Mathematics past questions: JAMB UTME 2024

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

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

1.
( \(\sqrt{a} +\sqrt{8a})^2\) = 54 + b \(\sqrt{2}\) , a and b are positive integers. Find the value of a and the value of b.
1. A.a = 24, b = 6
2. B.a = 6, b = 2
3. C.a = 6, b = 24
4. D.a = 2, b = 6
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Answer: C a = 6, b = 24
2.
A bag contains 7 red and 4 black identical balls. Two balls were picked at random from the bag and replaced each time. Find the probability the two balls were of same colour.
1. A.\(\frac{54}{121}\)
2. B.\(\frac{65}{121}\)
3. C.\(\frac{29}{55}\)
4. D.\(\frac{27}{55}\)
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Answer: B \(\frac{65}{121}\)
3.
A binary operation * is defined on a set of real numbers by x*y = x \(^y\) for all values of x and y, if x * 2 = x, find the possible values of x.
1. A.0, 2
2. B.1, 2
3. C.0, 1
4. D.2, 2
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Answer: C 0, 1
4.
A boy bought Oranges at the rate of #24.00 for 5 and sold it at the rate of # 30.00 for 4 Oranges. Find the profit made of the ones sold
1. A.# 24.00
2. B.#30.00
3. C.# 10.80
4. D.#20.00
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Answer: C # 10.80
5.
Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8
1. A.\(\sqrt{2}\)
2. B.\(\sqrt{3}\)
3. C.2
4. D.3
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Answer: A \(\sqrt{2}\)
6.
Convert the number 10111.11 \(_{two}\) to a mixed number.
1. A.23 \(\frac{1}{4}\)
2. B.23 \(\frac{3}{4}\)
3. C.22 \(\frac{1}{4}\)
4. D.24 \(\frac{3}{4}\)
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Answer: B 23 \(\frac{3}{4}\)
7.
Differentiate Cos25º - Sin 25º
1. A.- ( Sin25º + Cos25º)
2. B.- ( Sec25 + Cot25)
3. C.- ( Cot25 + Sec25)
4. D.- ( Sin25 + Sec25)
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Answer: A - ( Sin25º + Cos25º)
8.
Differentiate y = (5x + 1) \(^4\)
1. A.20 (5x + 1) \(^3\)
2. B.4(5x + 1) \(^3\)
3. C.5(5x + 1) \(^3\)
4. D.(5x) \(^3\)
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Answer: A 20 (5x + 1) \(^3\)
9.
Evaluate the determinant of the matrix M = \(\begin{bmatrix}3 & 4 & 6\\2 & 1 & -1\\-1 & 3 & 5\end{bmatrix}\)
1. A.20
2. B.25
3. C.30
4. D.35
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Answer: C 30
10.
Find the 7 \(^{th}\) term of the sequence -10, 50, -250 ...........
1. A.165250
2. B.156250
3. C.-156250
4. D.-165,250
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Answer: C -156250
11.
Find the amount if simple interest is paid yearly at 5% per annum for 3 years, on a principal of # 200,000.00
1. A.# 23, 000.00
2. B.# 30,000.00
3. C.# 300,000.00
4. D.# 230,000.00
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Answer: D # 230,000.00
12.
Find the angle subtended by an arc 33cm long of a circle of diameter 28cm.
1. A.105 \(^0\)
2. B.115 \(^0\)
3. C.120 \(^0\)
4. D.135 \(^0\)
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Answer: D 135 \(^0\)
13.
Find the perimeter of a triangle whose vertices pass through ( 3, 2), (4, 5) and (6, 2) in surd form.
1. A.3 + \(\sqrt{12} + \sqrt{13}\)
2. B.3 - \(\sqrt{10} + \sqrt{13}\)
3. C.3 + \(\sqrt{10} + \sqrt{13}\)
4. D.3 - \(\sqrt{12} + \sqrt{13}\)
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Answer: C 3 + \(\sqrt{10} + \sqrt{13}\)
14.
Find the roots of x \(^3\) - 19x - 30=0
1. A.-5, 3, and 2
2. B.5, 3, and -2
3. C.5, -3 and -2
4. D.-5, -3 and 2
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Answer: C 5, -3 and -2
15.
Find the variance of a group of data whose standard deviation is 12.34 to the nearest whole number.
1. A.150
2. B.151
3. C.152
4. D.153
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Answer: C 152
16.
Find x if \(\frac{16^{2 + x}}{4} = 64^x\)
1. A.3
2. B.- 3
3. C.5
4. D.- 5
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Answer: A 3
17.
From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?
1. A.350 ways
2. B.420 ways
3. C.550 ways
4. D.720 ways
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Answer: A 350 ways
18.
From the figure above, find the length of Chord PQ
1. A.17cm
2. B.18cm
3. C.7cm
4. D.9cm
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Answer: D 9cm
19.
