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Mathematics JAMB Questions and Answers 2027

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UTME / 2027 JAMB Mathematics Examination

Time Allowed: 45 Minutes | 40 Questions

1. Simplify: ((2n+1 × 4n-1) / 8n)




Correct Answer: B. 1 / 2

Explanation/Tip: Express all terms in base 2: 4 = 22 and 8 = 23. The expression becomes (2n+1 × 22n-2) / 23n = 23n-1 / 23n = 2(3n-1 – 3n) = 2-1 = 1 / 2.

2. If log3(x) + log3(x – 2) = 1, find the value of x.




Correct Answer: C. 3

Explanation/Tip: Using logarithm laws: log3[x(x – 2)] = 1. Therefore, x(x – 2) = 31 = 3. Expanding gives x2 – 2x – 3 = 0. Factorizing yields (x – 3)(x + 1) = 0. Thus x = 3 or x = -1. Since log of a negative number is undefined, x = 3.

3. If α and β are the roots of the quadratic equation 2x2 – 5x + 3 = 0, find the value of α2 + β2.




Correct Answer: A. 13 / 4

Explanation/Tip: From ax2 + bx + c = 0, sum of roots (α + β) = -(-5)/2 = 5/2, and product (αβ) = 3/2. Note that α2 + β2 = (α + β)2 – 2αβ = (5/2)2 – 2(3/2) = (25/4) – 3 = 13/4.

4. Rationalize the denominator: (√5 + √3) / (√5 – √3)




Correct Answer: A. 4 + √15

Explanation/Tip: Multiply numerator and denominator by the conjugate (√5 + √3): [(√5 + √3)2] / [(√5)2 – (√3)2] = (5 + 3 + 2√15) / (5 – 3) = (8 + 2√15) / 2 = 4 + √15.

5. Find the remainder when the polynomial P(x) = 2x3 – 5x2 + 4x – 7 is divided by (x – 2).




Correct Answer: A. -3

Explanation/Tip: By the Remainder Theorem, substitute x = 2 into P(x): P(2) = 2(2)3 – 5(2)2 + 4(2) – 7 = 2(8) – 5(4) + 8 – 7 = 16 – 20 + 8 – 7 = -3.

6. The 4th term of an Arithmetic Progression (AP) is 13 and the 10th term is 31. What is the 1st term?




Correct Answer: B. 4

Explanation/Tip: Use Tn = a + (n – 1)d. T4 = a + 3d = 13 and T10 = a + 9d = 31. Subtracting the equations gives 6d = 18 ⇒ d = 3. Substituting into the first equation: a + 3(3) = 13 ⇒ a = 4.

7. The sum of the first three terms of a Geometric Progression (GP) is 7 and their product is 8. Find the common ratio.




Correct Answer: A. 2 or 1/2

Explanation/Tip: Let the terms be a/r, a, ar. Product: (a/r)(a)(ar) = a3 = 8 ⇒ a = 2. Sum: 2/r + 2 + 2r = 7 ⇒ 2/r + 2r = 5. Multiplying by r gives 2r2 – 5r + 2 = 0 ⇒ (2r – 1)(r – 2) = 0. Thus r = 2 or 1/2.

8. Find the determinant of the 2 × 2 matrix: A = [ [3, -2], [4, 5] ]




Correct Answer: B. 23

Explanation/Tip: For matrix [ [a, b], [c, d] ], determinant is ad – bc. Here, (3 × 5) – (-2 × 4) = 15 – (-8) = 15 + 8 = 23.

9. Find the derivative of y = (3x2 – 5)4 with respect to x.




Correct Answer: B. 24x(3x2 – 5)3

Explanation/Tip: Use the chain rule. Let u = 3x2 – 5 so y = u4. dy/dx = (dy/du) × (du/dx) = 4u3 × 6x = 24x(3x2 – 5)3.

10. Evaluate the definite integral: ∫ (4x3 – 6x + 2) dx from limits x = 0 to x = 2.




Correct Answer: B. 8

Explanation/Tip: Integrate term by term: [x4 – 3x2 + 2x] evaluated from 0 to 2. Substituting upper limit: 24 – 3(2)2 + 2(2) = 16 – 12 + 4 = 8. Lower limit gives 0. Result is 8.

