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JAMB Mathematics 2025 Objective Past Questions

All 40 questions from the Joint Admissions and Matriculation Board (JAMB) Mathematics 2025 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

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Mathematics 2025 Objective — Question 2

Simplify (x²-9)/(x²-6x+9).

  • A. (x+3)/(x-3)Correct
  • B. (x-3)/(x+3)
  • C. (x+3)/(x-6)
  • D. (x-3)/(x+6)

Explanation

Factorise: (x²-9)=(x-3)(x+3); (x²-6x+9)=(x-3)². Cancel a common (x-3) to get (x+3)/(x-3).

Mathematics 2025 Objective — Question 3

From the top of a building, the angle of depression to a point on the ground is 30°. If the building is 20m high, how far is the point from the base of the building?

Diagram for question 3
  • A. 20m
  • B. 20√3mCorrect
  • C. 20√2m
  • D. 25m

Explanation

tan30° = 20/d ⇒ d = 20/tan30° = 20 × √3 = 20√3 m.

Mathematics 2025 Objective — Question 4

The roots of the quadratic equation 2x²-3x-5=0 are used to form a new quadratic equation. What is the equation whose roots are the squares of the roots of the original equation?

  • A. 2x²-4x-6=0
  • B. 4x²-25x+29=0
  • C. 4x²-29x+25=0Correct
  • D. 6x²-8x-12=0

Explanation

Roots of 2x²-3x-5=0 are 5/2 and -1. Their squares are 25/4 and 1. Sum=29/4, product=25/4. New equation: x²-(29/4)x+25/4=0 → 4x²-29x+25=0.

Mathematics 2025 Objective — Question 5

The nth term of a geometric progression is given by tn=3×2^(n-1). What is the sum of the first 5 terms of this progression?

  • A. 93Correct
  • B. 95
  • C. 96
  • D. 98

Explanation

Terms: 3,6,12,24,48. Sum = 3+6+12+24+48 = 93.

Mathematics 2025 Objective — Question 6

The equation of a circle is given as x²+y²-6x-8y+9=0. What is the centre of the circle?

  • A. (3,4)Correct
  • B. (-3,-4)
  • C. (3,5)
  • D. (2,5)

Explanation

Complete the square: (x-3)²+(y-4)²=16, so centre = (3,4).

Mathematics 2025 Objective — Question 7

A triangle has three sides 13cm, 14cm and 15cm. Find the area of the triangle.

  • A. 72cm²
  • B. 104cm²
  • C. 95cm²
  • D. 84cm²Correct

Explanation

Using Heron's formula, s=21. Area=√(21×8×7×6)=√7056=84cm².

Mathematics 2025 Objective — Question 8

Find the sum of the series: 5+10+20+...+1280.

  • A. 2555Correct
  • B. 3050
  • C. 3400
  • D. 2570

Explanation

GP with a=5, r=2. 5×2^(n-1)=1280 ⇒ n=9. Sn = 5(2⁹-1)/(2-1) = 5×511 = 2555.

Mathematics 2025 Objective — Question 9

The length of a chord in a circle is 12cm and the perpendicular distance from the centre to the chord is 5cm. What is the radius of the circle?

Diagram for question 9
  • A. 7cm
  • B. 8.3cm
  • C. 7.8cmCorrect
  • D. 5.3cm

Explanation

By Pythagoras: r² = 6²+5² = 61, r = √61 ≈ 7.8cm.

Mathematics 2025 Objective — Question 10

If the perimeter of a rectangle is 40cm and the length is 3cm more than twice the width, what is the area of the rectangle?

  • A. 76.14cm²
  • B. 81.22cm²Correct
  • C. 69.35cm²
  • D. 85cm²

Explanation

L=2B+3. 2(2B+3+B)=40 ⇒ 3B+3=20 ⇒ B=17/3, L=43/3. Area=(43/3)(17/3)≈81.22cm².

Mathematics 2025 Objective — Question 11

What is the value of (1+sinθ)/(1-sinθ) when θ=45°?

  • A. 3+2√2Correct
  • B. 3-2√2
  • C. √2/2
  • D. 2-3√2

Explanation

sin45°=√2/2. Substituting and rationalising gives 3+2√2.

Mathematics 2025 Objective — Question 12

A set contains 7 elements. How many subsets can be formed from the set?

  • A. 49
  • B. 14
  • C. 128Correct
  • D. 64

Explanation

Number of subsets of a set with n elements = 2ⁿ. For n=7, 2⁷=128.

Mathematics 2025 Objective — Question 16

If f(x)=x²-5x+6 and g(x)=2x-3, find the value(s) of x for which f(g(x))=0.

  • A. 3/2, 5/2
  • B. 5/2, 3Correct
  • C. 9/2, 1/4
  • D. 1, 5/4

Explanation

f(g(x))=4x²-22x+30=0 ⇒ 2x²-11x+15=0 ⇒ (2x-5)(x-3)=0 ⇒ x=5/2 or 3.

Mathematics 2025 Objective — Question 18

Find the derivative of y=(x²+1)/(x-1).

  • A. (x²-1)/(x-1)²
  • B. 2x/(x-1)²
  • C. (x²-2x-1)/(x-1)²Correct
  • D. (x²+2x+1)/(x-1)²

Explanation

Using the quotient rule with u=x²+1, v=x-1: y' = (2x(x-1)-(x²+1))/(x-1)² = (x²-2x-1)/(x-1)².

