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1. A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number.
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?
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
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]
5. Find the volume of prism below
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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9. Simplify ((2√3+3√5))/((3√5 -2√3 ))
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?
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?
12. In a triangle XYZ, if <XYZ = 60, XY = 3cm and YZ = 4cm, calculate the length of the side XZ
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
14. Differentiate (6x^3-5x^2+1)/(3x^2 )
15. d/dx cos (3×2 – 2x) is equal to
16. Find the range of value of x which satisfies the inequality 12×2 < x + 1
17. Sn is the sum of the first n terms of a series given by Sn = n^2 – 1, find the nth term.
18. Find the medium age of the frequency distribution in the table above.
19. Evaluate [1/0.03 ÷ 1/0.024]^-1 correct to 2 decimal places.
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
21. Simplify √((0.0023 × 750)/(0.00345 × 1.25))
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23. Find the value of x if √2/(x+√2)= 1/(x- √2)
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.
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
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
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
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:
29. Three angles of a nonagon are equal and the six other angles is 110°. calculate the size of one of the equal angles.
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
31. Given the quadrilateral RSTO inscribed in the circle with O as centre. Find the size angle x given RST = 60°
32. Find dy/dx if y = cosx.
33. Find the sum to infinity of the following series
0.5 + 0.05 + 0.005 + 0.0005 + ………………
34. Evaluate (sin45° + sin30°) in surd form
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.
36. Simplify 1/(3+ √5)= 1/(3- √5)
37. What is the product of 27/5, (3)^-3 and (1/5)^-1?
38. Find the sum of the 20 terms in an arithmetic progression whose first term is 7 and last term is 117
39.
In the figure above, find the value of x.
Hint for solution
40. Simplify (Cos^2)x ((Sec^2)x + (Sec^2)x (Tan^2)x)
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
42. The diagram below is a circle with centre O. find the area of the shaded portion.
43. Find the values of x satisfying the inequality
-11 ≤ 4 – 3x ≤ 28
44.
45. If y = x sinx, find (d^2 y)/(dx^2 )
46. In the figure, find x
47. Differentiate y = 3 cos2x-sin4x
48. If sinθ=12/13, find the value of 1 + cosθ
49. If y = 2x^3+6x^2+6x+1, find dy/dx
50. How many sides have a regular polygon whose interior angle is 135° each?