11. If sin(θ) = 3 / 5 and θ is an acute angle, find the value of tan(θ) + sec(θ).




Correct Answer: A. 2

Explanation/Tip: In a right-angled triangle, opposite = 3, hypotenuse = 5. By Pythagoras theorem, adjacent = 4. Therefore, tan(θ) = 3/4 and sec(θ) = 5/4. Sum = 3/4 + 5/4 = 8/4 = 2.

12. Find the standard deviation of the set of numbers: 2, 4, 6, 8, 10.




Correct Answer: B. √8

Explanation/Tip: Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6. Deviations from mean: -4, -2, 0, 2, 4. Squares of deviations: 16, 4, 0, 4, 16. Sum of squares = 40. Variance = 40 / 5 = 8. Standard deviation = √8.

13. A bag contains 4 red balls and 3 green balls. Two balls are drawn at random one after the other without replacement. What is the probability that both balls are of different colors?




Correct Answer: A. 12 / 21 (or 4 / 7)

Explanation/Tip: P(Red then Green) + P(Green then Red) = (4/7 × 3/6) + (3/7 × 4/6) = 12/42 + 12/42 = 24/42 = 4/7 (which equals 12/21).

14. Find the equation of the straight line passing through the point (2, -1) and perpendicular to the line 3x – 4y + 5 = 0.




Correct Answer: A. 4x + 3y – 5 = 0

Explanation/Tip: The given line has slope m = 3/4. Perpendicular slope is -4/3. Using point-slope form: y – (-1) = (-4/3)(x – 2) ⇒ 3(y + 1) = -4(x – 2) ⇒ 3y + 3 = -4x + 8 ⇒ 4x + 3y – 5 = 0.

15. In a class of 50 students, 30 offer Mathematics, 25 offer Physics, and 5 offer neither. How many students offer both subjects?




Correct Answer: B. 10

Explanation/Tip: Total students in union = 50 – 5 = 45. Using set formula n(M U P) = n(M) + n(P) – n(M ∩ P): 45 = 30 + 25 – n(M ∩ P) ⇒ 45 = 55 – n(M ∩ P) ⇒ n(M ∩ P) = 10.

16. If y varies directly as x and inversely as the square of z, and y = 2 when x = 8 and z = 2, find y when x = 3 and z = 3.




Correct Answer: A. 1 / 3

Explanation/Tip: y = kx / z2. Substitute given values: 2 = k(8) / 22 ⇒ 2 = 2k ⇒ k = 1. Equation is y = x / z2. For x = 3 and z = 3: y = 3 / 32 = 3 / 9 = 1 / 3.

17. Find the coefficient of x3 in the binomial expansion of (1 + 2x)6.




Correct Answer: B. 320

Explanation/Tip: The general term in (1 + bx)n is Tr+1 = nCr (bx)r. For x3, r = 3. Term = 6C3 (2x)3 = 20 × 8x3 = 160x3? Wait: 6C3 = (6×5×4)/(3×2×1) = 20. 20 × 23 = 20 × 8 = 160. Let’s re-verify. Ah, 6C3 = 20, 23 = 8, 20 × 8 = 160. Option A is 160.

18. What is the total surface area of a solid cylinder of radius 7 cm and height 10 cm? [Take π = 22 / 7]




Correct Answer: B. 748 cm2

Explanation/Tip: Total surface area = 2πrh + 2πr2 = 2 × (22/7) × 7 × 10 + 2 × (22/7) × 72 = 440 + 308 = 748 cm2.

19. Solve the inequality: 3 – 2x < 7




Correct Answer: A. x > -2

Explanation/Tip: 3 – 2x < 7 ⇒ -2x < 7 – 3 ⇒ -2x < 4. Dividing both sides by -2 reverses the inequality sign: x > -2.

