Kem Matematik PMR

1. 7.

2. 8.

3. 9.

4. 10.

5. 11.

6. 12.

13. 14.

DIRECTED NUMBERSCalculate the following and express the answer as a frantion in its lowest term

(PMR 04)

1. Calculate the following and express the answer as a decimal

6 – 1.8



6. Evaluate and give your answer in the decimal form

3.Calculate the following and express the answer as a decimal

7. Evaluate and give your answer in the decimal form6 ÷ 0.5 – 4.3 x 8.7

3. Evaluate and give your answer in the decimal form15 × 3.4 – 2 × (– 4) + 8

8. Evaluate and give your answer in the decimal form56 + 4 .1× 15 – 42 ÷ 3

INDICES

1. Simplify 9.Simplify 17.Simplify 25.Simplify

(PMR 04)




5. Simplify 13.Simplify 21.Find the value of 29.Find the value of

6.Simplify 14.Simplify 22.Find the value of 30.Find the value of 59 22

7.Simplify 15.Simplify 23.Find the value of 31.Find the value of

8.Find the value of 6.17Find the value of 24.Find the value of 32.Find the value of

1.Simplify 6.Simplify 11.Simplify 16.Simplify



4.Simplify 9.Simplify 14.Evaluate 19.Simplify

5.Simplify 10.Find the value of 15.Find the value of

20.Simplify

TOPIC : ALGEBRAIC EXPRESSION-EXPANSION

1 Expand the following

a. 2 ( r + t) b. p (2h – 6m)

2 Simplify 4k -6(5-3k)

3 Expand the following

a. 3 ( r - t) b. x (2x – 6y)

4 Simplify 3(x-2y) -2(x+y)

5 Expand the following.a. p (p - r) b. (p - m) (1+ k)

6 Simplify 2m(m+n) – (m+n)2

7 Expand each of the following expressions:

a. -2(5 - 3x) b. (3x-5)2

8 Simplify –3(p - 3) + (p + 2)2


a.q(2+p) b.(3m-n)2

10 Simplify (r+2)2 -8r + 5

11 Simplify 2t(3-s) – (4 - 9st) 12 Simplify (2y -1)2

13 Simplify (3m-1)2 + 2(m -3) 14 b. 2mplify (4n + m)2 – 2m(n-m)

15 Simplify (x-3)(x+2) – (4x-1) 16 Simplify 2(y-3) – (y+1)2


a.q(2+p)b.(3m-n)2

18 Expand (2a + b)2

19 Simplify 3(2p-5) + (p-3)2 20 Simplify (3m-1)2 + 2(m-3)

ALGEBRAIC EXPRESSION - FACTORISATION

1.Factorise the following completely

a. 2x -6

i. 5pq – 10q

b. 4k + 16

c. 2pq + 6p

d. 4mn + 6 kn

e. 3ab+12b

f. 3p2+6pq

g. 3p2 + 9pq

h. 14ab +28b2

j. 4e – 12ef

k. 16ab – 18b

l. 6p – 18pq

m. 3mn - 15n

n.

o. xy – y2

p. pq2 –p2q

2.Factorise the following completely

a. 2x2 – 8y2

3.Factorise of the following expressions.

a. p2 – 6(p + 1) – ( 8 – p)

b. 3a2 – 27

c. 3h2 – 12k2

d. 50 – 2m2

e. 12x2 – 3y2

f. 50k2 – 2

g. 4x2 – 25y2

h. 3x2 – 48y2

i. 12 – 3x2

b. am – 3m + an – 3n

c. pq –q2+4p-4q

d. 8eu – 2ew – 4fu +fw

e. aq – q + 3a – 3

f. 3a – a b + 6b – 2b2

g. xy + 2x – 3y – 6

TOPIC : ALGEBRAIC FRACTIONS

1Express as a single fraction.

5Express as a single fraction in

the lowest term.

2Express as a single fraction in the

lowest term.

