MATHEMATICS 2022 UTME PAST QUESTION
1. Evaluate (11
2
×11101
2
) +101
2
A. 101110
2
B. 101100
2
C. 1011100
2
D. 111001
2
2. (1
1
/
3
÷4/9) ÷ 5/16×4
1
/
6
simplify to?
A. 20
B. 30
C. 40
D. 5
IF 3log_2^a + 5〖log〗_2^(a )‐ 6〖log〗_2^a = 〖log〗_2^64 find the value of a.
A. 10
B. 2
C. 10
D. 8
4.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
5. what must be substracted from G(y) = 6y3+ 4y2 – y+5 so that it will be divisible by y-2..
A. 57
B. 67
C. 43
D. 33
Which of the following represent (A’∩B)∩C ON a ven diagram?
7. A binary operation is defined on the set R of real number, by x* y =x+1-1/2 xy for all a, b ∈ R. find the value of √36*√4.
A. -2
B. 2
C. 10
D. -10
8. 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
9. Simplify 6/((√5 -√2 )^2 )
A. (14+4√10)/3
B. (14-4√10)/3
C. 7-2√10
7+2√10
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
11. A class consisting of 8 boys and 7 girls. If two student 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
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
13. 13. How many term of the series 1+3+5+….. are needed for the sum to reach 169?
A. 12
B. 13
C. 14
D. 11
14 Find the differential coefficient of the curve 2X
4
-3X
3
+X
2
- 1/X -6 at point x =1.
A. 1
B. 2
C. -1
D. -2
15. If √(5+√2) /√(5-√2) = a+b√10, find a+b
A. 3
B. 9
C. 2
D. 10
16. Find he mid-point of the line joining the point A(1/2,1_3^2 ) and B(1/(2 ),1/3).
A. (5_3^2,1/2)
B. (2/3,5_3^2 )
C. (7/12,1)
D. (1/2,5_3^2 )
17. If an exterior angle of a polygon is 30°, determine the sum of the interior angle
A. 2520°
B. 1080°
C. 1960°
D. 1800°
18. The average weight 10 equipment ism120kg. if the heaviest equipment is removed, the average weight is reduced by 3kg. what is the weight in kilogram of the heaviest equipment?
A. 103
B. 133
C. 177
D. 147
19. A farm land of 160 acres was use in planting various fruits as shown in the figure below. what is the percentage of farm land used for planting oranges.
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
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
22. Evaluate ∫▒sin〖8xdx.〗
A. 8 sin8x + c
B. -1/8cos8x + c
C. 1/8cos8x + c
D. 8 sin〖x+c〗
23. If ʄ(x) = 2x
2
-3x+2, find the value of ʄ(y+2).
A. 2y
2
+ 3y -2
B. 2y
2
+5y+4
C. 2y
2
-3y-2
D. 2y
2
-5y+12
24. Find the value of sin24x - cos24x if x = π/6rad.
A. √3/2
B. 1
C. 1/2
D. - 1/2
25. In how many ways can 10 people be arranged in a row such that 2 particular person should always be together?
A. 9! ×2!
B. 8! × 2!
C. 10! ×2!
D. 12!
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
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
28. A salesman sold an article for #450 at a loss of 4%. At which 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
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
30. Find the value of 〖81〗^x/(3^(1+x)×〖27〗^x )
A. 1/2
B. 1/3
C. 3
D. 2
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
32. Evaluate (log3-log2)/(log√27-log√8)
A. 3/2
B. 2/3
C. -3/2
D. -2/3
If the exterior angle of a rectangle polygon is 40°, calculate the size of the interior angle and the number of the sides of the polygon.
A. 40° and 9 sides
B. 140° and 3 sides
C. 40° and 3 sides
D. 140° and 9 sides
34.The probability of a boy passing a biology test is 2/3 and the probability of him passing mathematics test is ¼. Find the probability of his failing both subjects.
A. 1/3
B. 2/3
C. 1/4
D. 1
35. The probability of a boy passing a biology test is 2/3 and the probability of him passing mathematics test is ¼. Find the probability of his failing both subjects.
A. 1/3
B. 2/3
C. ¼
D. 1
36. Calculate the variance of the following date: 13,7,8,9,10,11,12
A. 2
B. 4
C. 3
D. 8
37.Simplify (4/25)
-1/2
×2
4
÷(15/2)-2
A. 225
B. 2250
C. 150
D. 1125
38. The circumference of a circle is 56cm. find the angle subtended at the centre by an arc of the circle of the length 7cm.
A. 30°
B. 45°
C. 60°
D. 120°
39. Evaluate lim┬
(x→-3)
〖(x^2-9)/(x+3)〗
A. 0
B. 3
C. -3
D. 1
40. Find the value of (2+sin〖30°sin〖45°〗 〗)/sin〖45°+sin〖30°〗 〗
A. (7√(2+6))/2
B. (7√(2-6))/2
C. (2√(7+6))/7
D. (2√(7-6))/7
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