Maths MCQ Test – Trigonometry, Algebra, Calculus Combo Set with Answers (2025)
Title: Maths MCQ Test – Trigonometry, Algebra, Calculus Combo Set with Answers (2025)
Description:
Prepare for competitive exams and boost your math skills with our Maths MCQ Test – Trigonometry, Algebra, Calculus Combo Set (2025). This comprehensive question bank includes multiple-choice questions (MCQs) from key topics in mathematics—Trigonometry, Algebra, and Calculus—along with detailed answers and explanations. Perfect for students, teachers, and exam aspirants preparing for IIT-JEE, NEET, SAT, GRE, and other standardized tests. Practice smart, track your progress, and strengthen core mathematical concepts.
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📘 Maths MCQ Test – Trigonometry, Algebra, Calculus Combo Set with Answers (2025)
Boost your exam preparation with this curated Maths MCQ set for 2025, covering Trigonometry, Algebra, and Calculus. These multiple choice questions with answers are ideal for competitive exams, school tests, and entrance preparations.
🔢 Section 1: Trigonometry MCQs
Q1. What is the value of sin(30°)?
A) √3/2
B) 1/2
C) √2/2
D) 0
Answer: B) 1/2
Q2. If tan(θ) = 1, then the angle θ (0° ≤ θ ≤ 180°) is:
A) 30°
B) 45°
C) 90°
D) 135°
Answer: B) 45°
Q3. What is the exact value of cos(60°)?
A) 1
B) √2/2
C) 1/2
D) √3/2
Answer: C) 1/2
Q4. sec²(θ) − tan²(θ) is equal to:
A) 0
B) 1
C) sin²(θ)
D) cos²(θ)
Answer: B) 1
Q5. Which of the following is true for all values of θ?
A) sin(θ) = cos(θ)
B) sin²(θ) + cos²(θ) = 1
C) tan(θ) = sin(θ)/cos(θ) = 1
D) sin²(θ) − cos²(θ) = 0
Answer: B) sin²(θ) + cos²(θ) = 1
✴️ Section 2: Algebra Multiple Choice Questions
Q6. Solve: (x + 3)(x − 5) = 0
A) x = −3 or 5
B) x = 3 or −5
C) x = 3 or 5
D) x = −3 or −5
Answer: A) x = −3 or 5
Q7. Simplify: (2x² + 3x − 2) − (x² − 4x + 5)
A) x² + 7x − 7
B) x² + 7x + 3
C) x² − x − 3
D) 3x² − x − 7
Answer: A) x² + 7x − 7
Q8. The roots of the quadratic equation x² − 6x + 9 = 0 are:
A) x = 3 and x = −3
B) x = 0 and x = 9
C) x = 3 (repeated root)
D) x = 6 and x = −3
Answer: C) x = 3 (repeated root)
Q9. If a + b = 7 and ab = 10, find the quadratic equation with roots a and b.
A) x² − 7x + 10 = 0
B) x² + 7x − 10 = 0
C) x² − 10x + 7 = 0
D) x² − 17x + 70 = 0
Answer: A) x² − 7x + 10 = 0
Q10. Which expression is a factor of x² − 16?
A) (x − 8)
B) (x + 8)
C) (x + 4)(x − 4)
D) (x − 2)(x + 8)
Answer: C) (x + 4)(x − 4)
📐 Section 3: Calculus Objective Questions with Answers
Q11. What is the derivative of f(x) = x²?
A) 2x
B) x
C) x³
D) 1
Answer: A) 2x
Q12. ∫ x dx is equal to:
A) x²
B) x²/2 + C
C) 1/x + C
D) ln|x| + C
Answer: B) x²/2 + C
Q13. If f(x) = sin(x), what is f′(x)?
A) −cos(x)
B) cos(x)
C) tan(x)
D) −sin(x)
Answer: B) cos(x)
Q14. The derivative of e^x is:
A) x * e^x
B) e^x
C) ln(x)
D) e^(x+1)
Answer: B) e^x
Q15. What is the second derivative of f(x) = x³?
A) 6x
B) 3x²
C) 2x
D) 6
Answer: A) 6x
🔢 Section 1: Trigonometry MCQs (Continued)
Q16. What is the value of tan(45°)?
A) 1
B) 0
C) √3
D) √2
Answer: A) 1
Q17. Which identity is true for all angles θ?
A) sin(2θ) = 2sin(θ)
B) cos²(θ) − sin²(θ) = cos(2θ)
C) tan(θ) = cos(θ)/sin(θ)
D) sin²(θ) = 1 − tan²(θ)
Answer: B) cos²(θ) − sin²(θ) = cos(2θ)
Q18. If sin(θ) = 3/5 and θ is in Quadrant II, what is cos(θ)?