From the top of a building 10m high, the angle of elevation of a fruit on top of a tree 25m is 30º. Calculate the horizontal distance between the building and the tree.
1. A.15 \(\sqrt{3}\) m
2. B.5 \(\sqrt{3}\) m
3. C.25 \(\sqrt{3}\) m
4. D.30 \(\sqrt{3}\) m
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Answer: A 15 \(\sqrt{3}\) m
20.
Given P = \(\begin{bmatrix}1 & 2\\2 & 3\end{bmatrix}\) , find P \(^2\) - 4P - I where I is the identity matrix
1. A.\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
2. B.\(\begin{bmatrix}0 & 0\\0 & 0\end{bmatrix}\)
3. C.\(\begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}\)
4. D.\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)
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Answer: B \(\begin{bmatrix}0 & 0\\0 & 0\end{bmatrix}\)
21.
Given that P is the set of all prime numbers between 0 and 10, and Q is the set of all odd numbers between 0 and 10. Find the union of elements in P that are not in Q and the elements in Q that are not in P.
1. A.{2, 9}
2. B.{ 9}
3. C.{1, 9}
4. D.{1, 2, 9}
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Answer: D {1, 2, 9}
22.
How many proper and improper subsets are there in the set K = { a, b, c, d, e}?
1. A.10
2. B.25
3. C.32
4. D.50
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Answer: C 32
23.
Identify the equation of the shaded region in the given graph
1. A.y > 1
2. B.x < 1
3. C.X > 1
4. D.y < 1
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Answer: C X > 1
24.
If A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\) . Find A \(^T\) + B, ( where T means transpose)
1. A.\(\begin{pmatrix}4 & 8\\3 & 2\\4 & 1\end{pmatrix}\)
2. B.\(\begin{pmatrix}4 & -8\\3 & 2\\4 & 1\end{pmatrix}\)
3. C.\(\begin{pmatrix}4 & 8\\4 & -2\\3 & 1\end{pmatrix}\)
4. D.\(\begin{pmatrix}4 & 8\\2 & 3\\4 & 1\end{pmatrix}\)
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Answer: D \(\begin{pmatrix}4 & 8\\2 & 3\\4 & 1\end{pmatrix}\)
25.
If B varies inversely as c \(^{\frac{1}{3}}\) and C = 27 when B = 2, find the value of the constant of proportionality K.
1. A.3
2. B.6
3. C.9
4. D.12
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Answer: B 6
26.
If p * q = 2p + pq + q, find p when ( p * 2) - (p * 1) = 40
1. A.39
2. B.40
3. C.41
4. D.42
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Answer: A 39
27.
If tan \(\theta\) = \(\frac{8}{15}\) , simplify \(\frac{ Sin\theta - Cos\theta}{Sin^2\theta - Sin\theta}\)
1. A.\(\frac{-119}{72}\)
2. B.\(\frac{119}{72}\)
3. C.\(\frac{-7}{17}\)
4. D.\(\frac{8}{17}\)
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Answer: B \(\frac{119}{72}\)
28.
If x is inversely proportional to y and x = 9 when y = 4, find the law containing x and y
1. A.x = \(\frac{16}{y}\)
2. B.x = \(\frac{36}{y}\)
3. C.x = \(\frac{y}{36}\)
4. D.x = \(\frac{13}{y}\)
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Answer: B x = \(\frac{36}{y}\)
29.
In how many ways can 6 people sit around a table
1. A.120
2. B.240
3. C.60
4. D.30
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Answer: A 120
30.
In how many ways can a committee of 5 be selected from a group of 7 males and 3 females, if the committee must have one female?
1. A.105ways
2. B.135 ways
3. C.210 ways
4. D.231 ways
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Answer: A 105ways
31.
In the diagram above, T represents the construction of angle .....
1. A.15 \(^0\)
2. B.30 \(^0\)
3. C.45 \(^0\)
4. D.60 \(^0\)
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Answer: B 30 \(^0\)
32.
Let A = \(\begin{pmatrix}2 & -4 & 3\\5 & 1 & 0\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4 & -2\\-3 & 3 & -1\end{pmatrix}\) . Find A + 2B
1. A.\(\begin{pmatrix}4 & 4 & -1\\-1 & 7 & -2\end{pmatrix}\)
2. B.\(\begin{pmatrix}-1 & 4 & -1\\4 & 7 & -2\end{pmatrix}\)
3. C.\(\begin{pmatrix}4 & 4 & -1\\7 & 7 & -2\end{pmatrix}\)
4. D.\(\begin{pmatrix}-1 & 7 & -2\\4 & 4 & -2\end{pmatrix}\)
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Answer: A \(\begin{pmatrix}4 & 4 & -1\\-1 & 7 & -2\end{pmatrix}\)
33.