6Express as a single fraction

in the simplest form.


its simplest form.


its simplest form.


in its simplest form.


its simplest form.


in the simplest form.










its simplest form


its simplest form.


its simplest form.

a. x + 5 = 4

b. x + 5 = 2

c.

d.

e. k +10 = 4

f.

g.

h.

i. 3h = h -1

j. 2y =15 -3y

a.

b.

c.

d.

e. = 3.

f.

g. = 1

h. = 2

Solve each of the following equations

LINEAR EQUATION

k. g -12 = 2g

l. 3 - m = 2m – 6

m. 2 + p = 2 – 3p

n. 4x + 5 = 2x – 13

o. 3 - m = 2 (m -1)

p. 2 (k-1) = k+3

q. 5m – 3 = 2 – 3(1 + m)

r. 1 – 3(2 - x) = 1 + 2x

i. = m

j. 2n =

k.

l.

m. = 1 – p

n. = 3 – 2x

o. 2m = 3 –

p. = 3 – 2m

s. 4p – 3(1 + p) = 5

t. 3(x – 2) – 6 = x

u. 3p – 2 = 2 – (3 + p)

v. 2 – (2 + x) = 1 – 2x

w. 3 – 2(3 – 2x) = x

q. + 2 = 7

r. + 3 = 2

s.

t. – 2 = x

u.

. a. = 3 a. = 3.

b. = 5

c. = 5

d. = 3

e. -3n -7 =

f. 4 – (2 – 3m) =

.b.

c. 7x – = 1 – x

d. 4 + p = 3 – p

e. + k = 2 – 3k

h. 5p – 2(3 – p) =

i. (p – 2) = 2 – p

1. find the value of y for equation, where

Solution,

2. Find the value of for equation,

Solution

3. . Find the value of for equation,

Solution

3

Exercises

1.

a) Find the value of if

b) Find the value of if

2.



3. complete each of the following tables to obtain three possible solutions for each of the given linear equation

a)

2-1 3

b)

1 2 3

c)

-1 0 1

d)

0 20

e)

2 6 10-3 3

f)

0 2 46 2

4. Given a function

5. Given that find the value

of,

a)

b)

6.



7. Given that

a) Find the value of , when

b) Find the value of , when

8. Given that


b) Find the value of , when

9 . Given that


b) Find the value of ,when

10.

Copy and complete the following table.

ALGEBRAIC FORMULAE

1. Given that = 2p, express k in terms of p.

equation Value of Value of

(a) 2(b) -2

(c) -9

2. Given that = C, express A in terms of B and C.

3. Given that y – 2x(y – 3) = x + p, express y in terms of x and p.

4. Given that 3 = t, express p in terms of q and t.

5. Given that – = r, express p in terms of q and r.

6. Given that p = 3(2k + n), express k in terms of p and n.

7. Given that 4p – = 3,

8. Given that p = k 2m, express k in terms of p and m.

9. Given that , express m in terms of n.

10. Given that 4 – 2(1 – p) = c – p, express p in terms of c.

11. Given that 3 – r = r – , express p in terms of r.

12. Given that = 2, express y in terms of p and r.

TOPIC : LINEAR INEQUALITIES

1. Represent the inequalities below on the number lines.

a. x > 1 b. x > -2

c. x < - 2 d. x -1

e. x -2 f. x - 3

2. State the inequality in x represented by each of the following number lines.

a. b.

c. d.

3. Solve the following inequalities

a. x – 2 > 5 b. 3 + x 6

c. -5 + x < - 4 d. 7 + x 0

e. f.

1 2 0 -1 -2 -3 -4 1 2 0 -1 -2 -3 -4

1 2 0 -1 -2 -3 -4 1 2 0 -1 -2 -3 -4

1 2 0 -1 -2 -3 -4 1 2 0 -1 -2 -3 -4

0 1 -1 -2 -3 -4 -5 0 1 -1 -2 -3 -4 -5

0 1 -1 -2 -3 -4 -5 0 1 -1 -2 -3 -4 -5

g. - x > 8 h. 3x < 15

i. 3x + 5 17 j. 4 – 5x 12

k. 7 + 3x > -7 – 4x l. 5 – 7x < 10 – 2x

4. List all the integer value of x which satisfy both the inequalities

a. and < 0 b. and 1 – 2x < 5

C x – 1 > -3 and x – 3 4 d. 6 – k < 4 and k – 5 < 2

e. -6 3x + 12 18 f. 3 < 6 – 3m 1

5. Diagram 1 below represents two simultaneous linear inequalities on a number line.

Which inequality represents the common part of both the inequalities?

