Mathematics past questions: JAMB UTME 2025

55 objective questions, with answers. Free to read and practise.

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55 questions, one at a time, marked as you go or at the end. No account needed.

1.
A banker spent \(\frac{1}{5}\) of his salary on shirts, \(\frac{1}{3}\) of the remainder on transport, and kept the rest for contingencies. What fraction was left
1. A.\(\frac{6}{15}\)
2. B.\(\frac{8}{15}\)
3. C.\(\frac{7}{15}\)
4. D.\(\frac{4}{5}\)
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Answer: B \(\frac{8}{15}\)
2.
A binary operation * is defined on the set X = {1, 2, 3, 4, 5, 6} as a*b = ab + a + b. Compute 1 * 3
1. A.14
2. B.4
3. C.7
4. D.5
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Answer: C 7
3.
A bird flies from a tree P on a bearing of N60º E to a building, Q, a distance of 200 km. It then changes course and flies to another tree R on a bearing of S30ºE. Tree R is directly east of tree P. Calculate the distance of the building to tree R.
1. A.200 \(\sqrt{3}\)
2. B.100 \(\sqrt{3}\)
3. C.100
4. D.\(\frac{200}{\sqrt{3}}\)
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Answer: D \(\frac{200}{\sqrt{3}}\)
4.
A car dealer bought a used car for ₦270,000 and spent ₦70,000 to refurbish it. He later sold the car for ₦490,000. What was the percentage profit?
1. A.30%
2. B.35%
3. C.25%
4. D.45%
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Answer: D 45%
5.
A varies directly as b \(^2\) when A = 4, b = 1. Find A when b = 2
1. A.12
2. B.14
3. C.16
4. D.11
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Answer: C 16
6.
An amount of # 600,000.00 was realized when a principal y was saved for 5% simple interest for 4 years, find the value of y
1. A.# 570,000
2. B.# 500,000
3. C.# 300,000
4. D.# 400,000
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Answer: B # 500,000
7.
Calculate the interior angle of a 5 - sided regular polygon
1. A.120º
2. B.90º
3. C.108º
4. D.180º
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Answer: C 108º
8.
Convert 137 to base 5
1. A.\(1022_5\)
2. B.\(2102_5\)
3. C.\(2210_5\)
4. D.\(2201_5\)
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Answer: A \(1022_5\)
9.
Express \(\sqrt[4]{0.16}\) in standard form
1. A.2 \(\times 10^{-\frac{1}{2}}\)
2. B.2 \(\times 10^2\)
3. C.2 \(\times 10^{-2}\)
4. D.2 \(\times 10^{\frac{1}{2}}\)
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Answer: A 2 \(\times 10^{-\frac{1}{2}}\)
10.
Find the coordinates of the midpoint of line PQ given P(-3, 4) and Q(5, 6).
1. A.(1, 4)
2. B.(4, 1)
3. C.(5, 1)
4. D.(1, 5)
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Answer: D (1, 5)
11.
Find the derivatives of y = sin 4x
1. A.-4sin x
2. B.-4cos x
3. C.4sin4x
4. D.4cos4x
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Answer: D 4cos4x
12.
Find the limit of y = \(\frac{(x^3 - 2x^2 + 6x - 12)}{(x - 2)}\) as x goes to 2.
1. A.Infinity
2. B.10
3. C.0
4. D.12
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Answer: B 10
13.
Find the number of permutations of the letters of the word SCHOOL.
1. A.600
2. B.360
3. C.480
4. D.300
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Answer: B 360
14.
Find the probability of getting an even number in a single throw of a six-sided die.
1. A.\(\frac{1}{4}\)
2. B.\(\frac{1}{5}\)
3. C.\(\frac{1}{2}\)
4. D.\(\frac{1}{3}\)
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Answer: C \(\frac{1}{2}\)
15.
Find the sum of the entries in the inverse of \(\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}\)
1. A.1
2. B.-1
3. C.2
4. D.0.5
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Answer: B -1
16.
Find the value of t for which ( \(\frac{1}{2}\) ) \(^{t - 1}\) = 64
1. A.-6
2. B.-5
3. C.-7
4. D.-4
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Answer: B -5
17.
