JAMB Mathematics 2023 Objective Past Questions

All 40 questions from the Joint Admissions and Matriculation Board (JAMB) Mathematics 2023 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

Mathematics 2023 Objective — Question 1

What is the remainder if 4x³-3x+5 is divided by 2x-1?

• A. 1
• B. 2
• C. 3
• D. 4Correct

Explanation

By the remainder theorem, R=f(1/2)=4(1/8)-3(1/2)+5=1/2-3/2+5=4.

Mathematics 2023 Objective — Question 2

A motorcycle dealer bought a used motorcycle for ₦125,000 and spent ₦35,000 refurbishing it. He then sold it for ₦200,000. What is the percentage gain?

• A. 44%
• B. 30%
• C. 25%Correct
• D. 22%

Explanation

Total cost=₦160,000. %gain=(200,000-160,000)/160,000×100%=25%.

Mathematics 2023 Objective — Question 3

If α and β are the roots of the equation 3x²+5x-2=0, find the value of 1/α + 1/β.

• A. -5/3
• B. -2/3
• C. 5/2Correct
• D. 3/4

Explanation

Sum of roots=-5/3, product=-2/3. 1/α+1/β=(α+β)/αβ=(-5/3)/(-2/3)=5/2.

Mathematics 2023 Objective — Question 4

In a school of 300 students, 120 offer French while 160 offer English. How many students offer both subjects if 40 offer neither?

• A. 20Correct
• B. 60
• C. 50
• D. 14

Explanation

n(E∩F)=n(E)+n(F)-[n(U)-n(neither)]=160+120-(300-40)=280-260=20.

Mathematics 2023 Objective — Question 5

Each exterior angle of a regular polygon is 72°. Which of the following identifies the polygon?

• A. A quadrilateral
• B. An octagon
• C. A pentagonCorrect
• D. A heptagon

Explanation

Number of sides = 360°/72° = 5, which is a pentagon.

Mathematics 2023 Objective — Question 6

Evaluate ∫(cos4x + sin3x)dx.

• A. 1/4 sin4x + 1/3cos3x + k
• B. 1/4 sin4x - 1/3cos3x + kCorrect
• C. sin4x + cos3x + k
• D. sin4x - cos3x + k

Explanation

∫cos4x dx = 1/4 sin4x; ∫sin3x dx = -1/3 cos3x. Sum = 1/4 sin4x - 1/3 cos3x + k.

Mathematics 2023 Objective — Question 7

From the diagram (circle with points A, B, C, D and angle ABC=92°), find the value of angle ADC.

• A. 92°Correct
• B. 108°
• C. 88°
• D. 272°

Explanation

∠ABC+92°=180° (angles on a straight line) ⇒ ∠ABC=88°. Since ABCD is a cyclic quadrilateral, ∠ABC+∠ADC=180° ⇒ ∠ADC=92°.

Mathematics 2023 Objective — Question 8

Find the value of 110111₂ + 10100₂.

• A. 1001011₂Correct
• B. 1101011₂
• C. 1001001₂
• D. 1001111₂

Explanation

Adding in binary: 110111 + 10100 = 1001011₂.

Mathematics 2023 Objective — Question 9

If log6.5 = 0.8129, evaluate 2log65 + log650.

• A. 6.4387Correct
• B. 4.6258
• C. 4.4387
• D. 0.9218

Explanation

log65=log6.5+1=1.8129; log650=log6.5+2=2.8129. 2(1.8129)+2.8129=6.4387.

Mathematics 2023 Objective — Question 10

Simplify (2√2-√3)/(√2+√3).

• A. 3√6
• B. 3√6-1
• C. 3√6+7
• D. 3√6-7Correct

Explanation

Multiplying by the conjugate (√2-√3): result simplifies to 3√6-7.

Mathematics 2023 Objective — Question 11

If ab²-c-d=0, express 'a' as the subject of the formula.

• A. (c+d)/b²Correct
• B. (c-d)/b²
• C. (c+d)/b
• D. (c-d)/b

Explanation

ab²=c+d ⇒ a=(c+d)/b².

Mathematics 2023 Objective — Question 12

Find the value of m if x-1 is a factor of x³+4x²+mx-6.

• A. 1Correct
• B. 2
• C. 3
• D. 4

Explanation

f(1)=0: 1+4+m-6=0 ⇒ m=1.

Mathematics 2023 Objective — Question 13

The 4th term of an A.P is 13 while the 10th term is 31. Find the 24th term.

• A. 73Correct
• B. 84
• C. 102
• D. 47

Explanation

a+3d=13, a+9d=31 ⇒ 6d=18, d=3, a=4. T24=a+23d=4+69=73.