A. B C D

6. Which of the following number line represents the solution of the linear inequalities 7 2x – 3 < 15 ?

A. B

C. D

.7. The solution for the simultaneous linear inequalities 3x + 2 11 and –x 7 is

A. -7 x 3 B -3 x 7 C -7 x -3 D 3 x 7

RATIO, RATE AND PROPORTION

1. (a) Given that P : Q = 2 : 3 and Q : R = 4 : 7. Find P : R.

(b) Given that A : B = 4 : 3 and A : C = 5 : 7. Find B : C.

(c) Given that P : Q = 2 : 3 and Q : R = 6 : 8. Find P : Q : R.

2 3 1 0 -1 -2 -3

Diagram 1

2 6

5 9

2 6

5 9

(d) Given that A : B = 2 : 3 and A : C = 4 : 7. Find A : B : C.

(e) Given that P : Q = 4 : 3 and P : R = 2 : 7. Find P : Q : R.

2. A sum of money is given to Ali, Abu and Awang with the ratio of 4 : 5 : 9each. If Abu receives RM40, how much money is receives by Awang.

3. Some apples are given to Khaty and Feri with the ratio of 4 : x each.Given that Khaty receives 20 apples and Feri receives 35 apples.Find the value of x.

4. The total lost of 8 pens is RM48. How much do 20 same pens lost ?

5. The total lost of 5 books is RM15. How many books can be bought withRM60.

6. A car moves with a speed of 120 km/hr. What is the distance travelledin 15 minutes.

7. A helicopter moves with a speed of 300 km/hr. What is the time taken to move a distance of 450 km.

8. A sum of RM96 is given to John, Johnny and Jono with the ratio of3 : 2 : x. Given that John receives RM24. Find the value of x.

9. A bus moves from A with an average speed of 60 km/hr. Find the totaltime taken by the bus to reach B if the distance of AB is 330 km.

10. Some oranges are given to Abu, Ali and Ahmad. Abu receives 40oranges. Given that the ratio of Abu to Ali is 5 : 3 and the ratio of Ali to Ahmad is 4 : 5.Find,

(a) the total oranges received by Ahmad,

(b) the ratio of Abu to Ali and to Ahmad.

11. 4 cuboids of the same size weigh 32 kg. If a total of x cuboids weigh72 kg, find the value of x.

12. 8 baskets of the same size can be filled with 12 marbles.How many baskets are needed to fill in 180 marbles ?

13. 7 boxes of the same size can be filled with 210 chalks. How many chalks can be filled in 11 boxes ?

14. A bicycle moves with an average speed of 20 km/hr. Find the distancetravelled in 3 hours and 30 minutes.

15. A sum of money is given to Awang, Awie and Amy with the ratio of4 : x : 7 each. Awang receives RM36 and Awie receives RM81.Find,(a) the value of x,

(b) the sum of money received by Amy.

16. In 3 hours, Ahmad can utter 18000 words. How many words can be uttered within 4 hours and 30 minutes ?

CIRCLES

1. Using π = , calculate the area and the arc length of the circle or the

sector given where O is the centre.

(a) (b) (c)

14 cm

O

O 60 o

7 cm

7 cmO

(d) (e)

2. For each of the following, find the area of shaded region where O is the

centre of the circle or the sector [Using π = ].

(a) (b)

(c) (d)

O

7 cm 28 cmO

O 7 cm C B

D

A

3 cm

O

7 cm

CB

DA

8 cm7 cm

3 cm

GEF

O C

B

A10 cm

6 cm

O

B

A

OA = 12 cm, OB = 16 cm

(e) (f)

(g)

3. For each of the following, calculate the perimeter of the shaded

region where O is the centre of the circle or sector [Using π = ]

(a) (b)

(c) (d)

