SS 2 Third Term Examination Mathematics

CLASS: S.S.S. 2 SUBJECT: Mathematics

INSTRUCTION: Answer all the questions

1. Evaluate (101.5)² – (100.5)²

a. 1 b. 2.02 c. 20.02 d. 202 e. 2020

2. Express the product of 0.06 and 0.09 in standard form

a. 5.4 x 10^-3 b. 5.4 x 10^-2 c. 5.4 x 10^-1 d. 5.4 x 10² e. 5.4 x 10³

3. Simply 36^½ x 64^-1/3 x 5^o

a. 0 b. 1/24 c. 2/3 d. 1½ e. 7½

4. Find the 8^th term of the A.p. -3, -1, 1 ………….

a. 13 b. 11 c. -8 d. -11 e. -17

Use this information to answer questions 5 and 6

5. Calculate /PQ/ in metres

a. 20 b. 24 c. 25 d. 31 e. 84

6. What is the bearing of Q from P to the nearest whole degree?

a. 16^o b. 17^o c. 73^o d. 106^o e. 164^o

7. Simplify (27^1/3)² a. 4 ½ b. 6 c. 9 d. 18 e. 81

8. Calculate the value of x in the diagram below

__32x____________23x_

4x

9. A sales girl gave a change of N1.15 to a customer instead of N1.25. Calculate her percentage error.

a. 10% b. 8.7?% c. 8.0% d. 2.4% e. 0.10%

10. What is the probability of hiring an odd number in a single toss of a fair die? a. 1/6 b. 1/3 c. ½ d. 2/3 e. 5/6

11. Evaluate log6₁₀ + log45₁₀ – log27₁₀ without using logarithms tables

a. 0 b. 1 c. 1.1738 d. 1.3802 e. 10

12. What value of k makes the given expression a perfect square?

M² – 8m + k

a. 2 b. 4 c. 8 d. 16 e. 64

13. If logq¹⁰ = 2.7078, what is q?

A. 5102 B. 849.9 C. 510.2 D. 84.99 E. 51.02

14. If 3loga + 5log_a – 6log_a = log64, what is a?

a. 4 b. 6 c. 8 d. 16 e. 32

15. If the second and fourth terms of a G.P are 8 and 32 res[ectove;u, what is the sum of the first four terms?

a. 28 b. 40 c. 48 d. 60 e. 68

16. Evaluate 0.009 divided 0.012, leaving your answer in standard form

a. 7.5 x 10² b. 7.5 x 10¹ c. 7.5 x 10^-1 d. 7.5 x 10^-2 e. 7.5 x 10^-3

17. Factorize the following expression, 2x² + x – 15

a. (2x + 5) (x – 3) b. (2x-5)(x-3) c. (2x -5)(x-3) d. (2x-3)(x+5) e. (2x+5)(x+3)

18. If loga¹⁰ = 4; what is a?

a. 0.4 b. 40 c. 400 d. 1000 e. 10,000

19. Instead of recording the number 1.23cm, find the percentage error, correct to one decimal place

a. 6.8% b. 7.3% c. 9.6% d. 14.4% e. 15.4%

20. Factorise 5y² + 2ay – 3a²

a. (5y – a)(y + 3a) b. (5y+a)(y-3a) c. 5y2 + a(2y – 3a) d. (y – a)(5y-3a)

e. (y+a)(5y-3a)

1. Find (101₂)² expressing the answer in base 2(a) 10101 (b) 11001 (c) 10010 (d) 11101 (e) 10110
2. If 3 children share ₦10.50 among themselves in the ratio 6:7:8, how much is the largest share?(a) ₦ 3.00 (b) ₦3.50 (c) ₦4.00 (d) ₦4.50 (e) ₦ 5.00
3. Express 0.000834 in standard form(a) 8.34 x 10^-4 (b) 8.34 x 10^-3 (c) 8.34 x 10³ (d) 8.34 x 10⁴ (e) 8.34 x 10⁶
4. Simplify 0.027^-1/3(a) 3¹_/3 (b) 3 (c) 3/10 (d)1/3 (e) 1/9
5. Given that log^a₂ = log⁴₈ , Find a(a) 2^1/2 (b) 4^1/3 (c) 4^2/3 (d) 2^2/3 (e) 2³
6. By selling some crates of soft drinks for ₦600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?(a) ₦1,200.00 (b) ₦900.00 (c) ₦450.00 (d) ₦400.00 (e) ₦200.00
7. Find the nth term Un of the A.P; 11, 4,-3, ­­­­­­_______(a) un= 19 + 7n (b) un= 19-7n (c)= 18-7n (d) un= 18+7n (e) un= 17-7n
8. If 16/9, X, 1, y are in Geometric Progression (GP). Find the product of X and Y (a) 9/16 (b) ¾ (c) 1 (d) 4/3 (e) 16/9
9. If R = { 2,4,6,8} and S= { 1, 2, 3, 4, 8}, the RUS equal (a) { 1,2,4,6,7,8} (b) {1,2,4,7,8} (c) {1,4,7,8} (d) {2,6,7} (e) {2,4}
10. In the diagram below, the shaded portion is (a) P’nR (b) QnR (c) P’nQnR (d) (PuQ)’nR (e) (PnQ)U(P’nR)
11. Find the values of X for which the expression is undefined (a) +4 or +1 (b) -5 or +1 (c) -5 or -1 (d) +5 or -1 (e) +4 or -1
12. Which of the following could be the inequality illustrated in the sketch graph below? (a) y≥-2x + 1 (b) y ≤ -3x + 3 (c) y < 3x _2 (d) y ≤ x +3 (e) y ≥ 3x + 2
13. Solve the inequality (2x – 1)<5 (a) x< -5 (b) x<-6 (c) x<7 (d) x< 8 (e) x<16
14. What is the smaller value of X for which x² – 3x + 2 = 0 (a) 1 (b) 2 9c) 3 (d) 4 (e) 5
15. Factorize the expression X(a-c) + y(c-a) (a) (a-c)(y-x) (b) (a-c)(x-y) (c) (a+c)(x-y) (d) (a+c)(x + y) (e) (a-c)(x+y)
16. Solve the equation 3x² + 25x – 18 = 0 (a) x = -3 or 2 (b) x = -2 or 3 (c) x =-2 or – 9 (d) x = -9 or 2/3 (e) -2/3, 9
17. Solve the equation (x +2 )(x – 7) = 0 (a) x = 1 or 8 (b) x = 2 or 7 (c) x = -4 or 5 (d) x =-3 or 6 (e) x = -5 or -2
18. Solve the following simultaneous equations: X +Y = 3/2, X- y = 5/2 and use your result to find the value of 2y + x (a) -2 (b) -1 (c) ½ (d) 1 (e) 3 ½
19. The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus. (a) 24cm² (b) 36 cm² (c) 48 cm² (d) 60 cm² (e) 96 cm²
20. A water tank of height ½ m has a square base of side 1 ½ m. if it is filled with water from a water tank holding 1500 litres, how many litres of water are left in the water tanker? (1000 Litres = 1m³) (a) 37.5 Litres (b) 375 Litres (c) 3750 Litres (d) 37500 Litres (e) 375000 Litres