From the diagram above, find the area of the triangle PQR
1. A.143cm \(^2\)
2. B.120cm \(^2\)
3. C.130cm \(^2\)
4. D.117cm \(^2\)
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Answer: C 130cm \(^2\)
18.
From the table above, determine the upper - class boundary of the modal class
1. A.21.5
2. B.30.5
3. C.20.5
4. D.10.5
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Answer: B 30.5
19.
From the table above, estimate the mode of the distribution.
1. A.37.8
2. B.38.5
3. C.29.5
4. D.34.5
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Answer: A 37.8
20.
Given that \(P = \begin{pmatrix} 1 & 3 \\ 2 & -5 \end{pmatrix}\) and Q = \(\begin{pmatrix} 3 & -7 \\ 1 & 2 \end{pmatrix}\) . Find P + 2Q
1. A.\(\begin{pmatrix} 7 & -11 \\ 4 & -1 \end{pmatrix}\)
2. B.\(\begin{pmatrix} 7 & -11 \\ 4 & -9 \end{pmatrix}\)
3. C.\(\begin{pmatrix} -7 & 11 \\ -4 & -1 \end{pmatrix}\)
4. D.\(\begin{pmatrix}11 & -7 \\ 4 & -1 \end{pmatrix}\)
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Answer: A \(\begin{pmatrix} 7 & -11 \\ 4 & -1 \end{pmatrix}\)
21.
Given that a * b = \(\frac{a + b}{\text{ab}}\) + (a - b). Find the value of 3 * 2
1. A.-6
2. B.\(\frac{11}{6}\)
3. C.\(\frac{6}{11}\)
4. D.-1 \(\frac{5}{6}\)
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Answer: B \(\frac{11}{6}\)
22.
Given that Cos A = \(\frac{12}{13}\) for 0 ≤ A ≤ 90º, find Tan A.
1. A.\(\frac{5}{12}\)
2. B.\(\frac{12}{13}\)
3. C.\(\frac{5}{13}\)
4. D.\(\frac{13}{12}\)
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Answer: A \(\frac{5}{12}\)
23.
Given the construction in the figure above. What is X \(\hat{Y}\) Z
1. A.60º
2. B.30º
3. C.75º
4. D.45º
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Answer: D 45º
24.
Given the progression 3, 5, 7, 9,.... . . . find an expression for the (n - 2) \(^{th}\) term of the progression.
1. A.\(2n - 1\)
2. B.\(2n + 1\)
3. C.\(2n + 3\)
4. D.\(2n - 3\)
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Answer: D \(2n - 3\)
25.
Given the triangle XYZ above, calculate the value of Cot \(\theta\) and the length XY, respectively
1. A.\(\frac{\sqrt{48}}{13}\) , \(\sqrt{48}\)
2. B.\(\frac{\sqrt{48}}{11}\) , \(\sqrt{48}\)
3. C.\(\frac{\sqrt{13}}{11}\) , \(\sqrt{13}\)
4. D.\(\frac{13}{\sqrt{48}}\) , \(\sqrt{48}\)
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Answer: B \(\frac{\sqrt{48}}{11}\) , \(\sqrt{48}\)
26.
If 54 \(_{ten}\) = X \(_{four}\) , find the value of X to 3 decimal point
1. A.132 \(_{four}\)
2. B.312 \(_{four}\)
3. C.123 \(_{four}\)
4. D.321 \(_{four}\)
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Answer: B 312 \(_{four}\)
27.
If A = \(\frac{\theta}{360}\) \(\pi r^2\) , make \(\theta\) the subject of the formula
1. A.\(\theta\) = \(\frac{360}{π A}\)
2. B.\(\theta\) = \(\frac{360A}{π \theta}\)
3. C.\(\theta\) = \(\frac{360 A}{\pi r^2}\)
4. D.\(\theta\) = \(\frac{360 r^2}{\pi A}\)
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Answer: C \(\theta\) = \(\frac{360 A}{\pi r^2}\)
28.
