modul intermediate math pmr

PMR Mathematics Paper 2

1

MODULE FOR INTERMEDIATE STUDENT WHOLE NUMBERS / INTEGERS CALCULATE the value of …………. 1. 5 9 2. 3 8 3. 13 5 4. 12 ( 7) 5. 2 8 6. 5 8 7. 9 7 4 ( 2) 8. 36 9 3 ( )4 9. 72 12 3 3 10. 19 4 5 3 2 11. 16 4 15 4 12. 24 36 9 4 2 13. 16 7 4 3 5 14. 18 2 3 6 3 15. 20 4 3 6 8 PMR 2005 Calculate the value of 96 3 12 48 6 .


2

PMR 2007 Calculate the value of 14824 FRACTIONS CALCULATE the value of ……………. and express the answer as a FRACTION in its LOWEST TERM.

1. 1 13 2

2. 3 15 4

3. 2 13 5

4. 1 212 3

5. 3 2 127 7 3

6. 6 3 71 17 4 9

7. 1 4 117 7 9

8. 1

31

411

32

9. 971

83

76

2004

Calculate the value of 522

52

312

and express

the answer as a fraction in its lowest term. PMR 2006


3

Calculate the value of

32

54

811 and express

the answer as a fraction in its lowest term DIRECTED NUMBERS (Combination : Fractions + Decimals) CALCULATE the value of ……………. and express the answer : i. as a decimal, or ii. correct to 2 decimal place(s) 1. 2.35 0.2

2. 11 0.754

3. 4 3.25

4. 7.41 0.3

5. 1 20.354 5

6. 2 10.63 4

7. 23.25 0.45

8. 24.21 0.63

9 17.25 0.63

10. 53.25 0.96

PMR 2004

Calculate the value of 1 10.82 5

and

express the answer as a decimal.

PMR 2005


4

Calculate the value of 14.26 0.8 12

and

express the answer correct to two decimal places. SQUARES, , CUBES & 3 (a) FIND the value of ……… (b) CALCULATE the value of ……….

1. (a) 20.05

(b) 31149

2. (a) 3 0.027

(b) 238 216

3. (a) 33.0

(b) 23 564

4. (a) 38

343

(b) 32121

5. (a) 6400

(b) 231 125

PMR 2004 (a) Find the value of 3 0.512 . (b) Calculate the value of

2 32748

.

PMR 2005

(a) Find the value of 31

4

.

(b) Calculate the value of

234.2 27 .

PMR 2006 (a) Find the value of 49.0

(b) Calculate the value of

3

11625

marks3

PMR 2007


5

(a) Find the value of 3 64

(b) Calculate the value of 3

3621

marks3

LINEAR EQUATIONS SOLVE the following equations. 1. (a) 3 9h (b) ww 31223

2. (a) 172

x

(b) 6265 kk

3. (a) 854

m

(b) 9335 ww 4. (a) 2 6k (b) 2253 mm

5. (a) 3 2m (b) 52347 kk

6. (a) 43

3

x

(b) 2523 hh

7. (a) 3 1 3m

(b) 63

4

xx

8. (a) 12 5m

(b) 323415 uu

9. (a) 7 4 15k

(b) uu

34


6

10. (a) 1 43p

(b) 224352 nn

11. (a) 352

k

(b) 7342125 ff

12. (a) 935

h

(b) uu 21845

13. (a) 23

1

p

(b) 15121 xx 14. (a) 2 5 1h (b) ww 5825 15. (a) 3 4 2r

(b) 2 1 4 5 3 2k k PMR 2004 Solve each of the following equations : (a) 14k k

(b) 3 6 4 312

f f

PMR 2005 Solve each of the following equations : (a) 2 3 4n n

(b) 3 72

5kk

PMR 2006 Solve each of the following equations:

(a) 312

n

(b) 2( k – 1 ) = k + 3 marks3 PMR 2007 Solve each of the following linear equations:


7

(a) 410 x

(b) xx

3

45 marks3

ALGEBRAIC EXPRESSIONS (Factorisation) ab bc = b a c

Factorise completely each of the following expressions :

