UTME Past Questions
Mathematics · 2024
40 questions
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1
/ 40
Question 01
Differentiate with respect to x, y = sin2x -- cos2x
A
2sinx+cosx
B
2cos2x+sin2x
C
2cos2x+2sin2x
D
2sinx-cosx
Question 02
What is the perimeter of the triangle vertices A(3, 2), B(3, 5) AND (6, 2)
A
6 + 3√2
B
6+2√3
C
2+√10
D
3+√2
Question 03
What is the result of subtracting 142567 from 20045
7
?
A
5328
7
B
5640
7
C
2456
7
D
2546
7
Question 04
Convert 10111.11
2
to a number in base 10
A
23.75
10
B
15.23
10
C
15.75
10
D
75.23
10
Question 05
Evaluate (8+√28)/(2+√7)
A
(4-2√3)/3
B
(4√3+2)/3
C
(-4√3-2)/3
D
(4√7-2)/3
Question 06
If the total sum of interior angles of a regular polygon with n sides is 1260. Calculate the value of one interior angle
A
120
0
B
126
0
C
140
0
D
146
0
Question 07
The sum to infinity of a Geometric progression (G.P) is 100. If the common ratio is -- ½ , find the first term
A
150
B
200/3
C
150/3
D
133.33
Question 08
A goat tied with a rope to a wooden pole is grazing in a field. If the length of the rope is 6m and the goat makes from one point to another an arc with an angle of 700. Find the area of the grazing portion of the goat.
A
21m
B
22m
C
20m
D
24m
Question 09
The average age of 4 female teachers in a school is 40, and the average of 8 male teachers in the school is 25. What is the average age of all the teachers in school?
A
28
B
25
C
30
D
31
Question 10
A committee of 3 men and 3 women is to be formed from a group of 5 men and 3 women. How many different ways can this committee be formed?
A
30
B
20
C
10
D
150
Question 11
Find the mean deviation of the set of numbers 2,5, (c+2),7,(c+1).if their mean is equal to 6.
A
2.0
B
2.4
C
1.6
D
2.2
Question 12
(diagram)The pie chart shows the domestic expenditure of a household in a month. If the total monthly income of the household is #120,000, what is the total amount per month the household spends on food and medical combined?
A
76,000
B
66,000
C
65,000
D
48,000
Question 13
Find the value of x if the determinant of ■(5&x @3&x)is 14
A
7
B
4
C
28
D
3
Question 14
Simplify 51/2 - (3 1¦3 x2 1¦4) + 1/2
A
1/2
B
3/5
C
- 1/2
D
-1 1/2
Question 15
What is the equivalent of 41043 in octal?
A
117
8
B
171
8
C
1171
8
D
1711
8
Question 16
Integrate (2x+1)/2x with respect to x
A
x+1/2 ln|x|+c
B
1+1/2x+c
C
x+2ln 1/2x|x|+c
D
x+ln|2x|+c
Question 17
If #225 yields #27 simple interest in x years at the rate of 4% per annum, find x.
A
1 year
B
2 years
C
3 years
D
4 years
Question 18
If 121
three
-- X
three
= 11
three
find X
A
1101
3
B
101
3
C
11
3
D
110
3
Question 19
The midpoint of two points (m, 6) and (6, n) is (5, 0). Find the values of m and n respectively
A
(4, 1)
B
(-4, 6)
C
(4, -6)
D
(-6, 4)
Question 20
The 3rd and 6th terms of a geometrical progression (G.P) are 108 and 32 respectively. Find the common ration
A
∓1/3
B
∓2/5
C
∓1/2
D
∓2/3
Question 21
Find the positive value of k if the standard deviation of the data 2k, 3k, 5k, 4k and 6k is √2
A
1
B
0.5
C
3
D
4
Question 22
Find the equation of the line through (5, 7) and parallel to the line 7x + 5y = 12.
A
5x + 7y = 20
B
7x + 5y = 70
C
Xy = 7
D
15x + 17y = 9
Question 23
A cylindrical container has radius of 3cm and height 12cm. calculate its total surface area with both ends closed. (π=22/7)
A
251.88cm
2
B
94.29cm
2
C
282.86cm
2
D
88.32cm
2
Question 24
The ratio of the exterior angle to the interior angle of a regular polygon is 1:19. How many sides ha the polygon?
A
30
B
40
C
36
D
38
Question 25
is picked at random from the bag, what is the chance that it is red or green?
A
189/225
B
11/225
C
8/15
D
11/15
Question 26
Given that X and Y are two sets. Which of the following is the same as X' U Y'?
A
X∩Y'
B
X'∩Y'
C
(X∩Y)'
D
(X∪Y)'
Question 27
The curve y=px
2
+ 3x -- 8 has 9 as its gradient at the point (1, 0) . find the value of p
A
3.5
B
2
C
0.5
D
7
Question 28
Two fair dice are thrown once. What is the probability that the sum obtained will be a face of 12?
A
1/6
B
1/3
C
1/9
D
1/12
Question 29
If the polynomial g(y) = y
2
+ qy + 5 is divided by (y-1), the remainder is 9 find the value of q.
A
3
B
4
C
2
D
1
Question 30
If √(k+2) - 6/√(k+2) = -1 fine the possible value of k
A
9
B
7
C
2
D
4
Question 31
A binary operation is defined on the set of real numbers by a ∇ b = (b
2
-- a
2
/2ab. a, b ≠ 0 where a and b are real numbers. Find the value of -- ½ ∇ 2
A
-15/8
B
8/15
C
-8/15
D
15/8
Question 32
Given that M=2log2x and N=logx5, log0.4 x express in terms of M and N is ?
A
2M-N
B
M + 2N
C
½ M -- N
D
M - N
Question 33
If ln(10) = 2.3, solve for x in the equation e
(2x-1)
= 100
A
5.6
B
2.8
C
2.3
D
1.4
Question 34
Find the range of values of x for which x
2
+ 5x > -6.
A
x < -3 and x > 2
B
x < -3 and x > -2
C
x > -3 and x < 2
D
x > -3 and x < -2
Question 35
make x the subject of the equation 4x -- 5 = 3y/(4x+5)
A
∓√(3y+5)/4
B
∓√(3y+25)/16
C
∓√(3y+25)/4
D
∓(3y+25)/4
Question 36
A
8
B
5
C
3
D
2
Question 37
Find the value of (cos∅-sin∅)/(cos∅) if sin∅ + cos∅= √2sin∅
A
√2
B
-√2
C
1
D
-1
Question 38
In how many different ways can the letters of the word "MATIX" be arranged such that the vowels must always come together?
A
12O ways
B
240 ways
C
720 ways
D
1520 ways
Question 39
A box contains 5 blue, 4 green and 2 yellow balls. In how many different ways can two balls of the same color be selected from the box?
A
60 ways
B
20 ways
C
17 ways
D
12o ways
Question 40
What is the water level in cylindrical tank of radius 50cm which contains 10,000 liters of water (τ = 22/7}
A
12.73m.
B
5.06m
C
1.27m
D
0.51m
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