MATHEMATICS FIRST TERM EXAMINATION SS 1

FIRST TERM

Examination malpractices may lead to a repeat of the subject or suspensions don’t be involved.

SUBJECT:  GENERAL MATHEMATICS             CLASS: SSS 1 TIME APPROVED: 2¹/2 HRS

INSTRUCTION: Answer all questions in this part

1. If P = {x: 1 x 6} and Q = {x: 2 < x < 9}, where x R, find P A. {1, 2, 3, 4}
2. {3, 4, 5, 6}  C.  {4, 2, 9, 8}    D. {1, 2, 3, 5}
3. Simplify ^-2/3     4        B.  -1/4         C.  1/8       D.  –4
4. Simplify: ^-6)^{1/2      r}/₂          B. 2r            C. ¹/_2r           D. ²/_r
5. What is the product of ²⁷/₅ , 3^-3 and (¹/₅)^-1         5           B. 3           C. 1            D.¹/₂₅
6. Evaluate: (81)^3/4 – (27)^1/3 27            B. 1            C. ¹/₃          D. ¹/₈
7. Without using tables, evaluate: (343)^1/3 x (0.14)^-1 x (25)^-1/2 12       B. 10      C. 8     D. 7
8. If 23_X + 101_X = 130_X, find the value of x (a) 7   (b) 6   (c) 5   (d) 4
9. Simplify: (0.2)³ x 8

0.4²                 A. 40                 B. 0.4              C. 0.2             D. 0.04

1. Simplify:   4(2^{n + 1}) – 2^{n + 2}

2^{n + 1} – 2ⁿ           A. 2^{n + 2}            B. 2^{n + 1}               C. 4               D. 2           E. 2ⁿ

10. Express 0.0000407, correct to 2 significant figures. A. 0.0 B. 0.00004 C. 0.000041 0.0000407
11. If x varies inversely as y and y varies directly as z, what is the relationship between x and z?    x z                    B. x                     C. x z²                     D. x
12. Evaluate:                         B.                  C.                         D.

Fig 1                                        Fig 2

Fig 1 and Fig 2 are the addition and multiplication tables respectively in modulo 5. Use these tables to     solve the equation: (n x 4) + 3 = 0           A. 1                  B. 2                C. 3                 D. 4

14. The ages of Tunde and Ola are in the ratio 1:2. If the ratio of Ola’s age to Musa’s age is 4:5, what is the ratio of Tunde’s age to Musa’s age? 1:4               B. 1:5             C. 2:5             D. 5:2
15. If M = {x: 3 x < 8} and N = {x: 8 < x 12}, which of the following is true?
16. 8 M N II. 8 M N               III. M N =
17. III only B. I and II only C. II and III only              D. I, II and III
18. If x = and y = -6, evaluate: xy –           0             B. 5               C. 8               D. 9
19. Solve the equation: + = 3               B.                C.                 D.
20. A sum of 18,100 was shared among 5 boys and 4 girls with each boy taking 20 more than each girl. Find a boy’s share. 1,820     B. 2000     C. 2,020      D. 2,040
21. One of the factor of 7x² + 33x – 10 is 7x + 5   B. x – 2    C. 7x – 2       D. x – 5
22. Solve: = (3x – 2)                        B. ²/₃        C.   ¾                D.  ³/₅
23. Simplify: 3x – (p – x) – (r – p) 2x – r             B. 2x + r             C. 4x – r                D. 2x – 2p – r
24. An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [ take = ]
25. 29⁰ B. 57⁰ C. 65⁰                        D. 115⁰
26. Which of the following is true about parallelogram? opposite angles are supplementary     B. opposite angles are complementary        C. opposite angles are equal       D.  opposite angles are reflex angles
27. A bearing of 320⁰  expressed as a compass bearing is: N50⁰W      B. N40⁰W     C. N50⁰E    D. N40⁰E
28.                         Q

R

P

X                                                                    Y

O

In the diagram, XY is a straight line. <POX = <POQ and <ROY = <QOR. Find the value of <POQ + <ROY            A. 60⁰                 B. 90⁰               C. 100⁰                    D. 120⁰