1. 2 6c 2. 9 21t 3. 2 12h 4. 10 8c 5. w wy

6. 6 3 j

7. 4 10r 8. 8 6g

2 2a b a b a b


1. 22 fe 2. 22 dc 3. 12 r 4. 21 s 5. 42 w 6. 29 a


8

7. 162 b 8. 252 c

2x bx c x p x p Factorise completely each of the following expressions : 1. 122 xx 2. 442 bb 3. 962 cc 4. 1682 ff 5. 25102 gg 6. 36122 kk 7. 49142 mm 8. 64162 qq

ax ay bx by a x y b x y x y a b


1. bdbcadac 2. bdbcadac 3. tytxsysx 4. tytxsysx 5. nqnpmqmp 6. nqnpmqmp


9

7. vwvawav 2 8. vwvawav 2 PMR 2004

Factorise completely:

(a) 9xy – 3x2

(b) p2 – 6 ( p + 1 ) – ( 8 – p ) marks3 PMR 2005

Factorise completely each of the following expressions: (a) 4e – 12ef (b) 3x2 – 48 marks3 PMR 2006

Factorise completely 50 – 2m2 marks2 PMR 2007

Factorise completely each of the following expressions

(a) 2y + 6 (b) 12 – 3x2 marks3


10

ALGEBRAIC EXPRESSIONS (Expand and Simplify) a) Expansion

a (b + c) = ab + ac

a b c d = ac ad bc cd

b) (i) 2a b a b a b

2 22a ab b

(ii) 2a b a b a b

2 22a ab b

(iii) a b a b

2 2a ab ab b 2 2a b

1. (a) 2 3x y

(b) 2 2 2x y x y

2. (a) 3 3m n

(b) 22 2c d c d

3. (a) 2 2a b

(b) 2 2 2e f e f

4. (a) 3 2a a

(b) 42 2 rrr

5. (a) 3 1 5p

(b) nn 211 2


11

6. (a) 2 3 1n m

(b) 22 prp

7. (a) 3( 2)r

(b) 222 baba

8. (a) xx 428

(b) 131 2 nnn PMR 2004 Simplify ( 3x – 1)2 – (7x + 4) marks2 PMR 2005 Simplify qpqqp 42 2 marks2 PMR 2006 Simplify 23523 pp marks2 PMR 2007 Expand each of the following expressions (a) q ( 2 + p ) (b) ( 3m – n )2 marks3


12

ALGEBRAIC FRACTIONS EXPRESS each of the following as a SINGLE FRACTION in its SIMPLEST FORM :

1. 2 33 15r r

r

2. 3

4 8g g

g

3. 3 2

2 6u u

u

4. 5 10 44 8

tt

5. 4 12 3

2 8d

d

6. 3 4 3

5 10n

n

7. 1 5 22 12

cd

8. 1 2 5

4 8g

f f

9. 1 52 8

dc c

PMR 2004 Express

mp

p

m211

23 as a single fraction

in its simplest form marks3

PMR 2005 Express 262

21

mm

m

as a single fraction in

the simplest form. marks3

PMR 2006 Express mv

vm 15

2551

as a single fraction in

the simplest form. marks3


13

PMR 2007 Express n

wn 6

3235

as a single fraction in its

simplest form. marks3 ALGEBRAIC FORMULAE

Given …………….., express …….. in terms of …………..

1. Given 5m xy , express x in terms of m and y .

2. Given 24y x z , express x in terms of y and z .

3. Given 2 3n m m , express m in terms of n .

4. Given 2 5y x y , express x in terms of y.

5. Given 2

hkk , express h

in terms of k .