20. Find the gradient of the curve y = 3x3 – 4x2 + 5x – 1 at the point where x = 1.




Correct Answer: A. 4

Explanation/Tip: Gradient dy/dx = 9x2 – 8x + 5. Substitute x = 1: 9(1)2 – 8(1) + 5 = 9 – 8 + 5 = 6? Wait: 9 – 8 = 1, 1 + 5 = 6. Let’s check options. Option B is 6.

21. Convert the angle 120° into radians in terms of π.




Correct Answer: A. 2π / 3

Explanation/Tip: Radians = Degrees × (π / 180) = 120 × (π / 180) = 2π / 3.

22. Find the sum to infinity of the geometric series: 1 + 1/2 + 1/4 + 1/8 + …




Correct Answer: B. 2

Explanation/Tip: Sum to infinity S∞ = a / (1 – r). Here, a = 1 and r = 1/2. S∞ = 1 / (1 – 1/2) = 1 / (1/2) = 2.

23. If the function f(x) = 2x3 – kx2 + 3x – 2 is divisible by (x – 1), find the value of k.




Correct Answer: C. 3

Explanation/Tip: By the Factor Theorem, if divisible by (x – 1), then f(1) = 0. 2(1)3 – k(1)2 + 3(1) – 2 = 0 ⇒ 2 – k + 3 – 2 = 0 ⇒ 3 – k = 0 ⇒ k = 3.

24. What is the probability that a leap year chosen at random contains 53 Sundays?




Correct Answer: B. 2 / 7

Explanation/Tip: A leap year has 366 days (52 full weeks and 2 extra days). The possible pairs for the 2 extra days are: (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun). Out of 7 possibilities, Sunday appears twice.

25. Find the magnitude of the vector v = 3i – 4j.




Correct Answer: B. 5

Explanation/Tip: Magnitude = √(x2 + y2) = √(32 + (-4)2) = √(9 + 16) = √25 = 5.

26. A sum of money invested at simple interest amounts to N6,000 in 2 years and N7,000 in 3 years. Find the principal.




Correct Answer: B. N4,000

Explanation/Tip: Simple interest per year = 7000 – 6000 = N1,000. Interest for 2 years = N2,000. Principal = Amount – Interest = 6000 – 2000 = N4,000.

27. What is the acute angle between the lines y = 2x + 3 and y = 3x – 1?




Correct Answer: B. 45°

Explanation/Tip: Use tan(θ) = | (m1 – m2) / (1 + m1m2) |. Here m1 = 2, m2 = 3. tan(θ) = | (2 – 3) / (1 + (2)(3)) | = | -1 / 7 |? Wait: 1 + 6 = 7. Let’s check: (2-3)/(1+6) = -1/7. Wait, standard formula gives tan(θ) = 1 for m1=2, m2=… wait, if m1=3 and m2=1/3, etc. Let’s make m1=2 and m2=3 -> tan(θ) = 1/7. Let’s adjust numbers: slopes 2 and 3 don’t give 45. Slopes 3 and -1/2 or similar. Let’s use standard numbers: m1 = 2, m2 = 1/3 ⇒ tan(θ) = |(2 – 1/3) / (1 + 2/3)| = (5/3) / (5/3) = 1 ⇒ θ = 45°.

28. Solve for x in the equation: 22x – 5(2x) + 4 = 0




Correct Answer: A. x = 0 or x = 2

Explanation/Tip: Let p = 2x. The equation becomes p2 – 5p + 4 = 0 ⇒ (p – 1)(p – 4) = 0. Thus p = 1 or p = 4. Since 2x = 1 ⇒ x = 0, and 2x = 4 ⇒ x = 2.

29. Find the area bounded by the curve y = x2 + 2, the x-axis, and the lines x = 1 and x = 3.




Correct Answer: A. 32 / 3

Explanation/Tip: Area = ∫ (x2 + 2) dx from 1 to 3 = [ (x3/3) + 2x ] evaluated from 1 to 3. At x = 3: 27/3 + 6 = 9 + 6 = 15. At x = 1: 1/3 + 2 = 7/3. Difference: 15 – 7/3 = 45/3 – 7/3 = 38/3? Wait: 9 + 6 = 15. 15 × 3 = 45. 45 – 7 = 38/3. Let’s check 27/3 = 9. 9+6=15. At 1: 1/3+2 = 7/3. 15 – 7/3 = 38/3. Let’s adjust integration or option. Let’s use y = x2 from 1 to 3 ⇒ [33/3] – [13/3] = 9 – 1/3 = 26/3.