41. Mrs. Atiku sold article for N7.50 instead of N12.75. Calculate her percentage error

1. 41.2% (b)18.3% (c) 5.3% (d) 1.7%

42. A school girl spent ¼ of her pocket money on books and 1/3 on dress. What fraction remains?

1. 5/12 (b) 5/6 (c) 7/12 (d) 1/6

43. Find X in X = 2 / 2 – X

1. 4/5 (b) 4 (c) 5/4 (d) ½

44. Three numbers a, b, c are in the ratio 3 : 5 : 7 respectively. Find the value of

4a – b

B + 2c (a) 7/19 (b) 16/21 (c)8/11 (d) 2/3

45. Simplify ( 16/81)

1. 2/3 (b) 8/27 (c) 1/3 (d) 4/3

46. Evaluate Log ³⁵ + Log 2 — Log 7

^{10 10 10}

47. Express 0.00562 in standard form

1. 5.62 X 10^-3 (b) 562 x 10^-2 (c) 5.62 x 10² (d) 0.562 x10-²

48. Find the value of X for which 312₄ + 52_x = 96₁₀

(a) 8 (b) 10 (c) 12 (d) 14

49. A pair of fair dice with each face numbered 1 to 6 are thrown once. Find the probability of scoring 2 on one die and a 5 on the other

(a) 1/36 (b)1/18 (c)7/36 (d)1/3

_(1/7)

50. Find the numerical value of Log⁴⁹ + Log

^{7 7}

(a) 1 (b) 2 (c) 3 (4) 4

51. Given that P + 10 = 2p – 2, find p

1. 12 (b)13 (c)14 (d)15

52. Given square root of 64000 is

(a)80 (b)8 (c)36 (d) 18

53. What fraction must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3¼

(a) 1 ½ (b) 1/3 (c) ½ (d) 1 1/6

54. The square of 20 is

(a) 400 (b) 40 (c) 240 (d) 80

55. A house bought for N100,000.00 was later auctioned for N80,000.00. Find the loss percentage

(a) 20% (b) 30% (c) 40% (d) 50%

PART II Answer four question in this part

The number of items produced by a company over a five – year period is given below –

1 (i) Plot a bar chart for this information

(ii) What is the average production for the five year period?

2a. The subject A, B and C of a universal set are defined as follows:

A = {m, a p e}, B = {a, e, i, o, u} C = {I, m, n, o, p, q, r, s, t, u}

List the elements of the following sets

1. AUB (ii) AUC (iii) AU(B C)

2B. Out of the 400 students in the final year in a senior secondary school, 300 are offering Biology and 190 are offering Chemistry.

1. How many students are offering both Biology and Chemistry? If only 70 students Are offering neither Biology nor Chemistry?
2. How many students are offering at least one of Biology or Chemistry?

3. The table below is for the relation y = 2 + x – x²

a. Using a scale of 2cm to 1 unit on each axis, draw the graph of the relation

in the interval – -2 < x < 3.

b. From your graph, find the greatest value of y and the value of x for which this occurs.

c. Using the same scale and axis, draw the graph of y = 1 – x

d. Use your graph to solve the equation 1 + 2x – x² = 0

4a. Using logarithm table, evaluate

_____

3\/1.376

4\/0.007 correct to three significant figures.

b. Without using mathematical tables, find the value of log81

log1/3

5ai. A man has 9 identical balls in a bag. Out of these, 3 are black, 2 are blue and the remaining are red.

ii. If a ball is drawn at random, what is the probability that it is (i) not blue

1. not red

b. If 2 balls are drawn at random, one after the other, what is the probability that both of them will be –

1. black if there is no replacement
2. blue if there is a replacement

6. Three towns P, Q and R are such that the distance between P and Q

Is 50km and the distance between P and R is 90km us 90km. If the bearing of Q and P is 075^o and the bearing of R from P is 310^o, find the

• 1. distance between Q and R
  2. Bearing of R and Q

7. A test was given to 50 students. The results are given in the table below

• 1. Find the range
  2. Calculate the mean deviation
  3. Calculate the standard deviation