A) 4/5
B) −4/5
C) 3/4
D) −3/4
Answer: B) −4/5
Q19. The general solution of sin(x) = 0 is:
A) x = nπ, n ∈ ℤ
B) x = π/2 + nπ
C) x = nπ/2
D) x = 2nπ
Answer: A) x = nπ, n ∈ ℤ
Q20. The range of the function f(x) = cos(x) is:
A) (−∞, ∞)
B) [0, 1]
C) [−1, 1]
D) (−1, 1)
Answer: C) [−1, 1]
✴️ Section 2: Algebra MCQs (Continued)
Q21. What is the value of the expression: (a − b)²?
A) a² − b²
B) a² − 2ab + b²
C) a² + b²
D) a² + 2ab + b²
Answer: B) a² − 2ab + b²
Q22. Solve: 2x² − 3x − 2 = 0
A) x = −1, 2
B) x = 1, −2
C) x = 2, 1
D) x = −2, 3
Answer: A) x = −1, 2
Q23. Which of the following is a polynomial of degree 3?
A) x² + 2
B) x³ − 4x
C) 4x + 5
D) x⁴ − 3x + 1
Answer: B) x³ − 4x
Q24. The sum and product of the roots of the equation x² + 5x + 6 = 0 are:
A) Sum = 5, Product = 6
B) Sum = −5, Product = 6
C) Sum = 6, Product = 5
D) Sum = −5, Product = −6
Answer: B) Sum = −5, Product = 6
Q25. If x + 1 is a factor of x² + 2x + 1, what is the other factor?
A) x − 1
B) x + 2
C) x + 1
D) x − 2
Answer: C) x + 1
📐 Section 3: Calculus MCQs (Continued)
Q26. If f(x) = 3x⁴, what is f′(x)?
A) 12x³
B) 4x³
C) 3x³
D) 6x²
Answer: A) 12x³
Q27. Find d/dx of ln(x²).
A) 1/x
B) 2/x
C) 2x
D) 1/2x
Answer: B) 2/x
Q28. If f(x) = x³ − 3x² + 2, find f′(2).
A) 0
B) 2
C) 4
D) 1
Answer: C) 4
Q29. ∫ (1/x) dx equals:
A) ln|x| + C
B) x ln|x| + C
C) 1/x + C
D) x² + C
Answer: A) ln|x| + C
Q30. The derivative of sin(x)cos(x) using product rule is:
A) cos²(x) − sin²(x)
B) cos(x) − sin(x)
C) sin(x) − cos(x)
D) cos(x)cos(x) − sin(x)sin(x)
Answer: A) cos²(x) − sin²(x)
🔢 Section 1: Trigonometry MCQs (Set 3)
Q31. If sin(θ) = 0.6, what is cos(θ), assuming θ is in the first quadrant?
A) 0.4
B) 0.6
C) 0.8
D) 1
Answer: C) 0.8
(Using Pythagorean identity: cos²θ = 1 − sin²θ = 1 − 0.36 = 0.64, so cos(θ) = √0.64 = 0.8)
Q32. What is the value of sin(90° − θ)?
A) cos(θ)
B) sin(θ)
C) tan(θ)
D) 1 − cos(θ)
Answer: A) cos(θ)
Q33. Which quadrant does angle 210° lie in?
A) I
B) II
C) III
D) IV
Answer: C) III
Q34. What is the exact value of tan(60°)?
A) 1
B) √2
C) √3
D) 1/√3
Answer: C) √3
Q35. cot(θ) is undefined when:
A) sin(θ) = 0
B) cos(θ) = 0
C) tan(θ) = 1
D) θ = 30°
Answer: A) sin(θ) = 0
✴️ Section 2: Algebra MCQs (Set 3)
Q36. Solve: 3x² + 5x − 2 = 0
A) x = −2, 1/3
B) x = 2, −1/3
C) x = 1, −2/3
D) x = −1, 2/3
Answer: A) x = −2, 1/3
(Use quadratic formula)
Q37. Which of the following is a binomial expression?
A) x³ + 2x² + 1
B) x + 1
C) x³ − x² + x − 1
D) x²
Answer: B) x + 1
Q38. What is the degree of the polynomial: 4x⁵ − x³ + 7x − 2?
A) 3
B) 4
C) 5
D) 6
Answer: C) 5
Q39. If a polynomial has roots 2 and −3, what is the polynomial?
