MATHEMATICS 2024 UTME PAST QUESTION
1. Differentiate with respect to x, y = sin2x – cos2x
A. 2sinx+cosx
B. 2cos2x+sin2x
C. 2cos2x+2sin2x
D. 2sinx-cosx
2. 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
3. What is the result of subtracting 142567 from 20045
7
?
A. 5328
7
B. 5640
7
C. 2456
7
D. 2546
7
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
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
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
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
13. Find the value of x if the determinant of ■(5&x @3&x)is 14
A. 7
B. 4
C. 28
D. 3
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
15. What is the equivalent of 41043 in octal?
A. 117
8
B. 171
8
C. 1171
8
1711
8
16. Integrate (2x+1)/2x with respect to x
x+1/2 ln|x|+c
1+1/2x+c
x+2ln 1/2x|x|+c
x+ln|2x|+c
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
18. If 121
three
– X
three
= 11
three
find X
A. 1101
3
B. 101
3
C. 11
3
D. 110
3
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)
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
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
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
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
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
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
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)'
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
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
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
30.If √(k+2) - 6/√(k+2) = -1 fine the possible value of k
A. 9
B. 7
C. 2
D. 4
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
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
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
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
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
A. 8
B. 5
C. 3
D. 2
37.Find the value of (cos∅-sin∅)/(cos∅) if sin∅ + cos∅= √2sin∅
A. √2
B. -√2
C. 1
D. -1
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
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
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
Previous
Next