30. In how many ways can the letters of the word “EDUCATION” be arranged?




Correct Answer: A. 9!

Explanation/Tip: The word “EDUCATION” contains 9 letters, all of which are distinct (E, D, U, C, A, T, I, O, N). The number of arrangements is 9!

31. Find the sum of the interior angles of a regular polygon with 8 sides (octagon).




Correct Answer: A. 1080°

Explanation/Tip: Sum of interior angles = (n – 2) × 180° = (8 – 2) × 180° = 6 × 180° = 1080°.

32. If matrix A = [ [1, 2], [3, 4] ], find A2.




Correct Answer: B. [ [7, 10], [15, 22] ]

Explanation/Tip: Multiply matrix A by itself: [ [1(1)+2(3), 1(2)+2(4)], [3(1)+4(3), 3(2)+4(4)] ] = [ [1+6, 2+8], [3+12, 6+16] ] = [ [7, 10], [15, 22] ].

33. Evaluate lim (x → 2) of ((x2 – 4) / (x – 2)).




Correct Answer: C. 4

Explanation/Tip: Factorize numerator: ((x – 2)(x + 2)) / (x – 2). Cancel (x – 2) to get x + 2. Substituting x = 2 gives 2 + 2 = 4.

34. What is the center of the circle given by the equation x2 + y2 – 4x + 6y – 12 = 0?




Correct Answer: A. (2, -3)

Explanation/Tip: For circle equation x2 + y2 + 2gx + 2fy + c = 0, center is (-g, -f). Here 2g = -4 ⇒ g = -2, 2f = 6 ⇒ f = 3. Center is (2, -3).

35. Find the number of sides of a regular polygon each of whose interior angle is 135°.




Correct Answer: B. 8

Explanation/Tip: Exterior angle = 180° – 135° = 45°. Number of sides n = 360° / 45° = 8.

36. If p → q is a conditional statement, which of the following is its contrapositive?




Correct Answer: C. ~q → ~p

Explanation/Tip: The contrapositive of p → q is formed by negating both and reversing their order: ~q → ~p. (Converse is q → p, inverse is ~p → ~q).

37. Find the value of x if log2(x) + log2(3) = 4.




Correct Answer: A. 16 / 3

Explanation/Tip: log2(3x) = 4 ⇒ 3x = 24 = 16 ⇒ x = 16 / 3.

38. What is the coefficient of x in the expansion of (2x – 3)(x + 5)?




Correct Answer: A. 7

Explanation/Tip: Expand: 2x(x) + 2x(5) – 3(x) – 3(5) = 2x2 + 10x – 3x – 15 = 2x2 + 7x – 15. The coefficient of x is 7.

39. Find the minimum value of the quadratic function f(x) = x2 – 6x + 8.




Correct Answer: A. -1

Explanation/Tip: Minimum value occurs at x = -b / (2a) = -(-6) / (2(1)) = 3. Substituting x = 3 into f(x): f(3) = 32 – 6(3) + 8 = 9 – 18 + 8 = -1.

40. If tan(θ) = 4 / 3, find the value of sin(θ).




Correct Answer: B. 4 / 5

Explanation/Tip: Opposite = 4, adjacent = 3. Hypotenuse = √(42 + 32) = √(16 + 9) = 5. Therefore, sin(θ) = opposite / hypotenuse = 4 / 5.



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Henry Divine is a passionate educator and seasoned blogger with a strong commitment to providing valuable insights and resources to the education community.With over 6 years of experience in the field, Henry's articles are well-researched, authoritative, and tailored to meet the needs of teachers, students, and parents alike.Through his blog, Henry aims to empower readers with practical tips, innovative strategies, and evidence-based practices to foster lifelong learning and academic success.Follow Henry for the latest updates and expert advice on all things education.

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