If cos \(\theta\) = \(\frac{\text{x}}{\text{y}}\) , find tan \(\theta\) in terms of x and y
1. A.\(\frac{\sqrt{y^2 - x^2}}{x}\)
2. B.\(\frac{\sqrt{y^2 + x^2}}{x}\)
3. C.\(\frac{\sqrt{y + x}}{x}\)
4. D.\(\frac{\sqrt{x^2 - y^2}}{x}\)
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Answer: A \(\frac{\sqrt{y^2 - x^2}}{x}\)
29.
If I is a 2 × 2 identity matrix, find the determinant of the matrix.
1. A.1
2. B.2
3. C.-1
4. D.0
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Answer: A 1
30.
If the probability of death is q and the probability of survival is p, find the probability of one death and one survival in an accident involving two persons
1. A.p/q
2. B.pq
3. C.p - q
4. D.p + q
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Answer: B pq
31.
In a basket of fruits, there are 6 grapes, 11 bananas, and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?
1. A.\(\frac{17}{30}\)
2. B.\(\frac{11}{30}\)
3. C.\(\frac{6}{30}\)
4. D.\(\frac{5}{30}\)
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Answer: A \(\frac{17}{30}\)
32.
In the Venn diagram above, the shaded region is
1. A.(P \(\cap\) Q)' \(\cap\) R
2. B.(P \(\cap\) Q) \(\cup\) R)
3. C.(P \(\cup\) Q) \(\cap\) R
4. D.(P U R)' \(\cap\) Q
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Answer: B (P \(\cap\) Q) \(\cup\) R)
33.
Integrate the function y = 3x \(^2\) + 2x - 5 with respect to x.
1. A.x \(^3\) + x \(^2\) - 5x + C
2. B.x \(^2\) + 2x \(^2\) - 5x + C
3. C.x \(^2\) + 2x - 5 + C
4. D.x \(^3\) + 2x - 5 + C
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Answer: A x \(^3\) + x \(^2\) - 5x + C
34.
Integrate y = 4x \(^3\) + 2x + cos x.
1. A.x \(^4\) - x \(^2\) - sin x + C
2. B.x \(^4\) + x \(^2\) + sin x + C
3. C.x \(^4\) - x \(^2\) + sin x + C
4. D.x \(^4\) + x \(^2\) - sin x + C
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Answer: B x \(^4\) + x \(^2\) + sin x + C
35.
Obtain the equation of a straight line passing through (3, 15) whose slope = 3 \(\frac{1}{5}\) .
1. A.5y + 16x + 27 = 0
2. B.5y - 16x + 27 = 0
3. C.5y - 16x - 27 = 0
4. D.5y + 16x - 27 = 0
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Answer: C 5y - 16x - 27 = 0
36.
P is partly constant and varies partly as Q. If P = 32 when Q = 16 and P = 20 when Q = 12, find P when Q = 28
1. A.68
2. B.64
3. C.66
4. D.62
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Answer: A 68
37.
Simplify - log \(_{10}\) 0.00001.
1. A.-5
2. B.-4
3. C.5
4. D.4
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Answer: C 5
38.
Simplify ( \(\frac{3}{4} \div 2\frac{1}{4}\) ) of 1 \(\frac{7}{11}\) (3 \(\frac{2}{3}\) - \(\frac{15}{6}\) )
1. A.\(\frac{7}{11}\) .
2. B.\(\frac{11}{7}\) .
3. C.\(\frac{5}{11}\) .
4. D.\(\frac{11}{5}\) .
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Answer: A \(\frac{7}{11}\) .
39.
Simplify 125 \(^{−\frac{1}{3}}\) × 49 \(^{−\frac{1}{2}}\) × 10 \(^0\)
1. A.\(\frac{1}{35}\)
2. B.\(\frac{1}{350}\)
3. C.350
4. D.35
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Answer: A \(\frac{1}{35}\)
40.
Solve for y in \(\sqrt{75}\) - \(\sqrt{12}\) + \(\sqrt{27}\) = y \(\sqrt{3}\)
1. A.\(4\sqrt{3}\)
2. B.\(5\sqrt{3}\)
3. C.\(3\sqrt{3}\)
4. D.\(6\sqrt{3}\)
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Answer: D \(6\sqrt{3}\)
41.