OA

OA = 14 cm

OA

4 cm

F B

C D

E

AB = 14 cm, AE = FB = 2 cm

O

A8 cm

BC

D

3 cm

7 cm

60 o

14 cm

2 cm2 cm

7 cmO

10 cm

8 cm

O

7 cm

C

B

D

A

5 cm

7 cm 3 cm

G

E

F O 7 cm C B

D

A

20 cm

5 cm

(e) (f)

4. For each of the following, find the value of x where O is the centre.

(a) (b) (c)

(d) (e) (f)

O 7 cm B

A

7 cm

O

20 cm C

B

D

A

25 cm

7 cm

O

80 o

x o

O40 o

x o

O

50 o

x o

O

40 o x o

O

130 o

x oOA

x o

10 o10 o

B

(g) (h) (i)

(j) (k) (l)

(m) (n) (o)

TRIGONOMETRY

1. For each of the following, find the value of sin x, cos x and tan x.

(a) (b) (c)

O10 o

x o

20 oO

160 o

x o

O60 o

x o

70 o

O

60 o

x o50 o

40 oO

10 o

x o

140 o20 o

O

40 o

x o

70 o

O

x o

130 o

O10 ox o

20 o

O

60 ox o

a b

cx o

p

q

r

x o

l

m

kx o

(d) (e) (f)

(g) (h) (i)

(j)

2. (a) (b)

ABC and BED are straight lines. Given that cos x o = .

Given that cos x o = . Find the value of tan y o

5 12

x o

4 3x o

5

3

x o

13

5x o

20

12x o 8

10x o

4

5x o

AB C

D

E y o

x o

13 cm

8 cm

3 cmA B

CD y o

x o

13 cm

4 cm

Find the value of sin y o

(c)(d) Diagram below shows two right angles triangles,

DAB and CDB

ABC and BED are straight lines. It is given that tan yo = and sin xo =

E is midpoint of BD (a) Find the value of cos yo

Find the value of cos y o (d) Calculate the length, in cm, of BC

(e) (f)

7 cm

Given that cos x o = ABCD is a rectangle and tan x o = .

Find the value of sin y o Find the value of cos y o

(g) (h)

Given that sin x o = ADC is a straight line. Given that tan x o =

Find the value of cos y o Find the value of sin y o

A

B

CD

E

y o

x o

8 cm

A B

C

D

20 cm

y o

x o

8 cm

A B

C

D4 cmy o

x o

3 cmE

8 cm

AB

C

D

E

y o

x o

10 cm

8 cm4 cm

A B

CD

E

y o

x o

10 cm

6 cm

(i) (j)

Given that cos x o =

and sin y o = . Find CD. BCD is an equilateral triangle.

Given that tan x o = and sin y o = .

Find CE.

(k) (l)

Given that sin x o =

Find the value of tan y o

Given that cos x o =

Find the value of sin y o

Trigonometry (Enrichment)

1. In Diagram 1, tan x = . Find the value of y

DIAGRAM 1

A

B C

D

y o

x o

12 cm

A

B C

D

12 cm

y o

x o

E

AB

CD

y o

x o

9 cm

6 cm2 cm

E

A B

C

Dy o

x o

14 cm

5 cm

E

P cm5 cm

2 cm

12 cmy x

2. Diagram 2 below show a right angled triangle, PQR and QRS is a straight line.

DIAGRAM 2a) Find the value of sin xo

a) Given that tan y o = 1, calculate the length, in cm of RS

3. In Diagram 3, C is the midpoint of the straight line BD

DIAGRAM 3

Find the value of tan xo

5. Diagram 5 shows two right angles triangles, DAB and CDB

DIAGRAM 5

5 cm

12 cm

xo yo S

P

QR

It is given that tan yo = and sin xo =

(a) Find the value of cos yo (b) Calculate the length, in cm, of BC

6. Diagram 4 shows a right angled triangle, PQR

DIAGRAM 6

It is given that tan y = ,

(a) find the value of x (b) find the value of cos y

7. In Diagram 7, S is the midpoint of staright line TSQ.

DIAGRAM 7

Given that cos , calculate (a) The length of TQ(b) Find sin xo

9. In diagram 9 , PZV is a straight line.

DIAGRAM 9a) Find the value of sin x o

b) Given that cos , find the length of WP

10. In diagram 10 , JKL is a straight line.

DIAGRAM 10

It is given that cos x = and tan y=2 .Calculate , the length , in cm, of JL.

