13(a) Complete each of the following statements with the

13(a) Complete each of the following statements with the quantifier All or Some so that the statement is true.

[(i) All (ii) Some ](i) .. multiples of 9 are divisible by 3.

(ii) of the sum of the interior angles of a polygon is 360o.

13(b) State the converse of the following statement and hence determine whether its converse is true or false.

[ if 3x + 2 > 3y + 2 then x > y ; True ]

13(c) Complete the premise in the following argument.

[ If a number x is greater than 0 then x is a positive number ]

Premise 1 :

Premise 2 : p is not a positive number.

Conclusion : p is not greater than 0.

[5 marks ]

14.2 Exercise 4.

14.2.1 a)Complete the following table for the equation y =.

x42.510.50.5123.24

y11.68841.251

b)By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis ,draw the graph of y = for 4 < x < 4.

[5 marks]

c)From your graph, find

i)the value of y when x = 1.8

ii)the value of x when y =3.4

d)Draw a suitable straight line on your graph to find all the values

of x which satisfy the equation for 4 < x < 4.

State the values of x.

14.2.2 a)Table shows values of x and y which satisfy the equation y = 2x2 4x 3.

x21012344.55

yk3353m1319.527

Calculate the value of k and of m.

b)By using a scale of 2 cm to 1 unit in the x-axis and 2 cm to 5 units on the y-axis , draw the graph of y = 2x2 4x 3 for .

c)From your graph , find

i)the values of y when x = 1.5

ii)the values of x when y = 0.

d)Draw a suitable straight line on your graph to find a value of x which satisfies the equation 2x2 + x 23 = 0 for 2 < x < 5

State the value of x.

14.2.3 a)Complete table 1 in the answer space space for the equation y = 2x2 x 3

x 2 1 0.512344.55

y7 2 23123342

Table 1

b)by using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis , draw the graph of y= 2x2 x 3 for 2 < x < 5.

[4 marks]

c)From your graph , find

i)the value of y when x = 3.6,

ii)the value of x when y = 37.

d)Draw a suitable straight line on the graph to find all the values of x which satisfy the equation 2x2 3x = 10 for 2 < x < 5.

State these values of x.

14.2.4a) Complete table 2 in the answer space for equation by writing down the values of y when x = 3 and x = 1.5.

b)By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis draw the graph of for .

c)From your graph , find

i) the value of y when x = 2.9,

ii) the value of x when y = 13

d)Draw a suitable straight line on our graph to find a value of x which satisfies the question 2x2 + 5x = 24 for .

State this value of x

x432111.5234

y61224241286

Table 2

14.2.5 (a) Complete Table 3 in the answer space for the equation y = 6 x3 by writing

down the values of y when x = 1 and x = 2.

(2 marks )

x32.5210122.5

y3321.6314659.63

Table 3

(b)For this part of the question, use the graph paper provided. You may use a

flexible curve rule.

By using scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis,

draw the graph of y = 6 x3 for 3 x 2.5.

( 4 marks )

(c) From your graph, find

(i) the value of y when x = 1.5,

(ii) the value of x when y = 10.

( 2 marks )

(d) Draw a suitable line on your graph to find the values of x which satisfy the

equation x3 8x 6 = 0 for 3 x 2.5. State these values of x.

(4 marks )

14.3. Answer to 14.2 Exercise 4

14.2.1 (a)

x 1 2

y4 2

(b) (c) (i) x = 1.8 ; y = 2.22

(ii) y = 3.4 ; x = 1.18

(d) Straight line y = 2x 3

x012

y 3 5 7

x = 2.35 , 0,85

14.2.2 (a) k = 13 ; m = 3

(b)

(b) (i) x = 1.5 ; y = 7.46

(ii) y = 0 ; x = 0.59 and 3.16

(c) straight line y = 5x + 20

x012

y201510

x = 3.16

14.2.3 (a)

x 1 4

y025

(b)

(c) (i) x = 3.6 ; y = 19.35

(ii) y = 37 ; x = 4.73

(d) Straight line y = 2x + 7

x012

y7911

x = 1.61 , 3.10

14.2.4 (a)

x 3 1.5

y 816

(b)

(c) (i) x = 2.9 , y = 8.26 (ii) y = 13 , y = 1.85

(d) Straight line y = 2x + 5

x012

y579

x = 2.44

14.2.5 (a)

x 1 2

y 7 2

2.5(b) (c) (i) x = 1.5 ; y = 2.625

(ii) y = 10 ; x = 1.59

(d) Straight line y = 8xx012

y0816

x =2.32 , 0.84 , 3.14

15.3. Exercise 5

3.1 The data in Diagram 1 shows the donations in RM , of 40 families

to their childrens school welfare fund.

4024173022263519

2328333339343928

2735452138222735

3034313740321428

2032292632223844

a)Using the data in Diagram 1 , and a class interval of RM 5 ,complete the following table.

Donation (RM)FrequencyCumulative Frequency

11 15

16 20

b)By using a scale of 2 cm to RM5 on the x-axis and 2 cm to 5 families on the y- axis, draw an ogive based on the data.

c)From your ogive in (b)

i)find the third quartile,

ii)hence , explain briefly the meaning of the third quartile.