26. A stationary boat is observed from a height of 100m. if the horizontal distance between the observer and the boat is 80m, calculate, correct to two decimal places, the angle of depression of the boat from the point of observation. 36.87⁰                B. 39.70⁰                 C. 51.34⁰                    D. 53.13⁰
27. The average age of a group of 25 girls is 10 years. If one girl, aged 2 years and 4 months joins the group, find, correct to one decimal place, the new average age of the group.
28. 10.1 years B. 9.3 years C. 8.7 years               D. 8.3 years

28. N

P                                             T

100⁰            50⁰

R

Q                                              S

In the diagram, NQ//TS, <RTS = 50⁰ and <PRT = 100⁰. Find the value of <NPR.

1. 110⁰ B. 130⁰ C. 140⁰                  D. 150⁰
2. Simplify the expression: a² – b²          B. b² – a²           C. a²b – ab²           D. ab² – a²b
3. Find the 6^th term of the sequence: , , …..              B.              C.              D.
4. The diagonal of a square is 60cm. Calculate its perimeter. A. 20 40     C. 90    D. 120

1. The roots of a quadratic equation are – and . Find the equation.

1. 6x² – x + 2 = 0 B. 6x² – x – 2 = 0           C. 6x² + x – 2 = 0        D. 6x² + x + 2 = 0

1. Make x the subject of the relation: d =

1. x = B. x =                  C.                     D. x =

1. Consider the statements:

p: it is hot

q: it is raining

Which of the following symbols correctly represents the statement “it is raining if and only if it is cold”?     A. p q                  B. q p                 C.                    D. q p

In a class of 32, a student can either do Government, History or both. If 16 students do Government, 18 do History and 3 students do none of the two subjects, find how many do both. A. 2  B. 5  C. 37  D. 34.

Use the information below to answer questions 35 – 37.

In a class of 18, a student can either offer Biology, Economics or both. If 8 students offer Biology, 12 offer Economics and 5 students offer neither of the two subjects.

35. Find how many students offer both subjects. 25        B. 17      C. 7       D. 12.
36. How many students offer exactly one subject? 1      B. 6      C. 12        D.  5.
37. Find the number of students that offer at most one subject. 11        B. 14       C. 13      D. 5.
38. Which of the following brackets is recommended for set notation? Curly bracket    B. exposed bracket C. enclosed bracket        D. braces.
39. Solve for x if 15 – 2x < 5.
40. x > 25 B. x > 15 C. x > 5                D. x > -10                   E. x > -5
41. Twice a certain number x is less than 8. Find the range of values of the number.
42. x > 8 B. x > 2 C. x < 8                D. x < 4                      E. x < 2
43. Solve: (x – 1) > 4.
44. 2x – 2 > 4 B. x – 1 > 6 C. x > 9                  D. x > 8                     E. x < 8

x

-3  -2  -1  0   1    2    3                     Find the value of the inequalities

2. x > -2 x > -3                          C. x > 2                   D. x > 2.5                  E. x > -2.5
3. Find the area of a triangle whose base is 11cm and height 6cm.
4. 66cm² B. 17cm² C. 22cm²                 D. 33cm²
5. In a class of 53 students, x of them are boys. How many girls are in the class?
6. 53x B. 53 + x C.                        D. 53 – x                   E.
7. Calculate the perimeter of the trapezium below:

B              4cm                   C

3cm                                                    2cm

D    A. 8cm   B. 12cm    C. 15cm   D. 18cm

6cm

46. If 20(mod 9) is equivalent to y (mod 6), find y. 1    B. 2     C. 3     D.4

M       a                   f           N

b      c        g

e

Determine M¹ N from the Venn diagram.  A. {f, g}     B. {e}      C. {c, f, g}       D. {e, f, g}

48. What is the product of the roots of 3x² – 4x – 7 = 0? 2      B.       C.       D.
49. Which term must be added to make x² + 2x a perfect square?      B.   C.      D.
50. Expand: (y-6)² y² + 12y + 36        B. y² – 12y – 36        C. y² + 12y – 36         D. y² – 12y + 36

THEORY:   ANSWER FOUR QUESTIONS

1. Use a scale of 2cm to 1 unit on the x-axis and 1cm to 1 unit on the y-axis, draw on the same axes the graphs of: y = 3 + 2x – x²; y = 2x – 3 for -3 x 4.