11. Diagram 11 shows a right angled triangle PQM.

DIAGRAM 11

It is given that QN = 13 cm, MP=24 cm,and N is the midpoint of MNP. Find the value of tan yo

12. In diagram below PQR is straight line, Q is midpoint of PR.

It is given that tan xo =

a) Find the value of tan y

b) Calculate the length in cm of PS

LINES AND ANGLES

Find the value of x each of the following.

(a) (b) (c)

(d) (e) (f)

xº

120º

70º

130º

120º

xº

4xº

xº + 90º

xº 140º

60º xº

30º20º

30º

xº

P

9 cm

yo xo

S

Q R

(g) (h) (i)

(j) (k) (l)

(m) (n) (o)

(p) (q) (r)

POLYGONS

Find the value of x each of the following,

(a) (b)

20º

70º

xº xº3xº

80º xº

60º80º

60º 40ºxº 120º 120º

xº

120º

xº

4xº60º

20º xº60º

70ºxº

10º

120º

xº40º xº

60º

20º xº

110º

xºxº

(c) (d)

(e) (f)

(g) (h)

(i) (j)

(k) (l)

xº

120º

150º

80º xº

xºxº

20º

130ºxº

xº30º20º

xº xº

xº

xº

(m) (n)

(o) (p)

(q) (r)

Graphs of Functions

1. Use the graph paper provided below to answer this question. Table 1 shows the values of two variables, x and y, of a function.

x -3 -2 -1 0 1 2 3 y -7 -2 1 2 1 -2 -7

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 A graph for the function.

2. Use the graph paper provided below to answer this question.

xº130º

120º

120º

80ºxº

xº

xº

120º 120º

120º

110º 140º

40º 40º130º

40º

xº

60ºxº

100º

xº

100º

120º

Table 2 shows the values of two variables, x and y, of a function.

x -2 -1 0 1 2 3 4 y 32 18 8 2 0 2 8



x -3 -2 -1 0 1 2 3 y 15 5 -1 -3 -1 5 15



x -2 -1 0 1 2 3 4 y 15 8 3 0 -1 0 3

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2.5 units on the y-axis, draw A graph for the function.


x -3 -2 -1 0 1 2 3 y -25 -6 1 2 3 10 29


LOCI IN TWO DIMENSION

1. Diagram 1 in the answer space shows a square, PQRS with sides of 8 cm. W, X and Y are three moving points in the diagram.

a) W is the point which moves such that it is equidistant from straight lines SP and SR. By using the letters in the diagram, state the locus of W. b) On the diagram, draw

i) the locus for the point X that is constantly 4 cm from the point O.ii) the locus for the point Y that is constantly 2 cm from the straight line KM

c) Hence, mark with the symbol the intersection of the locus of X and the locus of Y.

( 5 marks )

Answer :

(a)

(b) (i) (ii)

(c)

Diagram 1

2. Diagram 2 in the answer space shows a hexagon with sides of 4 cm. X, Y and Z are three moving points in the diagram.

a) X is the point which moves such that it is equidistant from point A and point E.By using the letters in the diagram, state the locus of X.b) On the diagram, draw

i) the locus of point Y that is constantly 4 cm from the point C.ii) the locus for the point Z that is constantly 1 cm from the straight line FC.

c) Hence, mark with the symbol the intersection of the locus of Y and the locus of Z. ( 5 marks )

Answer :

(a)

(b) (i) (ii)

(c) F E

A D

P K Q

N O L

S M R

B C

Diagram 2

3. Diagram 3 below shows a rectangle ABCD. In the same figure, construct the loci for:

a) point T that moves in such a way that its distance from A is always 4 cm,b) point Y that moves in such a way that is always equidistant from lines AC and BD.

Subsequently, mark the point/points of intersection of the two loci using the symbol . ( 4 marks) D C

A B

Diagram 3

4. Diagram 4 below shows a circle with radius 2 cm and O as the centre. Point X moves in such a way that its distance is always 2 cm from O and 1.5 cm from the straight line AOB. Construct and mark with symbol for the possible position of point X.