PMR 2004 Given that 532

k

p , express p in terms of k

marks3

PMR 2005 Given 234

pyy , express y in terms of p

marks3

PMR 2006 Given 5

3 nknF , express n in terms of F and k

marks3


14

PMR 2007 Given pr 72 , express r in terms of p marks2 LINEAR INEQUALITIES

SOLVE the following inequalities. List all the integer values of …… which satisfy ………….. (Solve the following simultenous Inequalities)

1. 5 3x

2. 3 2 7p

3. 4 16x

4. 2 6 4g

5. 4 9k + k

6. 1 6x x + 3

7. 3 52n n

8. 2 5 7y y - 2

9. 2 5 8w w

10. 3 4w and

4 4

5w w

PMR 2004 (a) Solve the inequality 52 x (b) List all the integer value of x which satisfy

both the inequalities 132

x and 03 x marks4

PMR 2005 Solve the inequality xx 657 marks2 PMR 2006 List all the integer values of x which satisfy both

the inequalities 12

x and 521 x marks3


15

PMR 2007 Solve each of the following inequalities: (a) 26 w (b) 8 4 9 2v v marks3 INDICES

(a) EVALUATE …………. (b) FIND the value of …………. (c) SIMPLIFY ………………. Find the value of each of the following :

(a) 2327 (b)

2532

(c) 3225 (d)

5664

(e) 27128 (f)

6532

(g) 3416 (h)

23343

Evaluate each of the following :

1. 38 32

2. 31

12510

3. 38143

4. 2

43

25

5. 52

325

6. 54

1 322

7. 232

264

8. 41

4 813 Simplify each of the following :

1. nmnm 323

2. 524 23 ee

3. 2

3

34

yy


16

4. 2371 abba

5. 304 ggg

6. 21

623 ww

7. 444 33 yxxy

8. 39323 khkh

9. 7323 heeh

10. 51432 nmnm

11. 21

25

23

9

nn

12.

312

31

21

mnnm

13. 8332 pnnp

14. 2 21 2 2 3 22e f e f e f PMR 2004 Given that ,162 2 x calculate the value of x marks2 PMR 2004 Simplify 932422 kmkmk marks3 PMR 2005 Given 212 333 xx , calculate the value of x marks2

PMR 2005 Evaluate 32

21

21

8

123 marks3

PMR 2006 Simplify 2

4

k

kk marks2

PMR 2006 Find the value of 23

21

2 2183 marks3


17

PMR 2007 (a) Find the value of 21

23

55 (b) Simplify 234 hhg marks3

TRANSFORMATIONS 1. In Diagram 1, N is the image of M under a

translation hk

.

(a) State the value of h and k . (b) Given 'K is the image of point K under

the same translation, state the coordinates of K .

2. In Diagram 2, Q is the image of P under a rotation.

3. In Diagram 3, quadrilateral DEFG is the image of quadrilateral DJKL under an enlargement. (a) State the centre of the enlargement. (b) Find the scale factor of the enlargement. 4. In Diagram 4, L' is the image of L under transformation V.

x

y

O 2

2

4

4

6

6

8

8

D E

F G

J

K

L

x

y

2 4 2 4

2

4

6

2

M

N

K’

DIAGRAM 1

DIAGRAM 3

x

y

O 2 4 2 4

2

4

6

2

L’

L

DIAGRAM 4


18

(a) In the diagram, mark the centre of rotation. (b) State the angle of rotation.

(a) Describe fully transformation V. (b) In the diagram mark M ' , the image of point M under the same transformation.

PMR 2004 In Diagram 2, P1 is the image of P under transformation M

Describe in full transformation M marks2 PMR 2004 Diagram 3 in the answer space shows polygon ABCDEF and straight line PQ, drawn on a grid of equal squares. Starting from the line PQ, draw polygon PQRSTU which is congruent to polygon ABCDEF marks2

x O 2

2

4

4

6 8

Q

DIAGRAM 2

M

0 2

2

4

4

6

6

8

8

10

10

x

y

P

P1

F

B C

D E

P

Q

A


19

Diagram 3 PMR 2005

Diagram 3 in the answer space shows two quadrilaterals, ABCD and A1B1 C 1D1, drawn on a grid of equal squares. A1B1 C 1D1 is the image ABCD of under a reflection. On the diagram in the answer space, draw the axis of reflection marks2

Diagram 3 PMR 2005

Diagram 4 shows three triangles, P, Q and R, which are drawn on a Cartesian plane.