Make q the subject of the relation t = \(\sqrt{(\frac{pq}{r} - r^2q)}\)
1. A.q = \(\frac{rt^2}{p - r^3}\)
2. B.q = \(\frac{p - r^3}{rt^2}\)
3. C.q = \(\frac{t^2}{p - r^3}\)
4. D.q = \(\frac{rt}{p - r^3}\)
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Answer: A q = \(\frac{rt^2}{p - r^3}\)
34.
P(x, 4) and Q( 10, 8) are two points joined by a straight line in a plane. If the midpoint of the line is (9, 6), find the value of x.
1. A.12
2. B.9
3. C.8
4. D.7
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Answer: C 8
35.
PQR is a triangle such that |PQ| = |QR| = 8cm and QPR = 60º. Find the area of \(\angle\) PQR
1. A.16 \(\sqrt{3}cm^2\)
2. B.16 \(\sqrt{2}cm^2\)
3. C.8 \(\sqrt{3}cm^2\)
4. D.16 \(\sqrt{2}cm^2\)
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Answer: A 16 \(\sqrt{3}cm^2\)
36.
Simplify \(\frac{ 5 + \sqrt{7}}{3 + \sqrt{7}}\)
1. A.17 - \(\sqrt{7}\)
2. B.4 - \(\sqrt{7}\)
3. C.7 - \(\sqrt{7}\)
4. D.15 - \(\sqrt{7}\)
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Answer: B 4 - \(\sqrt{7}\)
37.
Solve 16 \(^x\) = 0.25
1. A.- \(\frac{1}{2}\)
2. B.\(\frac{1}{4}\)
3. C.- \(\frac{1}{4}\)
4. D.\(\frac{1}{2}\)
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Answer: A - \(\frac{1}{2}\)
38.
Subtract 14256 \(_{seven}\) from 20045 \(_{seven}\)
1. A.1256 \(_{seven}\)
2. B.2456 \(_{seven}\)
3. C.1356 \(_{seven}\)
4. D.2465 \(_{seven}\)
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Answer: B 2456 \(_{seven}\)
39.
The average age of the four female teachers in a school is 40 and the average age of eight male teachers in the school is 25. Calculate the average age of the teachers in the school.
1. A.20
2. B.31
3. C.32
4. D.30
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Answer: D 30
40.
The graph above represents inequalities
1. A.3x +4y ≥12, x >0, y > 0
2. B.3x + 4y \(\leq\) 12, x ≥ 0, y ≥ 0
3. C.3x + 4y <12, x \(\leq\) 0, y ≥ 0
4. D.3x + 4y < 12, x ≥ 0, y ≥ 0
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Answer: A 3x +4y ≥12, x >0, y > 0
41.
The mean of the numbers 13, 16, x, 18, 21, 2x, 35, is 22. Find the value of x
1. A.16
2. B.17
3. C.23
4. D.25
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Answer: B 17
42.
The number of 144 students who registered for mathematics, physics, and chemistry in an examination are shown in the Venn diagram. How many registered for physics and mathematics?
1. A.16
2. B.24
3. C.62
4. D.4
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Answer: B 24
43.
The ratio of men to women in a 20-member committee is 3:1. How many women must be added to the committee to make the ratio of men to women 3:2?
1. A.2
2. B.5
3. C.7
4. D.8
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Answer: B 5
44.
The scores of students in a test are recorded as follows: 4, 3, 3, 2, 1, 2, 5, 7, 8, 3, and 5. Find the mode of the mark.
1. A.2
2. B.3
3. C.4
4. D.5
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Answer: B 3
45.
The sum to infinity of a GP is 100, find its first term if the common ratio is - \(\frac{1}{2}\)
1. A.150
2. B.155
3. C.160
4. D.165
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Answer: A 150
46.
The Venn diagram above shows the number of students offering physics and chemistry in a class of 65. What is the probability that a student selected from the class offers physics and chemistry if every students offers at least one subject?
1. A.\(\frac{2}{13}\)
2. B.\(\frac{5}{13}\)
3. C.\(\frac{2}{5}\)
4. D.\(\frac{3}{13}\)
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Answer: A \(\frac{2}{13}\)
47.
The weights of 15 students in a class are given as 25, 30, 32, 30, 42, 45, 48, 50, 52, 51, 42, 38, 40, and 42. What is the mode of the given data?
1. A.51
2. B.45
3. C.42
4. D.25
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Answer: C 42
48.
U varies directly as the square root of V when U = 24, V = 9, find the value of V when U = 16.
1. A.0.32
2. B.4
3. C.6
4. D.0.25
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Answer: B 4
49.
Which of the following is a measure of central tendency?
1. A.Standard deviation
2. B.Range
3. C.Variance
4. D.Mean
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Answer: D Mean
50.
y is inversely proportional to x and y = 4, when x = \(\frac{1}{2}\) , find x when y = 10
1. A.2
2. B.10
3. C.\(\frac{1}{5}\)
4. D.\(\frac{1}{10}\)
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Answer: C \(\frac{1}{5}\)

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