Solve the inequality 2x + 3 > 5x + 8
1. A.x > 1 \(\frac{2}{3}\)
2. B.x > -1 \(\frac{2}{3}\)
3. C.x < -1 \(\frac{2}{3}\)
4. D.x < 1 \(\frac{2}{3}\)
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Answer: C x < -1 \(\frac{2}{3}\)
42.
Solve the simultaneous equation \(\frac{\text{x}}{2}\) - \(\frac{\text{y}}{5}\) = 1 and y - \(\frac{\text{x}}{3}\) = 8
1. A.x = 10, y = -6
2. B.x = 10, y = 6
3. C.x = 6, y = 10
4. D.x = 10, y = 6
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Answer: C x = 6, y = 10
43.
Solve x \(^2\) + 3x - 4 ≤ 0
1. A.-4 \(\geq\) x \(\geq\) 1
2. B.4 \(\leq\) x \(\leq\) - 1
3. C.4 \(\geq\) x \(\geq\) 1
4. D.\(- 4 \leq x \leq 1\)
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Answer: A -4 \(\geq\) x \(\geq\) 1
44.
The average weight of 15 iron bars is 1000 kg. If the heaviest iron bar is removed, the average weight is reduced by 5 kg. Find the weight in kg of the heaviest iron bar.
1. A.1170kg
2. B.1270kg
3. C.1070kg
4. D.1370kg
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Answer: C 1070kg
45.
The chord of a circle of radius 17 cm is 30 cm long. Calculate the distance of the chord from the centre of the circle.
1. A.15cm
2. B.47cm
3. C.8cm
4. D.169cm
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Answer: C 8cm
46.
The determinant of the matrix \(A = \begin{pmatrix} -2 & 3 & 1 \\ p & 2 & 1 \\ 1 & 4 & 2\end{pmatrix}\) is -5. Find the value of p.
1. A.0
2. B.2
3. C.3
4. D.1
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Answer: C 3
47.
The figure above is a pie chart. Use it to find in degrees those who are doctors
1. A.60 \(^\circ\) .
2. B.72 \(^\circ\) .
3. C.90 \(^\circ\) .
4. D.84 \(^\circ\) .
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Answer: A 60 \(^\circ\) .
48.
The mean of the numbers 0, x + 2, 3x + 6, and 4x + 8 is 4, find the value of x.
1. A.\(\frac{2}{5}\)
2. B.\(\frac{2}{9}\)
3. C.0
4. D.4
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Answer: A \(\frac{2}{5}\)
49.
The second and fifth terms of a G.P are 1 and \(\frac{1}{8}\) respectively. Find the common ratio
1. A.\(\frac{1}{4}\)
2. B.\(\frac{1}{5}\)
3. C.\(\frac{1}{2}\)
4. D.\(\frac{1}{3}\)
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Answer: C \(\frac{1}{2}\)
50.
The set {1,2,3,4,5} is equivalent to
1. A.{2,3,1,4}
2. B.{1,2,3,4,5,5}
3. C.{1,2,3,4}
4. D.{4,3,1,5,2}
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Answer: D {4,3,1,5,2}
51.
The table above shows the weights of twelve mathematics students. Find the modal weight.
1. A.54
2. B.58
3. C.60
4. D.62
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Answer: B 58
52.
The word HANDIER can be arranged in how many ways
1. A.3080
2. B.2650
3. C.4050
4. D.5040
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Answer: B 2650
53.
What is the minimum value of y = 2 - 4x - 2x \(^2\)
1. A.4
2. B.5
3. C.3
4. D.2
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Answer: A 4
54.
Which of the following angles cannot be constructed using a protractor, a compass, and a sharpened pencil?
1. A.135°
2. B.90°
3. C.145°
4. D.60°
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Answer: C 145°
55.
Y is partly constant and partly varies as x. When x = 3, y = 7 and when x = 5, y = 11. Find the constants of variation.
1. A.2,3
2. B.1,2
3. C.3,2
4. D.3,4
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Answer: B 1,2

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