1. Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculate the smaller of the two angles

2. The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is 10cm high, would be the height of the same quantity of water in Q?

3. In a cumulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What percentage of the distribution is at most 18 years or greater than 48 years?

4. In parallelogram PQRS, QR is produced to M such that |QR| = |RM|. What fraction of the area of PQMS is the area of PRMS?

5. The number of bottles of wine is directly proportional to the cost of bottle of wine. If 10 bottles of wine cost N400

(a) What is the cost of 18 bottles?

(b) How many bottles can N20 buy?

6. Express 11101.110 in base two to denary

7. Solve the equation

8.Find the HCF of the following algebraic expressions:

(i) 9ab and 27abc

(ii) 15xy 2 and 2.5x 2 y

9. Write the following as rational numbers

(i) 0.373 737 37

(ii) 4.142 142 142

10. The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname. If more than one surname begins with a letter besides A and O, how may surnames begin with that letter

11. Two numbers differ by 2. Three times one of the numbers added to the other gives 46. Find the numbers

12. Solve the equations () =

13. (a) Calculate the compound interest and the final amount on N40000 for 2 yrs at 5% per annum.

14. Factorise

(i) 4ms – 15mt – 6mt + 10ns

(ii) Mx + ny – nx – my

15. (a) convert (i) 214 to base 5

(ii) (10001) in base 2 to base 10

16. If 40 students can consume 100kg bag of beans in 5 weeks. How long will the bag of beans last for (a) 16 students(b) 60 students

17. Evaluate 111111 + 11 and leave your answer in base two

18. (a) The probability that a malaria patient (M) survives when administered with a newly discovered drug is 0.27 and the probability that a thyphoid patient (T) survives when injected with another newly discovered drug is 0.85. What is the probability that;

i. either of the two patients survives?

ii. of two patients survive?

iii. at least one of the two patients survive?

(b) Give your answers correct to 2 significant figures.

19. The frequency distribution of the weight of 100 participants in a high jump competition is as

shown below:

(a) Construct the cumulative frequency table.

(b) Draw the cumulative frequency curve.

(c) From the curve, estimate the:

(i) median;

(ii) semi-interquartile range;

(iii) probability that a participant chosen at random weighs at least 60 kg.

20. A sector of angle 135° is removed from a thin circular metal sheet of radius 40cm. It is then folded with the straight edges coinciding to form a right circular cone. Calculate the:

(a) base radius of the cone, correct to two decimal places.

(b) greatest volume of liquid which the cone can hold, leaving your answer correct to the nearest cm3. (Take p = 22/7).

21. (a) P varies directly as Q and inversely as the square of R. If P = 1 when Q = 8 and R = 2, find the value of Q when P = 3 and R = 5.

22. The table below shows the distribution of marks scored by students in an examination.

Class interval Frequency

60 – 64 2

65 – 69. 3

70 – 74 6

75 – 79 11

80 – 84 8

85 – 89 7

90 – 94 2

95 – 99 1

Calculate, correct to 2 decimal places, the

(a) mean;

(b) standard deviation of the distribution

23. A sector of a circle with radius 21 cm has an area of 280 cm2.

(a) Calculate, correct to 1 decimal place, the perimeter of the sector.

(b) If the sector is bent such that its straight edges coincide to form a cone, calculate, correct to the nearest degree, the vertical angle of the cone. [Take π = 22/7 ]

24. A = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x: 3 < x < 9} are subsets of the universal-set

U = {2, 3, 4, 5, 6, 7, 8, 9}. Find

(a) A n(B’nC’);

(b) (AuB) n(BuC).

25. (a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.

(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.

26. In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 passed Mathematics and Accounts only, 6 passed Mathematics only, 9 passed Accounts only, 2 Accounts and Economics only. If each student offered at least one of the subjects,

(a) How many students failed in all the subjects?

(b) Find the percentage number who failed in at least one of Economics and Mathematics.

(c) Calculate the probability that a student selected at random failed in Accounts.

27. (a) Using completing the square method, solve, correct to 2 decimal places, the equation 3y2 – 5y + 2 = 0

28. (a) P varies directly as Q and inversely as the square of R. If P = 1 when Q = 8 and R = 2, find the value of Q when P = 3 and R = 5.

29. An aeroplane flies from town A(20oN, 60oE) to town B(20oN, 20oE).

(i) If the journey takes 6 hours, calculate, correct to 3 significant figures, the average speed of the aeroplane.

(ii) If it then flies due north from town B to town C, 420 km away, calculate, correct to the nearest degree, the latitude of town C.

[Take radius of the earth = 6400 km and π = 3.142]

30. Two fair dice are thrown.

M is the event described by “the sum of the scores is 10” and

N is the event described by “the difference between the scores is 3”.

(a) Write out the elements of M and N.

(b) Find the probability of M or N.

(c) Are M and N mutually exclusive? Give reasons.

31. (a) In a class of 50 students, 30 offered History, 15 offered History and Geography while 3 did not offer any of the two subjects.

(i) Represent the information on a Venn diagram.

(ii) Find the number of candidates that offered: History only; Geography only.

32. A trader sold an article at a discount of 8% for N 828.00. If the article was initially marked to gain 25%, find the

(i) cost price of the article;

(ii) discount allowed.

33. The area of a rectangular football field is 7200m2 while its perimeter is 360m. calculate the:

(a) dimensions of the field;

(b) cost of clearing the field at N6.50 per square meter, leaving a margin of 2m wide along the longer sides;

(c) percentage of the part not cleared.

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