UTME Past Questions
Mathematics · 2022
40 questions
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1
/ 40
Question 01
Evaluate (11
2
× 11101
2
) + 101
2
A
101110
2
B
101100
2
C
1011100
2
D
111001
2
Question 02
(1
1
/
3
÷ 4/9) ÷ 5/16 × 4
1
/
6
simplifies to?
A
20
B
30
C
40
D
5
Question 03
If 3log
2
a + 5log
2
a – 6log
2
a = log
2
64, find the value of a.
A
10
B
2
C
10
D
8
Question 04
Solve the equation log
3
x = y = log
9
(2x-1)
A
x = 0, y = 0
B
x = 1, y = 11
C
x = 0, y = 1
D
x = 1, y = 0
Question 05
What must be subtracted from G(y) = 6y
3
+ 4y
2
– y + 5 so that it will be divisible by y-2?
A
57
B
67
C
43
D
33
Question 06
Which of the following represents (A′∩B)∩C on a Venn diagram?
A
B
C
D
Question 07
A binary operation is defined on the set R of real numbers by x*y = x+1- ½ xy for all a, b ∈ R. Find the value of √36 * √4.
A
-2
B
2
C
10
D
-10
Question 08
Obtain the equation of a line with y-intercept of 4/3 and is parallel to 5y – 4x + 7 = 0.
A
15y + 12x + 20 = 0
B
15y + 12x - 20 = 0
C
15y - 12x - 20 = 0
D
12y + 15x - 20 = 0
Question 09
Simplify 6/(√5 – √2)
2
A
(14+4√10)/3
B
(14-4√10)/3
C
7-2√10
D
7+2√10
Question 10
If the fifth term of an Arithmetic Progression is 11 and the 8th term is 26, find the first term.
A
19
B
-9
C
2
D
3
Question 11
A class consists of 8 boys and 7 girls. If two students are selected randomly to represent the class in a quiz competition, find the probability that both are of different sex.
A
8/15
B
7/15
C
4/15
D
2/7
Question 12
What is the nth term of a geometric progression (G.P) if the second term and the fourth term are 6 and 54 respectively?
A
2×3
n-1
B
2×3
n-1
C
2×3
2n
D
2×3
2n-1
Question 13
How many terms of the series 1+3+5+… are needed for the sum to reach 169?
A
12
B
13
C
14
D
11
Question 14
Find the differential coefficient of the curve 2x
4
-3x
3
+x
2
-1/x-6 at the point x = 1.
A
1
B
2
C
-1
D
-2
Question 15
If √(5+√2) / √(5-√2) = a+b√10, find a+b
A
3
B
9
C
2
D
10
Question 16
Find the mid-point of the line joining the point A(1/2, 1 2/3) and B(1/2, 1/3).
A
(5 2/3, 1/2)
B
(2/3, 5 2/3)
C
(7/12, 1)
D
(1/2, 5 2/3)
Question 17
If an exterior angle of a polygon is 30°, determine the sum of the interior angles.
A
2520°
B
1080°
C
1960°
D
1800°
Question 18
The average weight of 10 pieces of equipment is 120kg. If the heaviest is removed, the average weight is reduced by 3kg. What is the weight in kilograms of the heaviest equipment?
A
103
B
133
C
177
D
147
Question 19
A farmland of 160 acres was used in planting various fruits as shown in the figure below. What is the percentage of farmland used for planting oranges?
A
Option not provided in source
B
Option not provided in source
C
Option not provided in source
D
Option not provided in source
Question 20
Simplify log
3
40.5 - log
3
10.5
A
2-log
3
7
B
2+log
3
7
C
3-log
3
7
D
4-log
3
7
Question 21
Which of the following inequalities satisfies the number line below?
A
-6<x<3
B
-6≥x≤3
C
-6≤x<3
D
-6≥x≥3
Question 22
Evaluate ∫ sin 8x dx
A
8 sin8x + c
B
-1/8 cos8x + c
C
1/8 cos8x + c
D
8 sin x + c
Question 23
If f(x) = 2x
2
-3x+2, find the value of f(y+2).
A
2y
2
+3y-2
B
2y
2
+5y+4
C
2y
2
-3y-2
D
2y
2
-5y+12
Question 24
Find the value of sin
2
4x - cos
2
4x if x = π/6 rad.
A
√3/2
B
1
C
1/2
D
-1/2
Question 25
In how many ways can 10 people be arranged in a row such that 2 particular persons should always be together?
A
9! × 2!
B
8! × 2!
C
10! × 2!
D
12!
Question 26
In how many ways can 5 students and 3 lecturers be seated at a round table if all the lecturers do not sit together?
A
5040 ways
B
720 ways
C
4320 ways
D
120 ways
Question 27
For what value(s) of a is the inequality 0 < (a+3)/(a-1) satisfied?
A
-5 < a < -3
B
a > -3 and a > 1
C
a < -3 and a > 1
D
a < -3 and a > 5
Question 28
A salesman sold an article for ₦450 at a loss of 4%. At what price should he have sold the article to make a profit of 8%?
A
₦525.00
B
₦506.25
C
₦487.50
D
₦468.75
Question 29
Find the value of x for which the function x
2
+7x+5 is a minimum.
A
-7/2
B
7/2
C
3/2
D
-3/2
Question 30
Find the value of 81
x
/ (3
1+x
× 27
x
)
A
1/2
B
1/3
C
3
D
2
Question 31
Given that y is directly proportional to the square root of x, and y = 20 when x = 4, find x when y = 100.
A
400
B
100
C
300
D
200
Question 32
Evaluate (log3-log2)/(log√27-log√8)
A
3/2
B
2/3
C
-3/2
D
-2/3
Question 33
If the exterior angle of a regular polygon is 40°, calculate the size of the interior angle and the number of sides of the polygon.
A
40° and 9 sides
B
140° and 3 sides
C
40° and 3 sides
D
140° and 9 sides
Question 34
The probability of a boy passing a biology test is 2/3 and the probability of him passing a mathematics test is ¼. Find the probability of his failing both subjects.
A
1/3
B
2/3
C
1/4
D
1
Question 35
The probability of a boy passing a biology test is 2/3 and the probability of him passing a mathematics test is ¼. Find the probability of his failing both subjects.
A
1/3
B
2/3
C
¼
D
1
Question 36
Calculate the variance of the following data: 13, 7, 8, 9, 10, 11, 12
A
2
B
4
C
3
D
8
Question 37
Simplify (4/25)
-1/2
× 2
4
÷ (15/2)
-2
A
225
B
2250
C
150
D
1125
Question 38
The circumference of a circle is 56cm. Find the angle subtended at the centre by an arc of the circle of length 7cm.
A
30°
B
45°
C
60°
D
120°
Question 39
Evaluate lim
x→-3
(x
2
-9)/(x+3)
A
0
B
3
C
-3
D
1
Question 40
Find the value of (2+sin30°sin45°) / (sin45°+sin30°)
A
(7√(2+6))/2
B
(7√(2-6))/2
C
(2√(7+6))/7
D
(2√(7-6))/7
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