y

R

-4 2

2

4

4

6

6

8

10

0 -2 x

P

Q

R

A

B

C D

D1

A1

B1 C1


20

Diagram 4 (a) Q is the image of P under a rotation of 900

State (i) the direction of the rotation (ii) the coordinates of the centre of the rotation

(b) R is the image of P under transformation M Describe in full transformation M marks4 PMR 2006

Diagram 1 shows two polygons, H and H1, drawn on a grid of equal squares with sides of 1 unit H1 is the image of H under transformation L. Describe in full transformation L marks2 PMR 2006

Diagram 2 in the answer space shows object P and straight line MN drawn on a grid of equal squares. On Diagram 2 in the answer space, draw the image of P under a reflection in the straight line MN marks2

H1

H

P

M

N

P


21

PMR 2007

Diagram 1 in the answer space shows quadrilateral PQRS, R1S1 is the image of RS under a reflection in the straight line MN On Diagram 1 in the answer space, complete the image of quadrilateral PQRS marks2 Diagram 1 PMR 2007

Diagram 2 in the answer space shows two quadrilaterals, JKLM and J1K1L1M1, drawn on a grid of equal squares. J1K1L1M1 is the image of JKLM under an enlargement. On Diagram 2 in the answer space, mark P as the centre of enlargement. marks2

Diagram 2 PMR 2007

In Diagram 9 triangle EFG and HIJ are similar

J J1

K

L M

M1 L1

K1

E

F G

J

H

I 650

650 400

750

M

N

P Q

R

R1

S1

S


22

State (a) the angle in triangle HJI which corresponds to FEG

(b) the side in triangle HJI which corresponds to the side EF in triangle EFG marks2

GEOMETRICAL CONSTRUCTION (USING COMPASSES) Set squares and protractor are not allowed for construction (except for measuring angle).

BASIC SKILLS

1. Perpendicular Lines (a) Construction the perpendicular bisector of line AB . (b) Construct the perpendicular line to the line EF which passes through point M . (c) Construct the perpendicular line to the line PQ which passes through point K .

2. Angles (a) Construct the bisector of EFG . (b) Measure EFG (b) Construct the following angles : (i) 60 , 120 (ii) 30 , 75 (iii) 45 , 135 (a) Measure ABC (b) construct the figure above starting from line AB using the given measurement. (c) Based on diagram constructed in (a), measure ACB .

A

B

E F M

P

Q

K

F

E

G

2005

A

B

C

45 5 cm

A

B


23

LOCI IN TWO DIMENSIONS FOUR Types of Locus :

(b) locus of X such that it is 2 units from the

CONDITION LOCUS y-axis 1. constant distance from one point A CIRCLE

Example : (a) locus of X such that

EX = 2 cm 4. equidistant from two straight lines

The ANGLE BISECTOR

of the two intersecting lines

Example : (i) (b) locus of Y such that EY = EH

(a) locus of Z such that its distance from line FG and line GH are the same

(ii) 2. equidistant from two points

The PERPENDICULAR BISECTOR of the two points

Example : (a) locus of M such that it is KM = ML

(iii)

(b) locus of N such that its distance from point P and point Q are the same

(iv)

3. constant distance from one straight line

A pair of PARALLEL LINES

(b) (i) locus of Z such that

x

y

O

E

F

K

L

T

S R

Q

P

E F

G H H

G

F

E F

G H

E F

G H

D

E

F

H

G

C

R S C

D F O


24

(parallel to the straight

line)

it is equidistant from

Example : (a) locus of X such that it is 1 cm from line VW

line RS and line ST. (ii) By using the letters in the diagram, state the locus of Z.

1.

DIAGRAM 1

Diagram 1 shows a circle centered O touches the sides of the square KLMN at points P, Q, R and S. X and Y are two moving points in the diagram.

(a) By using the alphabets in the diagram, state : (i) the locus of X such that XM = XN. (ii) the locus of Y such that it is equidistant from line NK and line KL.

(b) State the number of intersection(s) of the locus of X and the locus of Y in (a).

2.

P, Q and R are three moving points in the

diagram.

