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1. A trader bought 100 oranges at 5 for N1.20, 20 oranges got spoilt and the remaining were sold at 4 for N1.50. Find the percentage gain or loss.
2. What is the answer when 24346 is divided by 426?
3. If 29 x (Y3)9 = 35 x (Y3)5, find the value of Y
4. If m∗n=( m/n-n/m) for m, n belong to R, evaluate -3*4
5. The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers
6. A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.
7. Divide 4×3 – 3x + 1 by 2x – 1
8. Find the tangent to the acute angle between the lines 2x + y = 3 and 3x – 2y = 5.
9. Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)
10. Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
11. Evaluate ∫_(-2)^1▒〖 〖(x-1)〗^2 〗dx
12. Find the value of x for which the function y = x3 – x has a minimum value.
13. If the minimum value of y = 1 + hx – 3×2 is 13, find h.
14. If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000?
15. If 31410 – 2567 = 340x, find x
16. A binary operation * is defined by a * b = ab. If a * 2 = 2 – a, find the possible values of a
17. Find the inverse of p under the binary operation * defined by p*q = p + q – pq, where p and q are real numbers and zero is the identity
18. if (x – 1), (x + 1) and (x – 2) are factors of the polynomial ax3 + bx2 + cx – 1, find a, b, c in that order.
19. 3y = 4x – 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.
20. If P and Q are fixed points and X is a point that moves so that XP = XQ, the locus of X is
21. If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.
22. In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
23. The variance of x, 2x, 3x, 4x and 5x is
24. A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?
25. The expression ax2 + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what are the values of a, b, c respectively?
26. Evaluate 21.05347 – 1.6324 x 0.43 to 3 decimal places
27. A car dealer bought a second-hand car for N250,000 and spent N70,000 refurbishing it. He then sold the car for N400,000. What is the percentage gain?
28. A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30°
29. Find the value of P if the line joining (P, 4) and (6, -2) is perpendicular to the line joining (2, P) and (-1, 3).
30. P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
31. Find the area bounded by the curves y = 4 – x2 and y = 2x + 1
32. Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1.
33. If 6Pr = 6, find the value of 6Pr+1
34. If dy/dx = 2x – 3 and y = 3 when x = 0, find y in terms of x.
35. The time taken to do a piece of work is inversely proportional to the number of men employed. if it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?
36. Find the maximum value of y in the equation y = 1 – 2x – 3×2
37. If x varies directly as √n and x = 9 when n = 9, find x when n = (17/9)
38. Find the coordinates of the mid-point of x and y intercepts of the line 2y = 4x – 8
39. The locus of a point P which is equidistant from two given points S and T is
40. The range of the data: k+2, k-3, k+4, k-2, k, k-5, k+3, k-1, and k+6 is
41. How many three-digit numbers can be formed from 32564 without repeating any of the digits?
42. The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set.
43. Simplify 2134 x 234
43. A cinema hall contains a certain number of people. If 22 1/2% are children, 47 1/2% are men and 84 are women, find the number of men in the hall.
45. The sum of four numbers is 12145. What is the average expressed in base five?
46. Find the midpoint of the line joining P(-3, 5) and Q(5, -3).
47. The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group
48. A farmer planted 5000 grains of maize and harvested 5000 cobs, each bearing 500 grains. What is the ratio of the number of grains sowed to the number harvested?
49. Three boys shared some oranges. The first received 1/3 of the oranges and the second received 2/3 of the remaining. If the third boy received the remaining 12 oranges, how many oranges did they share
50. Two lines PQ and ST intersect at 75°. The locus of points equidistant from PQ and ST lies on the
51. The determinant of matrix (■(x&1&0@1-x&2&3@1&1+x&4)) in terms of x is
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