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Question and Solution 1 of 50
1. Question
1. A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number.
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Question and Solution 2 of 50
2. Question
2. In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?
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Question and Solution 3 of 50
3. Question
3. Find the difference between the range and the variance of the following set of numbers 4,9,6,3,2,8,10,5,6,7 where εd2 = 60
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Question and Solution 4 of 50
4. Question
4. An arc of a circle subtends an angle to at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle [π = 22/7]
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Question and Solution 5 of 50
5. Question
5. Find the volume of prism below
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Question and Solution 6 of 50
6. Question
6. A cone with the sector angle of 45o is cut out of a circle of radius r cm. Find the base radius of the cone.
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Question and Solution 7 of 50
7. Question
7.
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Question and Solution 8 of 50
8. Question
8.
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Question and Solution 9 of 50
9. Question
9. Simplify ((2√3+3√5))/((3√5 2√3 ))
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Question and Solution 10 of 50
10. Question
10. A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo while only 9 students speak neither Hausa nor Igbo?
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Question and Solution 11 of 50
11. Question
11. The angle of elevation of a building from a measuring instrument placed on the ground is 30°. if the building is 40m high, how far is the instrument from the foot of the building?
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Question and Solution 12 of 50
12. Question
12. In a triangle XYZ, if <XYZ = 60, XY = 3cm and YZ = 4cm, calculate the length of the side XZ
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Question and Solution 13 of 50
13. Question
13. In the figure below, XYZ is a triangle with XY = 5cm XZ = 2cm and XZ is produced to E making the angle YZE = 150o. if the angle XYZ = θ, calculate the value of sinθ
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Question and Solution 14 of 50
14. Question
14. Differentiate (6x^35x^2+1)/(3x^2 )
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Question and Solution 15 of 50
15. Question
15. d/dx cos (3×2 – 2x) is equal to
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Question and Solution 16 of 50
16. Question
16. Find the range of value of x which satisfies the inequality 12×2 < x + 1
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Question and Solution 17 of 50
17. Question
17. Sn is the sum of the first n terms of a series given by Sn = n^2 – 1, find the nth term.
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Question and Solution 18 of 50
18. Question
18. Find the medium age of the frequency distribution in the table above.
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Question and Solution 19 of 50
19. Question
19. Evaluate [1/0.03 ÷ 1/0.024]^1 correct to 2 decimal places.
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Question and Solution 20 of 50
20. Question
20. Given the universal set μ = {1,2,3,4,5,6} and the set P = {1,2,3,4}, Q = {3,4,5} and R = {2,4,6}. Find P u (Q u R)I
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Question and Solution 21 of 50
21. Question
21. Simplify √((0.0023 × 750)/(0.00345 × 1.25))
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Question and Solution 22 of 50
22. Question
22.
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Question and Solution 23 of 50
23. Question
23. Find the value of x if √2/(x+√2)= 1/(x √2)
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Question and Solution 24 of 50
24. Question
24. In the figure below, PQST is a parallelogram and TSR is a straight line. If the area of ∆QRS is 20cm2, find the area of trapezium PQRT.
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Question and Solution 25 of 50
25. Question
25. If X, Y can take values from the set {1,2,3,4} find the probability that the product of X and Y is not greater 6
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Question and Solution 26 of 50
26. Question
26. A chord of a circle radius √3cm subtends an angle of 60° on the circumference of the circle. Find the length of the chord
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Question and Solution 27 of 50
27. Question
27. The first term of a geometrical progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8
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Question and Solution 28 of 50
28. Question
28. From a point P, the bearings of two points Q and R are N67°W and N23°E respectively. If the bearing of R from Q is N68°E and PQ = 150m, calculate PR.
Hint:
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Question and Solution 29 of 50
29. Question
29. Three angles of a nonagon are equal and the six other angles is 110°. calculate the size of one of the equal angles.
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Question and Solution 30 of 50
30. Question
30. The mean of the number 3,6,4,x and 7 is 5. Find the standard deviation.
NB// This image is to be used as part of the solution
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Question and Solution 31 of 50
31. Question
31. Given the quadrilateral RSTO inscribed in the circle with O as centre. Find the size angle x given RST = 60°
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Question and Solution 32 of 50
32. Question
32. Find dy/dx if y = cosx.
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Question and Solution 33 of 50
33. Question
33. Find the sum to infinity of the following series
0.5 + 0.05 + 0.005 + 0.0005 + ………………CorrectIncorrect 
Question and Solution 34 of 50
34. Question
34. Evaluate (sin45° + sin30°) in surd form
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Question and Solution 35 of 50
35. Question
35. The interior angles of a quadrilateral are (x + 15) (2x – 45)°, (x – 30)° and (x + 10)°. find the value of the least interior angle.
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Question and Solution 36 of 50
36. Question
36. Simplify 1/(3+ √5)= 1/(3 √5)
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Question and Solution 37 of 50
37. Question
37. What is the product of 27/5, (3)^3 and (1/5)^1?
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Question and Solution 38 of 50
38. Question
38. Find the sum of the 20 terms in an arithmetic progression whose first term is 7 and last term is 117
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Question and Solution 39 of 50
39. Question
39.
In the figure above, find the value of x.
Hint for solution
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Question and Solution 40 of 50
40. Question
40. Simplify (Cos^2)x ((Sec^2)x + (Sec^2)x (Tan^2)x)
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Question and Solution 41 of 50
41. Question
41. Determine the distance on the earth’s surface between two towns P (Lat 60°N, Long 20°) and Q (Lat 60°N, Long 25E) Radius of the earth = 6400km
Hint for Solution
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Question and Solution 42 of 50
42. Question
42. The diagram below is a circle with centre O. find the area of the shaded portion.
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Question and Solution 43 of 50
43. Question
43. Find the values of x satisfying the inequality
11 ≤ 4 – 3x ≤ 28CorrectIncorrect 
Question and Solution 44 of 50
44. Question
44.
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Question and Solution 45 of 50
45. Question
45. If y = x sinx, find (d^2 y)/(dx^2 )
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Question and Solution 46 of 50
46. Question
46. In the figure, find x
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Question and Solution 47 of 50
47. Question
47. Differentiate y = 3 cos2xsin4x
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Question and Solution 48 of 50
48. Question
48. If sinθ=12/13, find the value of 1 + cosθ
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Question and Solution 49 of 50
49. Question
49. If y = 2x^3+6x^2+6x+1, find dy/dx
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Question and Solution 50 of 50
50. Question
50. How many sides have a regular polygon whose interior angle is 135° each?
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