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15. Find the derivative of sinθ/cosθ
31. If the function f(x) = x3 + 2×2 + qx – 6 is divisible by x + 1, find q
47.
16. In a class of 60 students, offer physics and 40 offer chemistry. If a student is picked at random from the class, what is the probability that the student offer both physics and chemistry?
Hint on solution:
32. Find the minimum value of X2 – 3x + 2 for all real values of x
48.
1. In the cyclic quadrilateral, find <PRO.
17. From the cyclic quadrilateral TUVW below, find the value of x.
33. If X ∗ Y = X + Y – XY, find x when (x ∗ 2) + (x ∗3) = 68
49.
2. The Venn diagram shows a class of 50 students with this game they play. How many students play only two games?
18. Evaluate (81/16)^((-1)/4)×2^(-1)
34. Find the distance between the point Q (4,3) and the point common to the lines 2x – y = 4 and x + y = 2
50.
3. The pie chart below the distribution of subjects offered by students in sss3 level. If 80 students enrolled in the class, what is the size of the angle of the sector in Economics
19. Solve 5 ^ 2x – 2 x 5 ^ x + 1 = 0.04
35. Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
4. The 4th term of an A.P is 13 while the 10th term is 31. Find the 24th term.
20. The distance travelled by a particular from a fixed point is given as S = (t3 – t2 – t + 5)cm. find the minimum distance that the particle can cover from the fixed point
36. The length of a notebook 15cm, was measured as 16.8cm. Calculate the percentage error to 2 significant figures.
5. If the angle of a sector of a circle with radius 10.5cm is 120°, find the perimeter of the sector
21. Find the mean deviation of 2,4,5 and 9
Hint for solution
37. A worker’s present salary is N24,000 per annum. His annual increment is 10% of his basic salary. What would be his annual salary at the beginning of the third year?
6.
The table above represents the outcome of throwing a die 100 times. What is the probability of obtaining at least a 4?
22. Find the area of the figure below
38. If x – 1 and x + 1 are both factors of the equation x3 + px2 + qx + 6 = 0, evaluate p and q
7. If y = x^2-3x+4, find dy/dx at x = 5
23. Find the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle
Hint for solution:
39. Which of the following binary operations is commutative on the set of integers?
8. Evaluate (1.25 × 0.025)/0.05 correct to 1 decimal place
24. Evaluate (81^(3/4) – 27^(1/3))/(3 ×2^3 )
40. If a ∗ b = + √ab, evaluate 2 ∗(12 ∗ 27)
9. The mean of 2 – t, 4 + t, 3 – 2t, 2 + t and t – 1 is
24. A sector of a circle has an area of 55cm2. If the radius of the circle is 10cm, calculate the angle of the sector. [π = 22/7]
41. Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x – 2y + 4 = 0, find the equation of QR
10.
Find the mode of the distribution above
26. If sinθ=(-1)/2 for 0°<θ<360°, the value of θ is
42. Find the area bounded by the curve y = 3×2 – 2x + 1, the ordinates x = 1 and x = 3 and the x-axis.
11. Calculate the standard deviation of 5,4,3,2 and 1
Hint for solution
27. If the distance between the points (x, 3) and (-x, 2) is 5. Find x
43. The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number
12. If P = {x: x is odd, -1 < x ≤ 20} and Q = {y: y is prime, -2 < y ≤ 25}, find P n Q.
28.
44. A binary operation ⊕ is defines on the set of all positive integers by a ⊕ b = ab for all positive integers a, b. Which of the following properties does NOT hold?
13. Solve for x: (x – 2) < 3
29. find the equation of the curve which passes through 6x – 5 at (0, 3)
45. If M(4, q) is the mid-point of the line joining L(p, -2) and N(q, p). Find the values of p and q
14. What is the size of each interior angle of a 12-side regular polygon?
30. Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years
46.
The multiplication table above has modulo 10 on the set S = (2, 4, 6, 8). Find the inverse of 2