UTME Past Questions
Mathematics · 2023
40 questions
Progress
1
/ 40
Question 01
Evaluate 4610
8
– 2675
8
A
1713
8
B
1731
8
C
1935
8
D
2025
8
Question 02
A
2
8
/
15
B
5
8
/
15
C
6
7
/
8
D
8
1
/
3
Question 03
A
6
B
2
C
3
D
4
Question 04
A
2
B
-1
C
1
D
-2
Question 05
A
5
/
6
√5
B
6
/
25
√5
C
5
/
11
√5
D
6
/
5
√5
Question 06
Solve for x in 27
x
2
= 3
8x+3
A
1 and 3
B
–1 and 1/3
C
–1/3 and 1
D
0 and 1
Question 07
Solve the equation log
2
x
+ log
x
4
= 3
A
1 and 2
B
2 and 4
C
1 twice
D
2 twice
Question 08
Find the remainder when the polynomial 4x
3
-6x+1 is divided by 2x-1
A
2
1
/2
B
2
C
1/2
D
3
Question 09
Find the range of value of y for which (2+5y)/2 – (4+3y)/5 < y + 2
A
y > 2
B
y > –2
C
y < 2
D
y < 1
Question 10
The simple interest on a sum of money invested at 30% per annum for 4 years is ₦50,000. Find the principal.
A
41666.67
B
4166.67
C
416.67
D
416,666.67
Question 11
The first and last terms of an arithmetic progression (AP) are 5 and 89 respectively. If the sum of the AP is 611, find the common difference.
A
5
B
13
C
10
D
7
Question 12
The third and seventh terms of a geometric progression (GP) are 72 and 8/9 respectively. Find the fifth term.
A
81
B
648
C
8
D
24
Question 13
In a group of 72 students, 47 study Physics, 59 study Chemistry, and 42 study both subjects. How many students do not study any of the subjects?
A
8
B
25
C
13
D
34
Question 14
An operation ⊗ is defined on the set of real numbers R such that if x, y ∈ R, then x ⊗ y = (x+y)/2. Find (1/2 ⊗ 1/3) ⊗ 1
A
29/2
B
17/2
C
5/12
D
½
Question 15
A
x = 2
B
x = -2
C
x = -8/5
D
8/5
Question 16
Find the range of the value of y for which (2+5y)/2 – (4+3y)/5 < y + 2
A
y > 2
B
y > -2
C
y < 2
D
y > 1
Question 17
One of the parallel sides of a trapezium is longer than the other by 6cm. If the area and height of the trapezium are 180cm
2
and 9cm respectively, find the length of the shorter parallel side.
A
23cm
B
17cm
C
18cm
D
24cm
Question 18
What is the number of sides of a polygon whose sum of interior angles differ by 540°?
A
8
B
15
C
7
D
5
Question 19
Find the volume of a cone whose slant height is 17cm and radius of base is 8cm [Take π = 22/7]
A
893.5cm
3
B
1003.5cm
3
C
2003.5cm
3
D
4691.5cm
3
Question 20
If the volumes of two spheres are in the ratio 64:27, what is the ratio of their surface areas?
A
4:3
B
9:16
C
16:9
D
3:4
Question 21
If a solid metal cylinder of radius 7.5cm and height 10cm is melted and recast into a sphere, what then is the radius of the sphere?
A
1/3cm
B
13/2
C
7/8cm
D
15/2cm
Question 22
Which of the following represents (A∪B)∩(A∩B) on a Venn diagram?
A
B
C
D
Question 23
Evaluate 10!/2!7!
A
360
B
36
C
40
D
100
Question 24
Find the equation of a line that passes through the point (1,2) and whose gradient is 1/3
A
3y + x = 5
B
3y + x = 7
C
3y - x = 7
D
y - 3x = 7
Question 25
What is the value of n if n/9! + 1/8! = 100/10!?
A
4
B
3
C
2
D
1
Question 26
Find the variance of the observations 4.1, 4, 4.2, 4.3
A
0.3
B
0.28
C
0.31
D
0.27
Question 27
What is the value of Lim
x→3
(x
2
-9)/(x-3)?
A
Infinity
B
0
C
3
D
6
Question 28
If |7x-4| < 3, then
A
-3 ≤ x ≤ 3
B
x ≤ 1/7
C
1/7 ≤ x ≤ 1
D
1/7 ≤ x < 1
Question 29
A committee of five is to be selected from a group of 8 men and 10 women. How many ways can this be done if the committee must consist of 2 men and 3 women?
A
308
B
3360
C
252
D
120
Question 30
Simplify (cos 60° + sin 30°) / (1 + cos 45°)(1 - sin 45°)
A
-1
B
1
C
2
D
-2
Question 31
Integrate ∫ x/(x
2
+1) dx
A
1/2 ln(x
2
+1)+c
B
ln(x
2
+1)+c
C
2ln(x
2
+1)
D
x/(x
3
+1)+c
Question 32
Obtain the minimum value of the function y = 2x
3
-3x
2
-36x+6
A
-2
B
3
C
-7
D
80
Question 33
By selling an article for ₦2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:
A
₦2,500
B
₦2,700
C
₦2,800
D
₦3,000
Question 34
A
2
B
½
C
4
D
1
Question 35
A
30°
B
120°
C
60°
D
300°
Question 36
The letters of the word UNIVERSITY are cut and put into a box. One letter is drawn at random from the box. Find the probability of drawing a vowel.
A
5/9
B
2/5
C
½
D
2/9
Question 37
In a class of 60 pupils, the statistical distribution of the numbers of pupils offering Biology, History, French, Geography, and Additional Mathematics is as shown in the pie chart. How many pupils offer Additional Mathematics?
A
15
B
10
C
18
D
12
Question 38
In the figure, the area of the shaded segment is
A
3π
B
9
√3
/
4
C
3π-3
√3
/
4
D
3{
√3
/
4
- π}
Question 39
Simplify 0.0324 × 0.00064 / 0.48 × 0.012
A
3.6×10
2
B
3.6×10
-2
C
3.6×10
-3
D
3.6×10
-4
Question 40
Convert 241 in base 5 to base 8
A
71
8
B
107
8
C
176
8
D
241
8
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