A O B

Diagram 4

5. Diagram 5 in the answer space shows four squares, KUJS, ULVJ , JVMW and SJWN. X, Y and Z are three moving points in the diagram.

a) X moves such that it is equidistant from the straight lines KN and LM. By using the letters in the diagram, state the locus of X. b) On the diagram, draw (i) the locus of Y such that YJ = JS (ii) the locus of Z such that its distance from point L and point N are the same.

c) Hence, mark with the symbol all the intersections of the locus of Y and the locus of Z.

( 5 marks ) K U L

J S V

N W M

Diagram 5

6. Diagram 6 below shows a triangle, PQR.

a) On the diagram, construct : (i) locus T, which is always moving at a fixed distance of 2.5 cm from R. (ii) locus U which moves in such a way that its vertical distance is always the same from QP and QR.

c) Mark the point of intersection of locus T and locus U using the symbol .

( 3 marks ) P

Q R Diagram 6

7. (a) Diagram 7 below is a square EFGH. X is a point that moves equidistant from F and H. State the locus of X using the letters in the diagram. (b) Construct on the diagram, (i) locus Y which moves at a distance of 2 cm from T. (ii) locus Z which moves in such a way that its vertical distance from line HF is always at 1.5 cm. (c) Mark all the possible point/points of intersection between locus Y and locus Z.

( 5 marks )Answer :

(a)

(b) (i) (ii)

(c) E F

T

H G

Calculate the value of

i. 42 = ……………….ii. 62 = ………………iii. (-2)2 = ……………….

iv. = ……………

v. = …………

vi. = ………….

vii. = …………

Find the value of

D Cube Roots

Find the value of

v. = ……………

vii. = …………….

viii. = ……………

ix - 1 = ……………

x = …………

xi = ………….

i. = ……………

ii. = ……………..

iii. = ……………

iv = ……………

v = ………….

vi. = ………….

vii.

vii. = …………

viii. = ………….

ix. = …………

x . = ………..

xi. = ………

xii. = ………..

xiii = ………..

ix = ………..

i. = ……………...

ii. = ……………..

iii. = …………….

iv. = …………..

v. = ……………..

vi. = ……………..

vii. = …………….

v. = ……………..

vi. = ……………..

1. a) Find the value of 42 +

b) Find the value of

c) Calculate the value of ( 4.2 + )2

a) Find the value of

b) Calculate the value of 3.3 +

c) Calculate the value of 42 +

2.


b) Calculate the value of +


b) Calculate the value of 0.6 +

TOPIC : STATISTICSTIME : 2 HOURS

1. The data below shows the scores obtained by a group of boys in a game.

3 2 1 3 1 2 3 4 5 5 2 5 5 2 1 5 2

4 2 1 4 2 4 5 4 2 3 1 5 2 5 3 4 1

(a) Using the data, complete the frequency table in the answer space.

(PMR 04)

(b) State the mode of the score.

Answer::

(a)

Number 1 2 3 4 5

Frequency

(b)

2. The following data shows the grades obtained by students in Form 3 Jaya in a Mathematics monthly test.

A A C B B B B A C C D D A A B B C A A

B B B C C C C A A D C C B B B C C D

(a) Complete the frequency table in the answer space using the data above.

(b) State the mode of the data.

Answer:

(a) Grade A B C D

Frequency

(b)

3. The data below shows the marks obtained by the students in form three Bestari in a Science

topical test.

40 43 45 43 41 42 43 44 45 45 42

45 45 42 41 40 40 43 40 40 45 42



Answer::

(a)

Number 40 41 42 43 44 45

Frequency

(b)

4. The following data shows the modes of transport used by students in Form 3 to travel daily to school.

Bus Bus Bus Bicycle Car Car Bicycle Bicycle Bus

Bus Bus Car Bicycle Bicycle Bicycle Bus Bus

Bus Car Bicycle Bus Bus Bus Car Car Bicycle

Bus Car Car



Answer:

(a)

Mode of transport Bicycle Bus Car

Frequency

(b) 5. The data in the table below shows the numbers obtained when a dice is thrown 36 times..

