Mathematics past questions: JAMB UTME 2022

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

Sit this paper

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

1.
A poultry farmer realized 200 eggs from his birds and sold 5 \(\frac{1}{2}\) crates of eggs. What percentages of eggs are left?
1. A.82.5%
2. B.15%
3. C.17.5%
4. D.85%
Show answerHide answer
Answer: C 17.5%
2.
A rectangular pyramid has an area 24cm \(^2\) and height 7.5cm. Find its volume?
1. A.65.0cm \(^3\)
2. B.70.5cm \(^3\)
3. C.56.5cm \(^3\)
4. D.60.0cm \(^3\)
Show answerHide answer
Answer: D 60.0cm \(^3\)
3.
Calculate the median of 14, 17, 10, 13, 18 and 10.
1. A.12.5
2. B.13.5
3. C.13.2
4. D.14.5
Show answerHide answer
Answer: B 13.5
4.
Evaluate \((101_{two})^3\)
1. A.\(111101_{two}\)
2. B.\(11111101_{two}\)
3. C.\(1111101_{two}\)
4. D.\(11001_{two}\)
Show answerHide answer
Answer: C \(1111101_{two}\)
5.
Evaluate \(^{n^2 + 1}\) C \(_{n+5}\) if n = 3
1. A.55
2. B.45
3. C.35
4. D.25
Show answerHide answer
Answer: B 45
6.
Evaluate Log \(_2\) 8√2
1. A.3.0
2. B.4.5
3. C.3.5
4. D.2.5
Show answerHide answer
Answer: C 3.5
7.
Factorize 4a \(^2\) - 9b \(^2\)
1. A.(2a-3b) (2a+3b)
2. B.(2a-b) (2a+3b)
3. C.(2a-3b) (a+3b)
4. D.(a-3b) (a+3b)
Show answerHide answer
Answer: A (2a-3b) (2a+3b)
8.
Find the determinant of the matrix A = \(\begin{pmatrix} 2 & 3 \\ 1 & 3 \end{pmatrix}\)
1. A.4
2. B.2
3. C.5
4. D.3
Show answerHide answer
Answer: D 3
9.
Find the equation of a straight line parallel to the line 2x - y = 5 and having intercept of 5
1. A.2x + y = 5
2. B.2x + y = -5
3. C.2x - y = -5
4. D.2x - y = 5
Show answerHide answer
Answer: C 2x - y = -5
10.
Find the length of a chord 3cm from the centre of a circle of radius 5cm
1. A.8cm
2. B.5.6cm
3. C.7cm
4. D.6.5cm
Show answerHide answer
Answer: A 8cm
11.
find the limit of y = \(\frac{x^3 + 6x - 7}{x-1}\) as x tends to 1
1. A.9
2. B.8
3. C.0
4. D.7
Show answerHide answer
Answer: A 9
12.
Find x if the mean of 2x, 4x, 2x - 13 and 6x is 4.
1. A.1.5
2. B.2.0
3. C.1.0
4. D.0.5
Show answerHide answer
Answer: B 2.0
13.
Given that r = \(\sqrt \frac{3v}{\pi h}\) , make v the subject of the formula
1. A.v = 3 \(πr^2\) h
2. B.v = \(\frac{πrh}{3}\)
3. C.v = \(\frac{πr^2h}{3}\)
4. D.v = 3πrh
Show answerHide answer
Answer: C v = \(\frac{πr^2h}{3}\)
14.
Given that S = \(3t^{2}\) + 5t - 10 is displacement of a particle in metres, calculate it initial velocity.
1. A.10m/s
2. B.2m/s
3. C.5m/s
4. D.6m/s
Show answerHide answer
Answer: B 2m/s
15.
If 8, p, q and 26 is an A.P. Find the values of p and q
1. A.p = 14 and q = 14
2. B.p = 20 and q = 14
3. C.p = 20 and q = 20
4. D.p = 14 and q = 20
Show answerHide answer
Answer: A p = 14 and q = 14
16.
If A = \(\begin{pmatrix} 2 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \\ 4 & 2 \end{pmatrix}\) . Find AB
1. A.\(\begin{pmatrix} 18 & 6 \\ 12 & 10 \\ 10 & 6 \end{pmatrix}\)
2. B.\(\begin{pmatrix} 10 & 6 \\ 13 & 10 \\ 12 & 6 \end{pmatrix}\)
3. C.\(\begin{pmatrix} 10 & 6 \\ 12 & 10 \\ 11 & 6 \end{pmatrix}\)
4. D.\(\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}\)
Show answerHide answer
Answer: D \(\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}\)
17.
If a dress is sold for #3800.00 at 20% discount. what is its original price?
1. A.#3,000.00
2. B.#4,000.00
3. C.#5,000.00
4. D.#4,750.00
Show answerHide answer
Answer: D #4,750.00
18.
If a fair coin is tossed twice, what is the probability of obtaining at least one head?
1. A.0.25
2. B.0.75
3. C.0.5
4. D.0.33
Show answerHide answer
Answer: B 0.75
19.
If n(P) = 20 and n(Q) = 30 and n(PuQ) = 40, find the value n(PnQ)
1. A.10
2. B.30
3. C.15
4. D.40
Show answerHide answer
Answer: A 10
20.
If sec \(^2\) θ + tan \(^2\) θ = 3, then the angle θ is equal to?
1. A.90º
2. B.30º
3. C.45º
4. D.60º
Show answerHide answer
Answer: C 45º
21.
If sin θ = - \(\frac{3}{5}\) and θ lies in the third quadrant, find cos θ
1. A.\(\frac{4}{5}\)
2. B.- \(\frac{5}{4}\)
3. C.\(\frac{5}{4}\)
4. D.- \(\frac{4}{5}\)
Show answerHide answer
Answer: D - \(\frac{4}{5}\)
22.
If the mean of 2, 5, (x+1), (x+2), 7 and 9 is 6. Find the median
1. A.5.5