2.Solve the following equations: (i) x²+ 2x +3 =0 using factorization  method (ii) 3x²-x-2=0 using completing the square method (iii) 2x+7x+5=0 using the quadratic formula method

3(a) A chord AB is 45cm long on a circle of radius 41cm. calculate the angle subtended at the centre of the circle.

(b) The angles subtended by a chord at the centre of a circle of radius 13cm is 48⁰. How far is the chord to the centre of the circle?

4. In a market survey, 100 traders sell fruits, 40 sell apples, 46 sell oranges, 50 sell mangoes 14 apples and oranges, 15 apples and mangoes, while 10 sell all the three fruits. Each of the 100 traders sells at least one of the three fruits. Represent the information in a venn diagram and find the number that sell (i) only one type of fruit (ii) only two types of fruit.
5. Find the value of (i) STV (ii) TUV (iii)VT (iv) TU, in the diagram below if ST=3cm SV and UV=12cm:

      T                                               U  

3cm

12cm

S          4cm          V

6. Draw the Truth Table for statements p, q and r.

Consider the following statements:

p: Julie has diarrhoea

q: Julie is in hospital

If p q, state whether or not the following statements are valid.

1. If Julie is in the hospital, then she has diarrhea
2. If Julie is not in the hospital, then she does not have diarrhoea

• If Julie does not have diarrhoea, then she is not in the hospital

Mid Term Test

1. If P = {x: 1 x 6} and Q = {x: 2 < x < 9}, where x R, find P A. {1, 2, 3, 4}
2. {3, 4, 5, 6}  C.  {4, 2, 9, 8}            D. {1, 2, 3, 5}
3. If x varies inversely as y and y varies directly as z, what is the relationship between x and z?   x z                    B. x                     C. x z²                     D. x
4. If 20(mod 9) is equivalent to y (mod 6), find y. 1    B. 2     C. 3     D.4

x

-3  -2  -1  0   1    2    3                     Find the value of the inequalities

2. x > -2 x > -3                          C. x > 2                   D. x > 2.5                  E. x > -2.5
3. Solve: (x – 1) > 4.
4. 2x – 2 > 4 B. x – 1 > 6 C. x > 9                  D. x > 8                     E. x < 8
5. Which term must be added to make x² + 2x a perfect square?     B.   C.    D.
6. Expand: (y-6)² y² + 12y + 36      B. y² – 12y – 36      C. y² + 12y – 36     D. y² – 12y + 36
7. Which of the following brackets is recommended for set notation? Curly bracket    B. exposed bracket C. enclosed bracket        D. braces.
8. Solve: = (3x – 2)                        B. ²/₃        C.   ¾                D.  ³/₅
9. Simplify: 3x – (p – x) – (r – p) 2x – r      B. 2x + r      C. 4x – r    D. 2x – 2p – r

                        THEORY

1. In a market survey, 100 traders sell fruits, 40 sell apples, 46 sell oranges, 50 sell mangoes 14 apples and oranges, 15 apples and mangoes, while 10 sell all the three fruits. Each of the 100 traders sells at least one of the three fruits. Represent the information in a venn diagram and find the number that sell (i) only one type of fruit (ii) only two types of fruit.
2. Use a scale of 2cm to 1 unit on the x-axis and 1cm to 1 unit on the y-axis, draw on the same axes the graphs of:  y = 3 + 2x – x²; y = 2x – 3 for -3 x 4.
3. Solve the following equations: (i) x²+ 2x +3 =0 using factorization method (ii) 3x²-x-2=0 using completing the square method (iii) 2x+7x+5=0 using the quadratic formula method