(a) By using the alphabets in the diagram, state the locus of P such that its distance from line EF and line FG are the same.

(b) In the diagram, (i) construct the locus of Q such that QH =

QJ, (ii) construct the locus of R such that RK =

KG, (iii) hence mark by using all the intersections

of the locus of Q and the locus of R. 3.

DIAGRAM 3 Diagram 3 shows a square PQRS. X, Y dan Z are three moving points in the

diagram.

In the diagram, (a) construct the locus of

(i) X such that OX = 2 cm, (ii) Y such that YP = YQ,

V

W

S

P

Q

R

O

K L

M N

E

F G H

J K

P Q

R S

O


25

DIAGRAM 2 Diagram 2 shows two equal squares, EFGK and

KGHJ with sides of 3.5 cm each.

(iii) Z such that its perpendicular distance from line PQ and line QR are the same.

(b) mark with the symbol all the intersections of the locus of X and the locus of Z.

4.

DIAGRAM 4 Diagram 4 shows a regular hexagon PQRSTU with sides of 3 cm. X, Y and Z are three moving points in the

hexagon.

(a) By using the alphabets in the diagram, state the locus of X such that its perpendicular distance from line PU and line PQ are the same.

(b) in the diagram (i) construct the locus of Y such that PY = 3

cm (ii) construct the locus of Z such that its

perpendicular distance from line PS is 1 cm, (iii) mark with the symbol all the intersections of the locus of Y and the locus of Z.

5.

Diagram 5 shows a square ABCD with sides of 4 cm. X, Y and Z are three moving points in the

diagram.

(a) Given that X is the locus such that DX = BX. By using the alphabets in the diagram, state the locus of X.

(b) In the diagram, (i) construct the locus of Y such that OY =

1.5 cm, (ii) construct the locus of Z such that its

perpendicular distance from line OA and line OD are the same,

(iii) mark with the symbol all the intersections of the locus of Y and the locus of Z.

6.

DIAGRAM 6 Diagram 6 shows the Cartesian plane drawn on a grid of equal squares. M and N are two moving points in the diagram.

S

R

Q P

T

U

D

C A O

x

y

O 2 4 2 4

2

4

6

2

4

Q P


26

DIAGRAM 5

(a) In the diagram, construct (i) the locus of M such that it is equidistant

from the x–axis and the y–axis, (ii) the locus of N such that it is equidistant

from point P and point Q. (b) State the coordinates of all the points lie on the x–axis such that they are 2 units from the origin, O.

7.

DIAGRAM 7 Diagram 7 shows a square DEFG with sides of 4 cm. Diagonals DF and EG intersect at point O.

X, Y dan Z are three moving points in the diagram.


(i) X such that XD = 3 cm, (ii) Y such that YP = YQ, (iii) Z such that its perpendicular distance

is 1 cm from line DOF. (b) mark with the symbol all the intersections

of the locus of X and the locus of Z. 8.

DIAGRAM 8 Diagram 8 shows an equilateral triangle PQR with

(b) mark with alphabet (i) “W”, the intersection of the locus of X and the locus of Y. (ii) “K”, the intersection of the locus of X and the locus of Z. 9.

DIAGRAM 9 Diagram 9 shows a rhombus EFGH with sides of 5 cm. X, Y dan Z are three moving points in the

diagram.


(i) X such that XE = EF (ii) Y such that YH = YF (iii) Z such that it is equidistant from line HE and line HG.

(b) mark with the symbol the intersection of the locus of X and the locus of Z.

P Q O

G F

E D

P

R

Q

H G

F E


27

sides of 4 cm. X, Y dan Z are three moving points in the diagram.


