MATHEMATICS POST UTME

||1. Without using table, evaluate (243)⅕ * (0.09)-1 * 125-⅔
(A) 4
(B) ¾
(C) 3
(D) 4/3
2. Three consecutive positive integers a, b and c are such that b2 = 4(a + c). Find the value of c
(A) 6  
(B) 3  
(C) 9  
(D) 5
3. Find the principal which amount to =N= 4,400 at simple interest in 5years at 2% per annum.
(A) =N=3,800  
(B) =N=5.200  
(C) =N=5,000  
(D) =N=4,000
4. The suŵ of the fiƌst ϮϬ teƌŵs of the pƌogƌessioŶ ϯ, ϲ, ϭϮ, … is
(A) 3(221 - 1)
(B) 3(220 - 1)
(C) 3(220 + 1)
(D) 3(221 + 1)
5. Mr. Robson bought bags of orange for =N=2,500 each. He sold them for =N=90,000 at a loss of
20%. How many bags of orange did he buy?
(A) 60  
(B) 80  
(C) 50  
(D) 45
6. The second and fifth terms of a geometric progression are 21 and 567 respectively find the first
term and the common ratio of the progression.
(A) 3, 7  
(B) 7, 3  
(C) -7, 3  
(D) -3, 7


7. Tunse bought a house for =N=1,250,000 and spent =N=350,000.00 to renovate it. He then sold the
house for =N=2,000,000.00. What is the percentage gain?
(A) 40%  
(B) 65%  
(C) 35%  
(D) 32%
8. List the integral values of which satisfy the inequality -2 < 7 – 3x ≤ 10
(A) -1, 0, 1, 2  
(B) -2, 0, 1  
(C) 1, 2, 3  
(D) 0, 1,2
9. In a class, 120 students speak English or French or both. 70 speak English and 55 speak French.
 How many speak English but not French.
(A) 45  
(B) 50  
(C) 55  
(D) 60
10. The lengths of the sides of a right angled triangle are ym, (3y – 1)m  and (3y + 1)m, find y.
(A) 12  
(B) 9  
(C) 8  
(D) 4
11. Uche, Adamu and Ope share profit on a business deal. Uche received ⅓ of the profit and
Adamu received ⅔ of the remainder. If Ope received the remaining =N=12,000, how much profit did they
share?
(A) =N=54, 000
(B) =N=58,000
(C) =N=48, 000
(D) =N=42, 000
12. A ladder resting on a vertical wall makes an angle whose tangent is 2.5 with the ground. If the
distance between the foot of the ladder and the wall is 60cm, what is the length of the ladder?
(A) 2m  
(B) 1.6m  
(C) 0.8m  
(D) 3m


13. Three students share a bag of garri in such a way that the first student took¼ of the garri and the
second¾ of the remainder. What fraction of the bag of garri did the third student take?
(A) 3/16  
(B) 2/9  
(C) ⅗
(D) 4/15
14. Solve the simultaneous linear equations 2x + 5y = 11, 7x + 4y = 2
(A) 27/34, 34/27  
(B) -34/27, 73/27  
(C) ⅔, ⅘  
(D) ⅓, ⅖
15. If x + 1 is a factor of x3 + 3x2 + Kx + 4, find the value of K.
(A) 6  
(B) 4  
(C) -4  
(D) 3
16. Paul and his friend, Peter went to buy an article costing =N=600. Peter had 10% of the cost and
Paul 40% of the remainder. How much did they have altogether?
(A) =N=320  
(B) =N=440  
(C) =N=276  
(D) =N=196
17. Find all values of x satisfying the inequality -14 ≤ 4 – 3x ≤ 31
(A) -6 ≤ x ≤ 9
(B) -9 ≤ x ≤ 6
(C) 5 ≤ x ≤ 8
(D) 6 ≤ x ≤ 12
18. What factor is common to all the expressions x2 - x, 2x2 - x - 1 and x2 - 1?
(A) (2x - 1)  
(B) (x + 1)  
(C) (x - 1)  
(D) (2x + 3)
19. FiŶd the suŵ to iŶfiŶitLJ of the folloǁiŶg seƌies ϯ + Ϯ + ϰ/ϯ + ϴ/ϵ + ϭϲ/Ϯϳ + …
(A) 270  
(B) 9    
(C) 27    
(D) 90
20. Find the number of sides of a regular polygon whose interior angle is twice the exterior angle.
(A) 5  
(B) 6
(C) 8  
(D) 9
21. Find the value of p, if the line which passes through (-1, -p) and (-2p, 2) is parallel to the line 2y + 8x
– 17 = 0
(A) 6/7
(B) 4/7
(C) ⅖
(D) –6/7
22. Obtain a maximum value of the function f(x) = x3 - 12x + 11
(A) -15  
(B) 27  
(C) 15  
(D) 20
23. If y = 5cos (-6x), dx/dy is
(A) 30sin (-6x)
(B) 5sin (-6x)
(C) -30sin (-6x)
(D) -30cos (-6x)


