Systems of Equations
Covers solving systems by substitution, elimination, and graphing, including word problems and systems with no or infinite solutions.
Solve the system: y = 2x + 1 and y = -x + 7
Solve using elimination: 3x + 2y = 12 and 3x - 2y = 0
What does it mean graphically when a system of two linear equations has no solution?
Solve: x + y = 10 and 2x - y = 5
For what value of k does the system x + 2y = 6 and 2x + 4y = k have infinitely many solutions?
A coffee shop sells lattes for $5 and espressos for $3. In one hour, they sold 20 drinks for $84. How many lattes were sold?
Which method is most efficient for solving: y = 3x - 1 and 5x + 2y = 13?
Solve the system: 2x + 3y = 1 and 4x + 6y = 5
One number is 4 more than twice another. Their sum is 25. What are the two numbers?
A system of three equations in three unknowns can have which of the following numbers of solutions?
Scoring Guide
Total possible: 40
Study Recommendations
- Practice translating word problems into algebraic equations before solving them
- Check every answer by substituting back into the original equation
- Master exponent rules through repeated practice — confusing add vs. multiply is the most common error
- Use graphing tools like Desmos to visualize what equations look like geometrically
- When solving systems, choose the method (substitution vs. elimination) based on the equation structure
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