(i) X such that XP = 3 cm, (ii) Y such that it is equidistant from line

PQ and line QR, (iii) Z such that ZP = ZQ

TRIGONOMETRY

tan

cos

sin

opposite o TOAadjacent a

adjacent a CAHhypotenuse h

opposite o SOHhypotenuse h

Exercise 1. Based on the right-angled triangle PQR, name;

a) the hypotenuse =______________________ b) the opposite side to angle = ____________ c) the adjacent side to angle =_____________

2. Find the value of tan . a) tan = _________

b)

tan = __________

c) tan = __________

Q

P

R

C

A

opposite side hypotenuse

B adjacent side

6cm

8cm

10cm

26cm

10cm

24cm

2m

1m 5

12cm

4cm

2.5cm

2cm

1.5cm


28

d) tan = __________

e) tan = ___________

f) tan = __________

PMR 2004

In Diagram 1, C is the midpoint of the straight line BD Diagram 1 Find the value of tan x0 marks2 PMR 2005 Diagram 1 shows a right angled triangle EFG

Diagram 1 Find the value of cos x0 marks2 PMR 2005

In Diagram 2, QTS is a straight line

5 cm 13 cm

A

B C D

x

4 cm

2 cm E F

G

x

12 cm

8 cm

P

Q

R

S T x0

y0

3

1cm

2cm


29

Diagram 2

Given that sin x0 =54 and tan y0 =

512 ,

calculate the length, in cm, of TS marks2 PMR 2006

Diagram 3 shows two right angled triangles, DAB and CDB Diagram 3

It is given that tan y0 125

and sin x0 = 21

(a) Find the value of cos y0. (b) Calculate the length, in cm, of BC marks3

PMR 2007

Diagram 10 shows two right angled triangles PQT and SQR

PQR and TQS are straight lines

It is given that sin x0 = 135 and cos y0 =

53

(a) Find the value of tan x0

5 cm

A

B

C

D

x0

y0

y0

15 cm

5 cm

T

P Q

R

S

x0 y0


30

(b) Calculate the length, in cm, of PQR marks3 STATISTICS (Mode)

Find the mode for each of the following. 1. 1, 2, 3, 2, 4, 2, 3, 5 Mode = 2. 3, 4, 7, 4, 5, 4, 7 Mode = 3. 50, 60, 60, 70, 50, 40, 50 Mode = 4. 100, 104, 106, 104, 100, 105, 100 Mode = 5. 0.1, 0.2, 0.3, 0.1, 0.2, 0.1 Mode = 6. 15m, 18m, 20m, 15m, 18m, 21m, 15m Mode = State the mode for each of the following frequency table (Question 7 to Question 10) 7.

Size of shirt

S M L XL XXL

Frequency 33 40 48 25 18 Mode = 8.

Score 1 2 3 4 5 6 7 Frequency 4 1 6 3 7 2 4

Mode = 9.

Score 1 2 3 4 5 6 Frequency 2 8 7 4 3 1

Mode = 10.

Score 1 2 3 4 5 Frequency 3 4 8 6 5

Mode =

Answer: a) Marks 1 2 3 4 5 6 Frequency

b) Mode : 12. The data in the table below shows marks obtained by participants in a quiz.

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

a) Using the data above, complete the

frequency table in the answer space. b) State the mode.

Answer: a)

Marks 1 2 3 4 5 Frequency

b) Mode : 13. The data in the table below shows the grades obtained by participants in a quiz.

A B C A C B A A B B C A B C C A

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

b) State the mode.

Answer: a)

Grade A B C Frequency


31

11. The data in diagram below shows marks obtained by participants in a quiz.

1 3 4 3 2 5 1 2 3 1 1 4 4 3 3 5 6 4 6 3

a) Using the data above, complete the

following frequency table below. b) State the mode.

b) Mode: .

STATISTICS (Pictogram) 1. The diagram below shows the number of cassettes produced by a factory over three months.

July

Δ Δ Δ Δ Δ Δ Δ Δ Δ

August

Δ Δ Δ

September

Δ Δ Δ

Δ Represents 20 cassettes Find the total number of cassettes produced in three month. 2. The diagram below shows the number of car produced by a factory over four months

Jan

█ █ █ █ █ █

Feb

█ █ █ █

March

█ █ █ █ █

April

█ █

3. The diagram below shows the number of magazines produced by a company over three days.

Wednesday

Δ Δ Δ

Thursday

Δ Δ Δ Δ Δ Δ

Friday

Δ Δ Δ Δ

Δ Represents 10 magazines Find the total number of magazines produced in three days. 4. The diagram below shows the number of badges collected by a Maznah, Norliah and Ziana

Maznah

О О О О

Norliah

О О

Liana

О О О О О

О Represents 40 badges


32

█ Represents 5 car Find the total number of car produced in March.