24. Find the variance of the numbers k, k + 1, k + 2
(A) ⅓
(B) 3  
(C) ⅔
(D) 1
25. At what value of x is the function y = x2 - 6x - 7 minimum
(A) 3  
(B) 5  
(C) 6  
(D) 2
26. The chances of three independent events P, Q, R occurring are ½, ⅔, ¼ respectively. What are
the chances of P and Q only occurring?
(A) ¼
(B) ⅔
(C) 2/9
(D) ½
27. If x and y represent the mean and the median respectively of the following marks of students in a
Mathematics test 11, 12, 13, 14, 15, 16, 17, 18, 19, 21. Find x/y correct to 1 decimal places.
(A) 1  
(B) 3  
(C) 5  
(D) 2
28. Find the point on the Euclidean plane where the curve y = 2x2 - 2x + 9 has 2 as gradient.
(A) (2, 4)
(B) (3, 5)  
(C) (1, 3)  
(D) (1, 4)
29. Find the equation of the line through (5, 7) parallel to the line 7x + 5y – 5 = 0
(A) 5y + 7x= 70  
(B) 7x + 5y= 7  
(C) 5x + 7y= 110  
(D) y + 5x= 70
30. AAUA allocations to various Faculties in a school budget are as follows:
Science     =N=35,000,000.00
Education   =N=25,000,000.00
Law    =N=20,000,000.00
Social and Management- =N=20,000,000.00
In a pie chart to represent this information the corresponding angle to Science is
(A) 900
(B) 1260  
(C) 450  
(D) 1000
31. “iŵplifLJ ϯ ⅓ - ϭ¼ dž ⅔ + ϭ ⅖
(A) 3 ⅟10
(B) 3 9/10
(C) 3 ⅖
(D) 33 ⅕
32. Find the distance between points A(-4, 5) and B(-3, 2)
(A) 10  
(B) 2√5
(C) 3
(D) √10
33.
No of children 0 1 2 3 4 5 6
No of families 7 11 6 7 7 5 3

 Find the mode and median respectively of the distribution above.
(A) 3, 1  
(B) 1, 2  
(C) 1, 6  
(D) 1, 1
34. Rationalize (4√7 + √2)/(√2 - √7)
(A) -√14 - 6  
(B) 2√14 - 6  
(C) -3√14 - 28  
(D) √14 - 8


35. A housewife bought five yams at Y34 per yam and three oranges at Y5 each where Y is the currency
reckoned in base six. The total amount spent by the housewife is  
(A) Y2256
(B) Y2526
(C) Y3156
(D) Y3526
36. Justice Starts a 5km walk from P on a bearing 0230 . He then walks 4km on a bearing of 1130 to Q.
 What is the bearing of Q from P?
(A) 67.40
(B) 230
(C) 90.40
(D) 1130
37. Divide the L.C.M. of 36, 54 and 90 by their HCF  
(A) 15
(B) 20
(C) 30
(C) 45
38. If 125x = 2010 find x
(A) 4  
(B) 5  
(C) 3  
(D) 2
39. Simplify 4⅓ – (2½  - 1 ⅗)
(A) 7/30
(B) 2 ½
(C) 3  ⅟ 10
(D) 3  13/30
40. If x : y = ⅔ : ⅚ and y : z = ¾ : ½, find x : y : z
(A) 21 : 15 : 10  
(B) 15 : 12 : 10  
(C) 12 : 15 : 10  
(D) 10 : 15 : 12
41. The number 327,036 was corrected to 327,000. Which of the following can exactly describe the
degree of approximation used?
I. to 3 significant figures
II. to 4 significant figures
III to the nearest hundred  
IV to the nearest thousand
(A) I and III only  
(B) II and IV only  
(C) I, II and III only
(D) I, II, III and IV
42. If 1010102 = x10 + 11112 the value of x is
(A) 32  
(B) 27  
(C) 19
(D) 13
43. The population of a school is 1,376. Express this to three significant figures
(A) 1,370  
(B) 1,376  
(C) 1,380
(D) 138
44. A laďouƌeƌ͛s dailLJ ǁage is =N=80 for the first 10 days and =N=100 for the next 9 days. Find the
daily wage for the remaining 6 working days of the month, if his average daily wage for the month is
=N=90.80
(A) =N=110  
(B) =N=105
(C) =N=95
(D) =N=92.50
45. Find the value of x if 4logx + 5logx – 7logx = log16  
(A) 2  
(B) 4  
(C) 8  
(D) 16


46. A motorist drives from P to Q at an average speed of 80 km/hr and immediately returns from Q to P
through the same route at an average speed of 50km/hr. The average speed for the round-trip journey is  
(A) 53.3 km/hr  
(B) 60.0 km/hr
(C) 62.5 km/hr
(D) 65.0 km/hr
47. If X = {1, 2, 3, 4, 5, 6}, Y = {2, 4, 5, 7} and Z = {1, 4, 5} which of the following is (are) correct?  
I. n(X U Y U Z) = 13
II. (X ∩ Y) U Z = X ∩ (Y U Z)
III. n(X ∩ Y ∩ Z) = 2
(A) I only
(B) II only  
(C) I and III only  
(D) II and III only
48. X sold a radio set to Y at profit of 10% and Y sold it for =N=2, 612.50 at a loss of 5%. The cost of the
radio to X was  
(A) =N=2,500
(B) =N=2,488  
(C) =N=2,375
(D) =N=2,272
49. Factorize: 62m + 1 + 7(6m) - 5
(A) [3(6m) + 5][2(6m) – 1]  
(B) [3(6m) – 5][2(6m) + 1]
(C) [3(6m) – 5][3(6m) + 1]  
(D) [2(6m) + 5][3(6m) – 1]
50. The minimum point on the curve y = x2 – 4x + 3 is
(A) (2, -1)
(B) (0, 3)
(C) (1, 0)  
(D) (2, -4)


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