3.2 The data in Diagram 2 shows the masses, in kg, of suitcase for a group of tourists. Each tourist has one suitcase.

2710222821142925

2918221320212427

2725161916242627

2919332523242631

Diagram 2

a)Based on the data diagram and by using a class interval of 3 , complete table 1 provided in the answer space.

b)Based on the table in (a) , calculate the estimated mean mass of the suitcase.

c)By using a scale of 2 cm to 3 kg on the x-axis and 2 cm to 1 suitcase on the y-axis , draw the histogram for the data.

d)State one information obtained based on the histogram in (c)

a)

Class intervalFrequencyMidpoint

10 12

13 15

3.3 The data in the diagram shows the marks for English language monthly test for 42 pupils.

51204531264030

25323741213638

46382837392339

33354229383123

42342635432822

25473148443454

a)using data in diagram and a class interval of 5 marks , complete table 2 in the answer space.

[4 marks]

MarksMidpointFrequency

20 2422

25 29

Table 2

b)Based on your table in (a),

i)state the modal class,

ii)calculate the mean for the English Language monthly test and give your answer correct to decimal places.

[4 marks]

c)By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 pupil on the vertical axis, draw a histogram for the data.

[4 marks]

3.4 The data in Diagram 3 show the donation , in RM collected by 40 pupils.

4926383941454543

2230333945433931

2724324043403835

3434253446233537

4037482547302928

a)Based on the data in diagram and by using a class interval of 5, complete Table 3 in the answer space.

[3 marks]

b)Based on Table 3 in (a), calculate the estimated mean of the donation collected by a pupil.

[3 marks]

c)By using a scale 2 cm to RM 5 on the horizontal axis and 2 cm to 1 pupil on the vertical

axis, draw a frequency polygon for the data.

[5 marks]

d)Based on the frequency polygon in c), state one piece of information about donations.

[1 marks].

Class intervalMidpoint0Frequency

21 25

26 30

Table 3

3.5 Table 4 shows the frequency distribution of the mass, in kg, of a group of 80 students.

Mass ( kg)Frequency

30 - 345

35 - 398

40 - 4411

45 - 4921

50 - 5422

55 - 5910

60 - 643

Table 4

(a) (i) State a modal class.

(ii) Calculate the estimated mean of the mass of the group of students.

(4 marks)

(b) Based on table 4, complete Table 4 in the answer space to show the cumulative frequency distribution of the masses.

Upper BoundaryCumulative frequency

29.50

34.5

Table 4

(c) For this part of the question, use the graph paper provided .

By using the scale of 2 cm to 5 kg on the horizontal axis and 2 cm to 10 students on the vertical axis, draw an ogive for the data.

(4 marks)

(d) 25% of all the students in the group have a mass of less than p kg. These students will be supplied with nutritional food.

Using the ogive you had drawn in 16(c), find the value of p.4. Answers

3.1

Donation (RM)FrequencyCumulative frequency

11 1511

16 2034

21 25610

26 301020

31 351131

36 40738

41 45240

3.1(b)

3.2 (a)

Class IntervalFrequencyMidpoint

10 12111

13 15214

16 18317

19 21520

22 24623

25 27926

28 30429

31 - 33232

(a) Estimated mean =

3.2(b)

3.3 (a)

MarksMidpoint Frequency

20 - 24225

25 29277

30 34328

35 393710

40 44426

45 49474

50 - 54522

(b) (i) Modal class is 35 39

(ii) Estimated mean =

3.3(c)

3.4(a)

Class IntervalMidpoint Frequency

21 - 25235

26 30286

31 35338

36 403810

41 45437

46 49504

(b) (i) Modal class is 35 39

Estimated mean =

3.4 (c)

(d) Modal class of the donation is 36 40

3.5 (a)

Mass ( kg)Frequency

30 - 345

35 - 398

40 - 4411

45 - 4921

50 - 5422

55 - 5910

60 - 643

(i) Modal class is 50 54

(ii) Estimated mean =

(b)

Upper BoundaryCumulative frequency

29.50

34.55

39.513

44.524

49.545

54.567

59.577

64.580

3.5(c)

(c) 25 % of 80 students = 20 students

p = 43.0 kg

If x > y then 3x + 2 > 3y + 2

Diagram 1

Table 1

Diagram 3

Cumulative frequency

(c) (i) 35

(ii) 30 families donated RM35 or less

40

35

30

25

20

15

10

5

0

Donation (RM)

10.5 15.5 20.5 25.5 30.5 35.5 40.5 45.5

9.5 12.5 15.5 18.5 21.5 24.5 27.5 30.5 33.5

9

8

7

6

5

4

3

2

1

0

Frequency

Marks

19.5 24.5 29.5 34.5 39.5 44.5 49.5 54.5

Frequency

10

9

8

7

6

5

4

3

2

1

0

10

9

8

7

6

5

4

3

2

1

0

Frequency

Donation (RM)

15.5 20.5 25.5 30.5 35.5 40.5 45.5 50.5 55.5

Cumulative frequency

29.5 34.5 39.5 44.5 49.5 54.5 59.5 64.5

80

70

60

50

40

30

20

10

0

Mass (kg)

_1269422773.unknown

_1269435983.unknown

_1269438288.unknown

_1269439773.unknown

_1269437658.unknown

_1269422774.unknown

_1269421749.unknown

_1269421750.unknown

_378758463.unknown

_1269421748.unknown

_378584903.unknown