Mathematics 2023 Objective — Question 14

Simplify (3^(-5x))/(9^(1-x)) × 27^(2x+1).

• A. 3Correct
• B. 9
• C. 27
• D. 81

Explanation

Expressing all terms in base 3 and simplifying the exponents gives 3¹=3.

Mathematics 2023 Objective — Question 15

If s = √(t²-4t+4), find t in terms of s.

• A. s²-2
• B. s+2Correct
• C. s²+2
• D. s-2

Explanation

s²=t²-4t+4. Solving the quadratic in t gives t=2+s.

Mathematics 2023 Objective — Question 16

If a binary operation * is defined by x*y=x+2y, find 2*(3*4).

• A. 26
• B. 24Correct
• C. 14
• D. 11

Explanation

3*4=3+2(4)=11. 2*(11)=2+2(11)=24.

Mathematics 2023 Objective — Question 17

Find the inverse of A=[[5,3],[6,4]].

• A. [[2,-3/2],[-3,5/2]]
• B. [[-2,3/2],[-3,5/2]]
• C. [[2,-3/2],[-3,5/2]] (repeat)Correct
• D. [[-2,-3/2],[-3,-5/2]]

Explanation

|A|=(5)(4)-(3)(6)=2. A⁻¹=(1/2)[[4,-3],[-6,5]]=[[2,-3/2],[-3,5/2]].

Mathematics 2023 Objective — Question 18

If y=(2x+2)³, find dy/dx.

• A. 3(2x+2)²
• B. 6(2x+2)
• C. 3(2x+3)
• D. 6(2x+2)²Correct

Explanation

Let u=2x+2. dy/dx=3u²×2=6(2x+2)².

Mathematics 2023 Objective — Question 19

In how many ways can a student select 5 subjects from 8 subjects?

• A. 8!/5!
• B. 8!/3!
• C. 8!/(3!5!)
• D. 8!/(3!×5!)Correct

Explanation

Number of ways = ⁸C₅ = 8!/(3!5!).

Mathematics 2023 Objective — Question 20

From the diagram (a triangle with an exterior angle of 110° and a base angle of 15°), find the value of x.

• A. 30°
• B. 15°
• C. 40°Correct
• D. 45°

Explanation

Using the isosceles triangle and angle sum properties: x+110°+30°=180°, so x=40°.

Mathematics 2023 Objective — Question 21

If 2q3₅ = 77₈, find q.

• A. 1
• B. 2Correct
• C. 3
• D. 4

Explanation

2q3₅ in base 10 = 53+5q. 77₈ in base 10 = 63. 53+5q=63 ⇒ q=2.

Mathematics 2023 Objective — Question 22

If x, y and z are in the ratio 5:4:3, find the value of (2y-z)/x.

• A. 4
• B. 3
• C. 2
• D. 1Correct

Explanation

With x=5,y=4,z=3: (2(4)-3)/5 = 5/5 = 1.

Mathematics 2023 Objective — Question 23

Solve the inequality x²+2x > 15.

• A. x>3 or x<-5Correct
• B. x<-3 or x>5
• C. -5<x<3
• D. x<3 or x>3

Explanation

x²+2x-15>0 ⇒ (x-3)(x+5)>0 ⇒ x>3 or x<-5.

Mathematics 2023 Objective — Question 24

The second term of a G.P is 4 while the fourth term is 16. Find the sum of the first five terms.

• A. 62Correct
• B. 54
• C. 64
• D. 60

Explanation

r²=4 ⇒ r=2, a=2. S5=a(r⁵-1)/(r-1)=2(31)/1=62.

Mathematics 2023 Objective — Question 25

Find the equation of a line which passes through the point (4,2) and is perpendicular to the line 2y=5x+4.

• A. 5y+2x-18=0Correct
• B. 5y-2x+18=0
• C. 5y+2x-18=0 (variant)
• D. 5y-2x-18=0

Explanation

Gradient of given line=5/2, so perpendicular gradient=-2/5. y-2=-2/5(x-4) ⇒ 5y+2x-18=0.

Mathematics 2023 Objective — Question 26

Find the value of x at the minimum point of the curve y=x³+x²-x+1.

• A. -1
• B. 1
• C. -1/3
• D. 1/3Correct

Explanation

dy/dx=3x²+2x-1=0 ⇒ (3x-1)(x+1)=0 ⇒ x=1/3 or -1. Since d²y/dx²>0 at x=1/3, this is the minimum.

Mathematics 2023 Objective — Question 27

The sum of four consecutive integers is 34. Find the largest of these integers.