Mathematics 2025 Objective — Question 20

Find the equation of the tangent to y=x³-2x+1 at x=1.

  • A. y=x+1
  • B. y=x-1Correct
  • C. y=2x-1
  • D. y=2x+1

Explanation

dy/dx=3x²-2. At x=1, gradient=1 and y=0. Tangent: y-0=1(x-1) ⇒ y=x-1.

Mathematics 2025 Objective — Question 21

The rate of change of the volume of a sphere with respect to its radius when r=3 is:

  • A. 12π
  • B. 36πCorrect
  • C. 9π
  • D. 4π

Explanation

V=(4/3)πr³, dV/dr=4πr². At r=3, dV/dr=4π(9)=36π.

Mathematics 2025 Objective — Question 22

The probability of picking a red ball from a bag is 2/5. If there are 10 red balls, how many balls are in the bag?

  • A. 15
  • B. 30
  • C. 25Correct
  • D. 20

Explanation

Prob=10/n=2/5 ⇒ n = (5×10)/2 = 25.

Mathematics 2025 Objective — Question 23

If two fair dice are rolled, what is the probability that the sum is at least 10?

  • A. 1/6Correct
  • B. 1/12
  • C. 1/9
  • D. 1/14

Explanation

Favourable outcomes (sum ≥10): 6 out of 36 total outcomes = 1/6.

Mathematics 2025 Objective — Question 24

The area of a circle inscribed in a square of side 8cm is:

  • A. 8πcm²
  • B. 64πcm²
  • C. 16πcm²Correct
  • D. 4πcm²

Explanation

Diameter of the circle = side of square = 8cm, so r=4cm. Area = πr² = 16πcm².

Mathematics 2025 Objective — Question 30

The angle subtended by an arc of a circle at the centre is 120°. If the radius is 7cm, what is the length of the arc?

  • A. 28/3 cm
  • B. 22/3 cm
  • C. 44 cm
  • D. 44/3 cmCorrect

Explanation

Arc length = (θ/360)×2πr = (120/360)×2×(22/7)×7 = 44/3 cm.

Mathematics 2025 Objective — Question 31

In a circle, two chords AB and CD intersect at a point P inside the circle. If AP=6cm, PB=4cm, CP=3cm, find PD.

  • A. 6cm
  • B. 4cm
  • C. 8cmCorrect
  • D. 2cm

Explanation

By the intersecting chords theorem, AP×PB=CP×PD ⇒ 6×4=3×PD ⇒ PD=8cm.

Mathematics 2025 Objective — Question 32

In a cyclic quadrilateral, the opposite angles are in the ratio 2:3. What is the smaller angle?

  • A. 108°
  • B. 72°Correct
  • C. 60°
  • D. 120°

Explanation

Let the angles be 2x and 3x; 2x+3x=180° ⇒ x=36°. Smaller angle=2x=72°.

Mathematics 2025 Objective — Question 33

A sum of ₦10,000 is invested at 5% per annum compound interest. What is the amount after 3 years?

  • A. ₦11,576.25Correct
  • B. ₦11,250
  • C. ₦12,000
  • D. ₦10,500

Explanation

A=P(1+r)^t = 10000(1.05)³ = 10000×1.157625 = ₦11,576.25.

Mathematics 2025 Objective — Question 34

A sum doubles in 5 years at a certain rate of simple interest. How many years will it take to triple at the same rate?

  • A. 12
  • B. 8
  • C. 10Correct
  • D. 7.5

Explanation

2P=P+PRT/100 gives R=20%. For tripling, 3P=P+P(20)(T)/100 ⇒ T=10 years.

Mathematics 2025 Objective — Question 36

A mixture contains water and alcohol in the ratio 5:3. If 8 litres of water is added, the new ratio becomes 7:3. What is the original volume of the mixture?

  • A. 24litres
  • B. 20litres
  • C. 16litres
  • D. 32litresCorrect

Explanation

Let volumes be 5x and 3x. (5x+8)/3x=7/3 ⇒ 15x+24=21x ⇒ x=4. Original volume=8x=32 litres.

Mathematics 2025 Objective — Question 37

A sum of ₦12,000 is divided among A, B and C in the ratio 2:3:5. If C gives ₦1,000 to A, what is the new ratio of A's share to B's share?

  • A. 11:9
  • B. 17:18Correct
  • C. 7:6
  • D. 3:2

Explanation

Shares: A=2400,B=3600,C=6000. New A=2400+1000=3400; B unchanged=3600. Ratio A:B=3400:3600=17:18.

Mathematics 2025 Objective — Question 39

The mean of five numbers is 20. If one number is removed, the mean becomes 18. What is the removed number?

  • A. 24
  • B. 20
  • C. 14
  • D. 28Correct

Explanation

Sum of 5 numbers=100. Sum of remaining 4=18×4=72. Removed number=100-72=28.

Mathematics 2025 Objective — Question 40

The position vectors of points A and B are (3i+4j) and (5i-2j) respectively. What is the magnitude of vector AB?

  • A. 2√5
  • B. 2√10Correct
  • C. 2√15
  • D. 3√6

Explanation

AB = (5-3)i+(-2-4)j = 2i-6j. |AB|=√(4+36)=√40=2√10.

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