3 2 1 3 1 2 3 4 5 5 2 5 5 2 5 2 4 2

1 4 2 4 5 4 2 3 1 5 2 5 3 4 1 3 5 3


(b) State the median of the data.

Answer::

(a)

Number 1 2 3 4 5 6

Frequency

(b)

6. Azian draws cards with the letters A, B, C, D and E from a satck of cards 29 times. The data shows the letters obtained by her for each draw.

A A C B B E B A E C D D A A B

C B B C C C E A A D C C E B



Answer:

(a)

GradeA

B C DE

Frequency

(b) 7. The data below shows the marks obtained by the students in form 3 Usaha in a Mathematics

topical test.

20 23 25 23 21 22 23 24 25 25 22

25 25 22 21 20 20 23 20 20 25 22


(b) State the median score.

Answer::

(a)

Number 20 21 22 2324

25

Frequency

(b)

8. The following data shows the amount of daily liquid consumption, in ml, of 25 adults.

550 600 550 550 600 650 700 800 750 550

600 600 650 600 800 750 700 800 600 650

700 650 750 800 550



Answer:(a)

Liquid consumption (ml)

550 600 650 700 750 800

Frequency

(b) 9. The incomplete pictogram below shows the number of students in Form 3 who sat for an

examination. If there are 300 students in Form 3 and the number of students who obtained grade C is 75, complete the pictogram

Answer ::

Grade A Grade B

Grade C represents ______ students

10. The pictogram shown below is incomplete. It shows the number of cakes sold by the Home Science Society during the Food Fair Week. If the number of cakes sold for the three days is 200 pieces, complete the pictogram.

Answer :

represents 25 pieces of cakes

11. The incomplete pictogram below shows the number of books read by 3 students in the NILAM programme. If Awwal read 80 books and the total number of books read by the three boys is 200, complete the pictogram

Answer :

Azhar

Ameen

Monday Tuesday Wednesday

Awwal represents ______ books

12. The incomplete pictogram below shows the number of members of the Mathematics Society in a school. If the total number of members of the society is 156, complete the pictogram in the answer space.

Answer :

Form 1 ♀ ♀ ♀ ♀ ♀ ♀Form 2 ♀ ♀ ♀ ♀ Form 3

♀ represents 12 members

13. Marina sold 195 cupons to parents in three housing areas for the school Food Fair. The incomplete pictogram below shows the information on the number of cupons sold. If 60 cupons were sold to parents in Taman Daya, complete the pictogram in the answer space.

Answer :

Taman Daya Taman Mega

Taman Sura represents _______ cupons

14. Sameer collects 85 samples of tadpoles in carrying out a scientific experiment. The incomplete pictogam below shows the information on the number of tadpoles collected from three different places. If 45 tadpoles were collected from Pond B, complete the pictogram in the answer space.

Answer :

Pond A

Pond B

Pond C represents ___________ tadpoles

15. The table shows three types of games played by 45 students in Form 3 Tekun.

Games Number of students

Soccer 24

Netball K

Badminton 8

(a) Find the value of K.

(b) Represent all the information in the table as a bar chart in the answer space.

Answer :

(a)

(b)

4

8

Soccer Netball Badminton

Num

ber o

f stu

dent

s

Games

12

16

20

24

1. A stationary shop sold 250 pens in three months. The table below shows the number of pens sold.

Month Number of students

January 80

February 120

March M

(a) Find the value of M.

(b) Represent all the information in the table as a bar chart in the answer space.

Answer :

(a)

(b)

20

40

80

100

120

140

January February March

Num

ber o

f pen

s

Month

16. The total rainfall for three months is recorded to be 40 mm. The table below shows the amount of rainfall.

Month Total rainfall (mm)

June H

July 15

August 13

(c) Find the value of H.

(d) Represent all the information in the table as a line graph in the answer space.

Answer :

(a)

(b)

2. Adriana earns RM 2400.00 in a month. The table below shows her monthly expenditure.

Item Amount (RM)

Savings Y

Rent Z

Food 1000.00

(c) Find the value of Y.

(d) Represent all the information in the table as a pie chart in the answer space.