Find the total number of badges collected by these three girls.

5. Diagram below shows the number of books in three classes, A, B and C.

Class Number of books A

B

C

Given that the total number of books of the 3 classes is 180. Each represents ……………… books. 6. Diagram below shows the number of computers sold by Mr. Tan over three months.

Month Number of computers sold Jan

Feb

March

Given that the total number of computers sold in three months was 96. Each represents …………………. computers. 7. Diagram below shows the number of tyres manufactured over four years.

Year Number of tyres manufactured 2002


33

2003

2004

2005

Given that the total number of tyres manufactured over the past four years was 48,000. Each represents …………………. tyres. STATISTICS (BAR CHART)

1. Grade Number of

students A 25 B 40 C 20 D 15 E 10

Table 1 Table 1 shows the grade obtained by a group of students in a test. On the square grid provided, construct a bar chart to represent all the information given in the table.

2.

Month Number of lorries January 10 February 8

March 12 April 6

Table 2 Table 2 shows the productions of lorries by an automobile factory in the first four months of 2004. On the square grid

3.

Month Number of lorries January 800 February 1000

March 750 April 500

Table 3 Table 3 shows the productions of lorries by an automobile factory in the first four months of 2005. On the square grid provided, construct a bar chart to represent all the information given in the table.


34

provided, construct a bar chart to represent all the information given in the table.

4. Grade Number of students

A 12 B 18 C 20 D 10

Table 4 Table 4 shows the grade obtained by a group of students in a test. On the square grid provided, construct a bar chart to represent all the information given in the table

5. Club Number of

students Science 2

Geography 6 History 5

Mathematics 8 English 10

Table 5 Table 5 shows the number of members in the five clubs. On the square grid provided, construct a bar chart to represent all the information given in the table.

6. Plantation Number of trees

A 20 B 5 C 15 D 10 E 35

Table 6 Table 6 shows the number of trees in 5 plantations. On the square grid provided, construct a bar chart to represent all the information given in the table

7. School Number of teachers

A 16 B 4 C 8 D 20 E 10

Table 7 Table 7 shows the number of teachers of 5 schools in Kulim. On the square grid provided, construct a bar chart to represent all the information given in the table.


35

STATISTICS (PIE CHART) Solve the following

1. 1 3602

2.3 3604

3.5 3606

4.2 3603

5.3 360

12

6.25 360

100

7.60 360

100

8. 50% X 360° = 9. 70% X 360° =

Tables in Question 11 to 14 show the scores for five players in one competition. Answer the question according to the given table. 11.

Score 1 2 3 4 5 Frequency 3 8 15 6 3

a) Find the total frequency. b) Find the fraction of score 3. 12.

Score 1 2 3 4 5 Frequency 10 15 5 12 8

a) Find the total frequency. b) Find the fraction of score 2. 13

Score 1 2 3 4 5 Frequency 2 7 6 3 12

a) Find the total frequency. b) Find the fraction of score 4.


36

Badmin

10. 80% X 360° =

14.

Score 1 2 3 4 5 Frequency 8 6 7 9 13

a) Find the total frequency. b) Find the fraction of score 4.

STATISTICS (PIE CHART) Complete each of the following table. 1. a) Table 1

Type of games

Number of students

Angles of the sector

Table tennis 8

Badminton 15

Hockey 25

Hand ball 12

b) Complete the pie chart to represent all the information in Table 1. 2. a) Table 2

Type of games

Number of students


Table tennis 12

Badminton 20

Hockey 18

b) Complete the pie chart to represent all the information in Table 2.

3. a) Table 3

Nutrients

Mass (g)


Carbohydrate 140

Protein 90

Fat 50

Mineral 20

c) Complete the pie chart to represent all the information in Table 3.

