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20 hard math quiz questions and answers for expert-level trivia fans on algebra and functions.
1. What is the discriminant of x² + 4x + 4 = 0?
💡 The discriminant is b² - 4ac = 16 - 16 = 0, indicating one repeated root.
2. What is the derivative of f(x) = x²?
💡 Using the power rule, the derivative of x² is 2x.
3. What is the value of log₁₀(1000)?
💡 Since 10³ = 1000, log₁₀(1000) equals 3.
4. What is e (Euler's number) approximately equal to?
💡 Euler's number e is approximately 2.71828, commonly rounded to 2.72.
5. Simplify: x³ / x².
💡 Subtracting exponents when dividing gives x³⁻² = x.
6. What is the vertex of y = (x-2)² + 3?
💡 In vertex form y = (x-h)² + k, the vertex is at (h,k), which is (2,3).
7. Solve for x: x² - 5x + 6 = 0.
💡 Factoring gives (x-2)(x-3) = 0, so x = 2 or x = 3.
8. What is the product of the roots of x² - 5x + 6 = 0?
💡 For a quadratic ax² + bx + c, the product of roots equals c/a, which is 6.
9. What is the value of 5⁰?
💡 Any non-zero number raised to the power of 0 equals 1.
10. Simplify: (x+3)(x-3).
💡 This is a difference of squares, expanding to x² - 9.
11. Simplify: (2x²)(3x³).
💡 Multiplying coefficients and adding exponents gives 6x⁵.
12. What is the value of x in log₂(x) = 5?
💡 Since 2⁵ = 32, x equals 32.
13. Solve for x: 2^x = 32.
💡 Since 2⁵ = 32, x equals 5.
14. What is the sum of the roots of x² - 7x + 12 = 0?
💡 For a quadratic ax² + bx + c, the sum of roots equals -b/a, which is 7.
15. What is the inverse of f(x) = x + 5?
💡 To find the inverse, swap x and y and solve, giving f⁻¹(x) = x - 5.
16. What is f(3) if f(x) = 2x² - 5?
💡 Substituting x = 3: 2(9) - 5 = 18 - 5 = 13.
17. Solve the system: x + y = 10, x - y = 4. What is x?
💡 Adding both equations gives 2x = 14, so x = 7.
18. What is the general form of a quadratic equation?
💡 A quadratic equation is written in the general form ax² + bx + c = 0.
19. What is the domain restriction for f(x) = 1/(x-4)?
💡 The function is undefined when the denominator equals zero, so x cannot equal 4.
20. What is the axis of symmetry of y = x² - 4x + 3?
💡 The axis of symmetry is found using x = -b/2a = 4/2 = 2.