A) x² + x − 6
B) x² − x − 6
C) x² + x + 6
D) x² − x + 6
Answer: A) x² + x − 6
Q40. Which is NOT a factor of x² − 9?
A) (x − 3)
B) (x + 3)
C) (x − 9)
D) (x² − 9)
Answer: C) (x − 9)
📐 Section 3: Calculus MCQs (Set 3)
Q41. What is d/dx of tan(x)?
A) sec(x)
B) sec²(x)
C) cos²(x)
D) 1 + tan²(x)
Answer: B) sec²(x)
Q42. If f(x) = x⁵, then f″(x) (second derivative) is:
A) 5x⁴
B) 20x³
C) 25x²
D) 10x
Answer: B) 20x³
Q43. ∫ cos(x) dx equals:
A) sin(x) + C
B) −sin(x) + C
C) tan(x) + C
D) sec(x) + C
Answer: A) sin(x) + C
Q44. The limit lim(x→0) (sin x)/x is:
A) 0
B) 1
C) ∞
D) undefined
Answer: B) 1
Q45. What is ∫ e^(2x) dx?
A) e^(2x) + C
B) 2e^(2x) + C
C) (1/2)e^(2x) + C
D) ln(2x) + C
Answer: C) (1/2)e^(2x) + C
🔢 Section 1: Trigonometry MCQs (Set 4)
Q46. Which of the following is the period of the function f(x) = sin(2x)?
A) π
B) 2π
C) π/2
D) 4π
Answer: A) π
(Period of sin(kx) is 2π/k, so for k = 2 → 2π/2 = π)
Q47. What is the principal value of sin⁻¹(−1/2)?
A) −30°
B) −π/6
C) π/6
D) −π/4
Answer: B) −π/6
Q48. cos(θ) is positive and sin(θ) is negative. In which quadrant is θ?
A) I
B) II
C) III
D) IV
Answer: D) IV
Q49. If tan A = √3 and A is acute, then A equals:
A) 30°
B) 45°
C) 60°
D) 90°
Answer: C) 60°
Q50. Which of the following represents an identity?
A) tan(θ) + cot(θ) = 2
B) sin(θ)/cos(θ) = tan(θ)
C) sin(θ) + cos(θ) = 1
D) sec(θ) − 1 = tan(θ)
Answer: B) sin(θ)/cos(θ) = tan(θ)
✴️ Section 2: Algebra MCQs (Set 4)
Q51. What is the cube of (a + b)?
A) a³ + b³
B) a³ + b³ + 3ab
C) a³ + b³ + 3a²b + 3ab²
D) (a + b)²
Answer: C) a³ + b³ + 3a²b + 3ab²
Q52. Factor: x² − 10x + 25
A) (x + 5)(x − 5)
B) (x − 5)(x − 5)
C) (x + 10)(x − 2.5)
D) (x − 10)(x + 2.5)
Answer: B) (x − 5)(x − 5)
Q53. Which is the correct expansion of (x − 2)(x + 2)?
A) x² − 4
B) x² + 4
C) x² − 2x + 4
D) x² − 2x − 4
Answer: A) x² − 4
Q54. Find the discriminant of the quadratic equation x² − 4x + 3 = 0
A) 16
B) 1
C) −1
D) 4
Answer: B) 4² − 4×1×3 = 16 − 12 = 4
Q55. The expression (x − 1)² + (y + 2)² represents:
A) A line
B) A point
C) A parabola
D) A circle
Answer: D) A circle
(Standard form of a circle: (x − h)² + (y − k)² = r²)
📐 Section 3: Calculus MCQs (Set 4)
Q56. d/dx (x² + 1)⁵ = ?
A) 10x(x² + 1)⁴
B) 5(x² + 1)⁴
C) 10(x² + 1)³
D) 5x(x² + 1)⁴
Answer: D) 5x(x² + 1)⁴
(Use chain rule)
Q57. What is the integral of sec²(x)?
A) tan(x) + C
B) sec(x) + C
C) cot(x) + C
D) ln|sec(x)| + C
Answer: A) tan(x) + C
Q58. If f(x) = ln(x²), then f′(x) = ?
A) 2ln(x)
B) 2x
C) 2/x
D) 1/x
Answer: C) 2/x
(d/dx of ln(x²) = d/dx [2ln|x|] = 2/x)
Q59. What is lim(x→∞) (1 + 1/x)^x?
A) 0
B) 1
C) e
D) ∞
Answer: C) e
(Definition of e)
Q60. If f′(x) = 0 for all x in ℝ, then f(x) is:
A) Constant
B) Linear
C) Quadratic
D) Undefined
Answer: A) Constant
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