• A. 7
• B. 10Correct
• C. 8
• D. 9

Explanation

x+(x+1)+(x+2)+(x+3)=34 ⇒ 4x+6=34 ⇒ x=7. Largest integer = x+3 = 10.

Mathematics 2023 Objective — Question 28

What is the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle?

• A. 90°
• B. 60°Correct
• C. 45°
• D. 30°

Explanation

A chord equal to the radius forms an equilateral triangle with the two radii, so the subtended angle is 60°.

Mathematics 2023 Objective — Question 29

Evaluate ∫₁²(6x²-2x)dx.

• A. 16
• B. 13
• C. 12
• D. 11Correct

Explanation

∫(6x²-2x)dx=2x³-x². Evaluating from 1 to 2: (16-4)-(2-1)=12-1=11.

Mathematics 2023 Objective — Question 30

Factorize completely (4x+3y)²-(3x-2y)².

• A. (x-5y)(7x-y)
• B. (x-5y)(7x+y)
• C. (x+5y)(7x-y)
• D. (x+5y)(7x+y)Correct

Explanation

Using difference of two squares: (7x+y)(x+5y).

Mathematics 2023 Objective — Question 31

If p-2q+1=q+3p and p-2=0, find q.

• A. -2
• B. -1Correct
• C. 1
• D. 2

Explanation

p=2. Substituting: -2p-3q=-1 ⇒ -4-3q=-1 ⇒ q=-1.

Mathematics 2023 Objective — Question 32

If tan x=1, evaluate sin x + cos x in surd form.

• A. 2√2
• B. √2Correct
• C. 1/2√2
• D. 2

Explanation

tanx=1 ⇒ x=45°. sin45°+cos45°=1/√2+1/√2=√2.

Mathematics 2023 Objective — Question 33

Given the sets X={1,2,3,4} and Y={2,3,5,9}. If a number is selected at random from set Y, what is the probability that the number is prime?

• A. 3/8
• B. 3/4Correct
• C. 2/3
• D. 3/5

Explanation

Prime numbers in Y are 2,3,5 (3 out of 4). Probability=3/4.

Mathematics 2023 Objective — Question 34

Two ladders of length 5m and 7m lean against a pole and make angles 45° and 60° with the ground respectively. What is the distance apart on the pole, correct to two decimal places?

• A. 2.00m
• B. 2.53mCorrect
• C. 2.54m
• D. 6.06m

Explanation

|PA|=7sin60°=6.0622m; |QA|=5sin45°=3.5355m. Distance=6.0622-3.5355≈2.53m.

Mathematics 2023 Objective — Question 35

The probability that event A occurs is 1/2 and the probability that event B occurs is 1/3. What is the probability that only one of them occurs?

• A. 1/3
• B. 1/6
• C. 1/2Correct
• D. 2/3

Explanation

P(only one)=P(A)P(B')+P(B)P(A')=(1/2)(2/3)+(1/3)(1/2)=1/3+1/6=1/2.

Mathematics 2023 Objective — Question 36

Find the coefficient of xy in the expansion of (x-4y)(3x+2y).

• A. -10Correct
• B. 14
• C. 10
• D. -14

Explanation

(x-4y)(3x+2y)=3x²-10xy-8y². Coefficient of xy = -10.

Mathematics 2023 Objective — Question 37

If n + 1/n = 9, evaluate n² + 1/n².

• A. 63
• B. 81
• C. 79Correct
• D. 38

Explanation

(n+1/n)²=81=n²+2+1/n² ⇒ n²+1/n²=79.

Mathematics 2023 Objective — Question 38

If 321₄ divided by 23₄ leaves a remainder t, what is the value of t?

• A. 1
• B. 0
• C. 2Correct
• D. 3

Explanation

321₄=57ten, 23₄=11ten. 57÷11=5 remainder 2. So t=2.

Mathematics 2023 Objective — Question 39

The radius r of a cylinder disc is increasing at the rate of 0.5cm/s. At what rate is the area of the disc increasing when its radius is 6cm?

• A. 36πcm²/s
• B. 3πcm²/s
• C. 18πcm²/s
• D. 6πcm²/sCorrect

Explanation

A=πr², dA/dt=2πr(dr/dt)=2π(6)(0.5)=6πcm²/s.

Mathematics 2023 Objective — Question 40

For what values of y is the expression (6y-1)/(y²-y-6) undefined?

• A. 0,1
• B. 3,2
• C. -3,2Correct
• D. 3,-4

Explanation

Denominator zero: y²-y-6=0 ⇒ (y+2)(y-3)=0 ⇒ y=-2 or 3.