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# MATHEMATICS TEST

1. Evaluate (1/2 – 1/4 – 1/8 – 1/16 + …) – 1

2.

Evaluate ∫1−2(x−1)2dx

3.

If (a2b3c)34a1b4c5=apbqcr What is the value of p+2q?

4. If 29 x (3Y)9 = 35 x (3Y)5, find the value of Y.

5. Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)

6. 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?

7.

A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

8. What is the derivative of t2 sin (3t – 5) with respect to t?

9. Evaluate (2.813 x 10-3 x 1.063) ÷ (5.637 x 10-2)

10. Factorize completely X2+2XY+Y2+3X+3Y-18

11. The 3rd term of an A.P is 4x – 2y and the 9th term is 10x – 8y. Find the common difference.

12. A two-digit number, say AB was mistakenly written as BA by an overworked student. Due to this error, the student was working with a number bigger in value, and its difference with the actual number is one less than the actual number. If the sum of the two digits is half a score. What is the actual number?

13.

If {(a2b-3c)3/4/a-1b4c5} = apbqcr; what is the value of p+2q?

14. Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.

15. What is the derivative of t2 sin (3t – 5) with respect to t?

16. A binary operation * is defined by a*b = ab. If a*2 = 2-a, find the possible values of a.

17. Solve the inequality 2 – x > x2.

18. Naijamod bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X

19. 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

20. If (2√3√2)/(√3+2√2) =m+n√6, find the values of m and n respectively.

21. From a point P, the bearings of two points Q and R are N670W and N230E respectively. If the bearing of R from Q is N680E and PQ = 150m, calculate PR

22. If P3446 – 23P26 = 2PP26, find the value of the digit P.

23. Three consecutive positive integers k, l and m are such that l2 = 3(k+m). Find the value of m

24. Three consecutive positive integers k, l and m are such that l2 = 3(k+m). Find the value of m

25. In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?

26. Find a positive value of ã if the coordinate of the centre of a circle X2+y2-2ãx+4y-ã = 0 is (ã,-2) and the radius is 4 units.

27. If the minimum value of y = 1 + hx – 3x2 is 13, find h

28. The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.

29. Evaluate 12(x1)^2dx

30. Divide 4x3-3x+1 by 2x-1

31. A man 1.7m tall observes a bird on top of a tree at an angle of 300. if the distance between the man’s head and the bird is 25m, what is the height of the tree?

32. A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit?

33. Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.

34. 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.

35. Find the value of x for which the function y = x3 – x has a minimum value.

36. Factorize completely X2+2XY+Y2+3X+3Y-18

37. Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}.

Determine (P-Q) ∩ R

38. Express 1/X31 in partial fractions

39. In ∆MNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of and M meets NO at P, calculate NP

40. If 31410 – 2567 = 340x, find x.

41. The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers

42. Tope bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X.

43.

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.

44. A trader realizes 10x – x2 naira profit from the sale of x bags on corn. How many bags will give him the desired profit?

45. What is the answer when 24346 is divided by 426?

46. If (a2b3c)34a1b4c5=apbqcr What is the value of p+2q?

47.

Look at this series: 2, 1, 12, 14, … What number should come next?

48. Find the tangent to the acute angle between the lines 2x+y = 3 and 3x-2y = 5.

49. if (x – 1), (x + 1) and (x – 2) are factors of the polynomial ax3 + bx2 + cx – 1, find a, b, c in that order.

50. Simplify 3(2n+1) – 4(2n-1) ÷ 2n+1 – 2n

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