2. B.5
3. C.6.5
4. D.6
Show answerHide answer
Answer: C 6.5
23.
If y varies inversely as x and x = 3 when y =4. Find the value of x when y = 12
1. A.4
2. B.1
3. C.2
4. D.3
Show answerHide answer
Answer: B 1
24.
In how many ways can the letter of ZOOLOGY be arranged?
1. A.720
2. B.360
3. C.840
4. D.120
Show answerHide answer
Answer: C 840
25.
In the diagram above angle LNM and angle YNZ are represented by g and h respectively. Find ∠MNY
1. A.180º - gº - hº
2. B.360º - (g-h)º
3. C.180º - (g-h)º
4. D.360º - gº - hº
Show answerHide answer
Answer: A 180º - gº - hº
26.
In the diagram above, XY = 8cm and OX = 5cm. Find Oz
1. A.9cm
2. B.3.4cm
3. C.9.1cm
4. D.3cm
Show answerHide answer
Answer: D 3cm
27.
Integrate (2x+1) \(^3\)
1. A.\(\frac{{2x+1}^3}{8}\) + C
2. B.\(\frac{{2x+1}^4}{8}\) + C
3. C.\(\frac{{2x+1}^4}{4}\) + C
4. D.\(\frac{{2x+1}^2}{6}\) + C
Show answerHide answer
Answer: B \(\frac{{2x+1}^4}{8}\) + C
28.
Let (*) be a binary operation on a natural number defined by a * b = a - b + (ab) \(^2\) , then find 3 * 5
1. A.223
2. B.232
3. C.32
4. D.-232
Show answerHide answer
Answer: A 223
29.
Mr Adu spends his annual salary on food(f), rent(r), car maintenance, gifts(g), savings(s) and some miscellaneous (m) as indicate in the table below:
F R C G S M
28% 15% 20% 14% 10% 13%
If the above information is represented on a pie chart. What angle represents his spending on food? [ d 120.5 ]
1. A.108.5
2. B.100.8
3. C.98.8
4. D.120.5
Show answerHide answer
Answer: B 100.8
30.
Simplify \(\frac{1}{3-√2}\) in the form of p + q√2
1. A.\(\frac{7}{3}\) - \(\frac{1}{7√2}\)
2. B.\(\frac{7}{3}\) + \(\frac{1}{7√2}\)
3. C.\(\frac{3}{7}\) - \(\frac{1}{7√2}\)
4. D.\(\frac{3}{7}\) + \(\frac{√2}{7}\)
Show answerHide answer
Answer: D \(\frac{3}{7}\) + \(\frac{√2}{7}\)
31.
Solve for k in the equation \(\frac{1}{8}^{k+2}\) = 1
1. A.2
2. B.-4
3. C.-2
4. D.4
Show answerHide answer
Answer: C -2
32.
The 10th term of an AP is 32. If the first term is 3/2, what is the 4th term?
1. A.35/3
2. B.64
3. C.16
4. D.35/2
Show answerHide answer
Answer: A 35/3
33.
The coordinates of the mid-point of the line joining the points (-3,5) and (2,10) is given by?
1. A.( \(\frac{1}{2}\) , \(\frac{15}{2}\) )
2. B.( \(\frac{1}{2}\) , \(\frac{-15}{2}\) )
3. C.( \(\frac{-1}{2}\) , \(\frac{-15}{2}\) )
4. D.( \(\frac{-1}{2}\) , \(\frac{15}{2}\) )
Show answerHide answer
Answer: D ( \(\frac{-1}{2}\) , \(\frac{15}{2}\) )
34.
The cost C of running a school is directly proportional to the number of students N, if 20 students cost #10,000, How many students can #1,000,000 cover?
1. A.3000
2. B.1000
3. C.2000
4. D.4000
Show answerHide answer
Answer: C 2000
35.
The equivalent of (10110.011) \(_2\) in base 10 is?
1. A.26.325
2. B.24.372
3. C.42.443
4. D.22.375
Show answerHide answer
Answer: D 22.375
36.
The locus of points equidistant from a fixed point.
1. A.circle
2. B.perpendicular lines
3. C.straight line
4. D.bisector
Show answerHide answer
Answer: A circle
37.
The number line represented by the inequality
1. A.x≤2
2. B.x<2
3. C.x≥2
4. D.x>2
Show answerHide answer
Answer: C x≥2
38.
The shaded portion in the venn diagram above represents?
1. A.F - (E n F) - (G n F)
2. B.E' n F n G'
3. C.E u F u G
4. D.F
Show answerHide answer
Answer: B E' n F n G'
39.
Three times a certain number (x), minus 2 is less than the number minus 6.Find the possible values of x.
1. A.x <-2
2. B.x>2
3. C.x>-2
4. D.x<2
Show answerHide answer
Answer: A x <-2
40.
What will be the result obtained when the numerator of \(\frac{96}{50}\) is decreased by 37.5% and its denominator decreased by 20%.
1. A.1.5
2. B.\(\frac{5}{2}\)
3. C.\(\frac{96}{48}\)
4. D.0.5
Show answerHide answer
Answer: A 1.5

Printing is turned off here to protect the question bank. Get the SmarTest app to study offline.

More free Mathematics papers

JAMB Mathematics 1978–2020 is in the app

The latest five years of each paper are free here. The SmarTest app has every year we hold, a worked explanation for each answer, and timed mock exams. It works offline.

Get the app

Android, Windows, Mac and Linux

F	R	C	G	S	M
28%	15%	20%	14%	10%	13%