# NDA PAST QUESTIONS ON MATHEMATICS 2010

2. If tan Ɵ = 3/4, find Sin 2Ɵ
A. 9/16
B. 13/15
C. 1/4
D. 24/25

4. Solve for sin x, if sin2 x ÷ (sinx-2) = 4
A. 2, -3
B. 1, -3
C. 2, 4
D. 3, -2

5. Calculate the angle < between the vectors
U – 2i +2j
V=-2i + 2j

A. < = 45˚
B. < = 60˚
C. < = 90˚
D. < = 75˚

6. Find the value of sin 2Ɵ when sin Ɵ = 2/3
A. 4√5
B. 3/2
C. -5/12
D. -3/12

7. If Sin Ɵ=1/4. What is sec Ɵ.
A. 2
B. 12
C. 31/3
D None of the above

9. If y =x sin x, find dy/dx
A. 2Cosx-xsinx
B. Sinx+xCosx
C. Sinx - xCosx
D. xSinx-2Cosx

10. If y Sin(2x2 + 5) then dy/dx is
A. 4xCos(2x2 + 5)
B. -3Sin(2x2+ 5)
C. 2x2sin(2x+5)
D. 4Cos (2x2+ 5)

12. Without using tables, evaluate
(343)1/3 x (0.14)-1 x (25)-1/2
A. 12
B. 10
C. 8.
D. 7

13. In a school. 220 students Biology or Mathematics or both,125 offer Biology and 110 Mathematics. How many offer Biology but not Mathematics?
A. 110
B. 95
C. 80
D. 125

15. A trader bought goats for ₦4000 each. He sold them for ₦180000 at a loss of 25%. How many goats did he buy?
A. 50
B. 60
C. 36
D. 45

16. Simplify 52.4 — 5.7 — 3.45- 1.75
A. 42.1
B. 41.4
C. 42.2
D. 41. 5

17. The range of the data k+2, k-3, k+4, k-2, k, k-5, k+3,
k- I and k + 6 is
A. 11
B. 10
C. 8
D. 6

18. The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector for cassava in a pie chart?
A. 180°
B. 36°
C. 60°
D. 108°

19. The probability of a student passing any examination is i& If the student takes three examinations, what is the probability that he will not pass any of them?
A. 4/9
B. 2/3
C. 1/27
D. 8/27

20. The means of a set. or six numbers is 60. if the mean of the first five is 50. find the sixth number in the set.
A. 95
B. 100
C. 110
D. 105

21. Let U = {a,b,c,d,e}
A = {a,b,d}
and B ={a,d,e}Then B/A Is equal to:
A. {e}
B. {b}
C. {c}
D. {d}

22. Let A = {2,3,4}
B = {4,5,6}
and U = {1,2,3 .......} Then :

A. A\B ={1,2}
B. A\B ={1,4}
C. A\B ={2,4}
D. A\B ={1,2,3}

23. Let U be a universal set. A and B are subsets of U. Then A’ꓴB’ =? by:
A. AꓴB
B. A'ꓴB’
C. A'ꓴB
D. (AՈB)’

24. Simplify sin45° cos45°
A. 1/2
B. 2√2
C. 1/2
D. 2/2

25. If sin A 3/4 What is the value of tan A?
A. 1
B. ½
C. ¼
D. 3/√7

26. If tan(x+y) = 2 and tan x = 1. find tan-1 y
A. 2
B. 1/3
C. 1
D. 3

27. Evaluate the expression sin (cos-1  √3/2)
A. 1/3
B. 1/2
C. 2/3
D. 3/2

28. In a parallelogram ABCD, the lengths of sides AB and AD are 5m and 6m respectively. if A = 60°, find the length of the longest diagonal of the parallelogram.
A. 8.12
B. 3.01
C. 9.45
D. 8.94

29. The sides of a rectangle are 18m and 31m, Find the angle the diagonal makes with the shorter side
A. 20˚
B. 30˚
C. 60˚
D. 50˚

30. Two roots of the equation x3 +px+q = 0 are -1 and 3. The third root is:
A. -1
B. 1
C. 2
D. -2

31. Find the principal of which amount ₦5,500 at simple interest in 5 years at 2% per annum,
A. ₦5,000
B. ₦4,900
C. ₦4,800
D. ₦4,700

31. A car dealer bought a second-hand ear for ₦250,000.00 and spent ₦70,000.00 refurbishing it. He then sold the car for ₦400.000,00. What is the percentage gain?
A. 20%
B. 25%
C. 32%
D. 60%

33. Evaluate 21.05347 — 1.6324 × 0.41, to 3 decimal places.
A. 20.351
B. 20.352
C. 20.980
D. 20.98

38. Factorize 4x2 — 9y2 + 20x + 25
A. (2x — 3y)(2x + 3y)
B. (2x + 5)(2x - 9y + 5)
C. (2x — 3y + 5)(2x - 3y-5)
D. (2x — 3y + 5) (2x + 3y + 5)

40. Solve the equations: m2+ n2 = 29, m + n = 7
A. (5,2) and (5,3)
B. (5,3) and (3,5)
C. (2,3) and (3,5)
D. (2,5) and (5,2)

1. C
2. C
3. A
4. B
5. A
6. A
7. C
8. B
9. A
10. C
11. C
12. A
13. C
14. D
15. D
16. C
17. B
18. C
19. D
20. B
21. B
22. C
23. A
24. A
25. B
26. B
27. A
28. A
29. B
30. D
31. C
32. A
33. C
34. D
35. D
36. A
37. D
38. B
39. A
40. B