Answer :

(a)

(b)

4

8

12

16

20

24

June July August

Tota

l rai

nfal

l (m

m)

Month

Savings

11. 2005 Table below shows the number of students who play four type of game.Jadual di bawah menunjukkan bilangan pelajar yang bermain empat jni permainan.

3. Suseela prepares three types of dishes using 25 kg of beef. The table below shows the amount of beef used.Suseela menyediakan tiga masakan menggunakan 25 kg daging. Jadual di bawah menunjukkan jumlah daging yang digunakan.

Types of dishJenis masakan

Amount of beef (kg)Kuantiti daging(kg)

Masakan/Dish A M

Masakan/Dish B 10

Masakan/Dish C 8

(e) Find the value of M.Cari nilai M

(f) Represent all the information in the table as a pie chart in the answer space.Wakilkan semua pernyataan dalam jadual sebagai carta pai dalam ruang jawapan

Answer : (a)

(b)

Types of gamesJenis permainan

Number of studentsBilangan Pelajar

Ping Pong 8Badminton 15

Hocky 25Hand Ball/Bola Baling 12

The information for Badminton is shown fully in the pie chart in the answer space.Complete the pie chart to represent all the information in Table above.Maklumat bagi permainan Badminton ditunjukkan sepenuhnya dalam carta pai di ruang jawapan. Lengkapkan carta pai itu untuk mewakili semua maklumat dalam jadual diatas.

Jawapan:

12. 2006 Diagram 5 is a pie chart which shows the number of pupils in five groups who complete an assignment during a motivational camp.

Badminton

Rajah 5 ialah carta pai yang menunjukkan bilangan murid dalam lima kumpulan yang Berjaya menyiapkan tugasan semasa kem motivasi.

It is given that the total number of pupils who complete the assignment is 36.Diberi bilangan murid yang Berjaya menyiapkan tugasan ialah 36 orang

(a) Find the value of x.Cari nilai x.

(b) Calculate the angle of the sctor representing the Tuah group. Show your working.Kira sudut sektor yang mewakili kumpulan Tuah. Tunjukkan cara kerja.

(c) State the mode of the data.Nyatakan mod data itu.

Jawapan:

(a) (b)

(c)

13. 2008 Table 15 in the answer space shows the number of gold medals obtaind by four schools in a sport competation. The information for school L is shown fully in the pie chart in Diagram 15.

Jebatx

Kasturi2x

Lekir8

Lekiu12

Tuah10

Diagram 5

Jadual 15 dalam ruang jaapan menunjukkan bilangan piala emas yang dperolehi empat buah sekolah dalam satu prtandingan sukan.. Maklumat bagi sekolah L ditunjukkan sepenuhnya dalam carta pai di Rajah 15.

CompleteLengkapkan

(a) The angle of the sectors for school M and School L in the Table 15Sudut sektor bagi Sekolah M dan Sekolah L dalan Jadual 15

(b) The pie chart in Diagram 15 to represent all the information in Table 15Carta pai dalam Rajah 15 untu mewakili semua maklumat dalam Jadual 15.

Jawapan: (a)

(b)

BAB 4 : STATISTIK II – CARTA PAI

Contoh:

SchoolSekolah

Number of Gold MedalsBilangan Pingat Emas

Angle of sectorSudut sektor

K 10L 60 180˚M 20N 30

180˚

1. Jadual di bawah menunjukkan bilangan kemalangan dalam masa seminggu.

Jenis Jalan Lebuhraya Persekutuan Bandar Lain-lainBil. Kemalangan 4 9 14 3

Sudut Penyelesaian:

Jumlah kemalangan = 4+9+14+3 = 30

a) Sudut Lebuhraya =

=

= 48°

2. Jadual di bawah menunjukkan keputusan ujian bulanan Matematik Tingkatan 3D.

Gred A B C D

b) Sudut Persekutuan =

c) Sudut Bandar = d) Sudut Lain-lain =

Bil. Pelajar 4 12 18 6Sudut

Penyelesaian:

Jumlah Pelajar =

b) Sudut Gred A=

b) Sudut Gred B =

c) Sudut Gred C = d) Sudut Gred D =

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