100 Algebra Quiz Questions & Answers for Students 2026

Basic Algebra — 25 Questions

1. Solve: x + 5 = 12 → x = 7
2. Solve: 2x = 18 → x = 9
3. Solve: x - 9 = 3 → x = 12
4. Solve: x/4 = 5 → x = 20
5. Solve: 3x + 6 = 21 → x = 5
6. Solve: 5x - 10 = 40 → x = 10
7. Simplify: 3x + 2x → 5x
8. Simplify: 4a × 3b → 12ab
9. Expand: 2(x + 5) → 2x + 10
10. Expand: 3(2x - 4) → 6x - 12
11. Solve: 2(x + 3) = 14 → x = 4
12. Solve: 4x = -16 → x = -4
13. Solve: x/5 + 3 = 7 → x = 20
14. Factorise: x² + 5x → x(x + 5)
15. Evaluate 2x + 3y when x=4, y=2 → 14
16. Solve: 7 - x = 3 → x = 4
17. Solve: 2x + 3 = x + 10 → x = 7
18. Simplify: (x³)(x²) → x⁵
19. Simplify: x⁶ ÷ x² → x⁴
20. What is x⁰? 1 (any non-zero number raised to power 0 = 1)
21. Solve: |x| = 7 → x = 7 or x = -7
22. Solve: 3x - 7 = 2x + 5 → x = 12
23. Expand: (x+2)(x+3) → x² + 5x + 6
24. Factorise: x² + 7x + 12 → (x+3)(x+4)
25. What does "linear" mean in algebra? Variable has power of 1 — graph is a straight line

Quadratic Equations & Functions — 25 Questions

1. What is a quadratic equation? (Equation of form ax² + bx + c = 0)
2. What is the standard form of a quadratic? (ax² + bx + c = 0)
3. Solve: x² = 25 → x = ±5
4. Solve: x² - 5x + 6 = 0 → x = 2 or x = 3
5. Solve: x² + 2x - 8 = 0 → x = 2 or x = -4
6. What is the discriminant? (b² - 4ac — determines nature of roots)
7. If discriminant > 0, how many real roots? (2 distinct real roots)
8. If discriminant = 0, how many real roots? (1 repeated real root)
9. If discriminant < 0, how many real roots? (No real roots — complex roots)
10. What is vertex form of a quadratic? (y = a(x-h)² + k — vertex at (h,k))
11. What is f(x) notation? (Function notation — f of x — the output when x is input)
12. What is f(3) if f(x) = 2x + 1? (7)
13. What is the inverse of a function? (Swaps input and output — undoes the function)
14. What is a parabola? (U-shaped curve — graph of a quadratic function)
15. What is the axis of symmetry of y = ax² + bx + c? (x = -b/2a)
16. What is the y-intercept of a quadratic function in standard form? (The value of c, when x = 0)
17. Solve: x² - 9 = 0 → x = 3 or x = -3
18. What is "completing the square" used for? (Rewriting a quadratic into vertex form to solve or graph it)
19. What shape does every quadratic function graph form? (A parabola)
20. Solve: x² + 4x + 4 = 0 → x = -2 (repeated root)
21. What is a root or zero of a function? (A value of x where f(x) = 0)
22. What is the domain of a function? (The set of all possible input values)
23. What is the range of a function? (The set of all possible output values)
24. What does it mean for a function to be "even"? (f(-x) = f(x) — symmetric about the y-axis)

Functions & Graphs — 25 Questions

1. What is a linear function's general form? (f(x) = mx + b)
2. What does "m" represent in y = mx + b? (The slope of the line)
3. What does "b" represent in y = mx + b? (The y-intercept)
4. What is the slope of a horizontal line? (0)
5. What is the slope of a vertical line? (Undefined)
6. If two lines have the same slope, what is true about them? (They are parallel)
7. If two lines' slopes multiply to -1, what is true about them? (They are perpendicular)
8. What is the point where a graph crosses the x-axis called? (The x-intercept)
9. What is composition of functions, written f(g(x))? (Applying one function to the result of another)
10. What is an exponential function's general form? (f(x) = a·bˣ)
11. What does a positive slope indicate about a line's direction? (It rises from left to right)
12. What does a negative slope indicate about a line's direction? (It falls from left to right)
13. What is the vertical line test used for? (Determining if a graph represents a function)
14. What is a piecewise function? (A function defined by different expressions over different intervals)
15. What is the graph of f(x) = |x| called? (An absolute value graph, forming a V shape)
16. What transformation does f(x) + k apply to a graph? (A vertical shift by k units)
17. What transformation does f(x - h) apply to a graph? (A horizontal shift by h units)
18. What is the midpoint formula for two points? (((x₁+x₂)/2), ((y₁+y₂)/2))
19. What is the distance formula between two points? (√((x₂-x₁)² + (y₂-y₁)²))
20. What does it mean for a function to be "odd"? (f(-x) = -f(x) — symmetric about the origin)
21. What is a rational function? (A function expressed as a ratio of two polynomials)
22. What is an asymptote? (A line that a graph approaches but never touches)
23. What is the graph of a cubic function's general shape? (An S-shaped curve)
24. What does solving a system of two linear equations graphically find? (The point where the two lines intersect)
25. What is a one-to-one function? (A function where each output corresponds to exactly one input)

Polynomials & Word Problems — 25 Questions

1. What is a polynomial? (An expression with variables and coefficients combined using addition, subtraction, and multiplication)
2. What is the degree of a polynomial? (The highest power of the variable in the expression)
3. Simplify: (3x² + 2x) + (x² - 5x) → 4x² - 3x
4. Simplify: (5x² - 3x) - (2x² + x) → 3x² - 4x
5. Multiply: (x + 1)(x - 1) → x² - 1
6. What is the difference of squares formula? (a² - b² = (a+b)(a-b))
7. Factor: x² - 16 → (x+4)(x-4)
8. What is a trinomial? (A polynomial with exactly three terms)
9. Word problem: A number plus 8 equals 20. What is the number? (12)
10. Word problem: Twice a number minus 4 equals 10. What is the number? (7)
11. Word problem: The sum of two consecutive integers is 25. What are they? (12 and 13)
12. Word problem: A rectangle's length is 3 more than its width, and perimeter is 26. What is the width? (5)
13. What is direct variation? (A relationship where y = kx for a constant k)
14. What is inverse variation? (A relationship where y = k/x for a constant k)
15. Word problem: If 3 apples cost $1.50, how much do 7 apples cost? ($3.50)
16. What is the formula relating distance, rate, and time? (Distance = Rate × Time)
17. Word problem: A car travels 60 mph for 3 hours. How far does it go? (180 miles)
18. What is a like term in algebra? (Terms with the same variable raised to the same power)
19. Simplify: 2x² + 3x² → 5x²
20. What is the zero product property used for? (Solving equations by setting each factor equal to zero)
21. Factor: x² + 6x + 9 → (x+3)²
22. What is a perfect square trinomial? (A trinomial that factors into the square of a binomial)
23. Word problem: Half of a number is 15. What is the number? (30)
24. What is the term for an equation with no solution? (An inconsistent equation)
25. What is the term for an equation true for every value of the variable? (An identity)
26. What is the term for the constant term in a polynomial, with no variable attached? (The constant)