Badminton 90°

Hand ball 600


37

Hand ball 10

Protein 108°


38

GRAPH OF FUNCTIONS (Use the graph paper to answer the following questions.) a) Table A shows the values of two variables x and y, of a function, draw the graph of a function

x 0 1 2 3 4 5 6 y 6 5 4 3 2 1 0

Table A By using a scale 2cm to 1 unit for both x-axis and y-axis. b) Table B shows the values of two variables x and y, of a function.

x 0 1 2 3 4 5 6 y 0 2 4 6 8 10 12

Table B By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 2 units on y-axis, draw the graph of the function. c) Table C shows the values of two variables x and y, of a function.

x -2 -1 0 1 2 3 4 5 y -10 -4 0 2 2 0 -4 -10

Table C By using a scale of 2 cm to 1 unit for both x-axis and y-axis. draw the graph of the function d) Table D shows the values of two variables x and y, of a function.

x -3 -2 -1 0 1 2 3 y -5 -9 -10 -5 3 15 31

Table D 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 the function. e) Table E shows the values of two variables x and y, of a function.

x -3 -2 -1 0 1 2 3 y -35 -16 -9 -8 -7 0 19

Table E 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 the function.


39

f) Table F shows the values of two variables x and y, of a function.

x -3 -2 -1 0 1 2 3 4 y 27 7 -7 -15 -17 -13 -3.5 13

Table F By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function. g) Table G shows the values of two variables x and y, of a function.

x -2 -1 0 1 2 3 4 4.5 y 18 5 -1.5 -2 -1 -5.5 -17 -25

Table G By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function. h) Table H shows the values of two variables x and y, of a function.

x -3 -2 -1 0 1 2 3 3.5 4 y 32 12 -2.5 -15 -21 -15 -9 -15 -45

Table H By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 10 units on y-axis, draw the graph of the function. i) Table I shows the values of two variables x and y, of a function.

x -3 -2 -1 0 1 2 3 3.5 4 y -50 -25 -7 -5 11.5 12 12.5 19 37.5

Table I By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 10 units on y-axis, draw the graph of the function. j) Table J shows the values of two variables x and y, of a function.

x -3 -2 -1 0 1 2 3 4 5 y -7 0.5 2 0.5 -1 0.5 8 20 35

Table J By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function.


40

MATHEMATICS PMR 2006 Paper 50/1 (Selected Questions- refer to PMR 2006 question paper)

1. Rounded off to the nearest thousand does not become 312 000

A. 311 509 = 312 000 B. 311 805 = 312 000 C. 312 409 = 312 000 D. 312 505 = 313 000

2. Helmi receives RM30 pocket money per week. He saves 20% every week.

Calculate the difference between the amount of pocket money and he saves over period 4 weeks Receives 4 x RM30 = RM120

Saves 12010020 RM = – RM24

Difference = RM96 3. Combination of parts represents

52

of semicircle

52

1800 = 720

4. 90 pupils, 53

of them Chess Club and

94

of Chess Club are Choir Club

Choir Club = 249053

94

7. Ramli runs 2.75 km on P and 3 km 50 m on Q. Total distance in km 2.75 + 3.05 5.8

600 480 400

200

120


41

8. x = (5 – 2) 180 – 100 – 105 – 100 – 105 = 540 – 410 = 130 9. Exterior angle 360 = 60 6 x = 180 – 30 = 150 11. Which pairs of lines are perpendicular (900) PR and PU 13 x + x + x + x + x +50 + 50 = 310 5x = 310 – 100 x = 210 ÷ 5 EL = 42 14.

21

(8 cm + 14 cm) x 10 – 8 cm x 6 cm

110 cm2 – 48 cm2 = 62 cm2

x 1

2 3

4

5 6

60

30

50 cm

50 cm

E

L

x

x

x

x

x

8 cm

10 cm 6 cm

14 cm

x0

800

800

1050

1050

1

2 3

4 5

1000

1000

20 20

30 30 30

P

Q R S

T

U

V


42

15. X is the locus of a point which moves such that its distance from P always constant Y is the locus of a point which moves such that its distance from SR and RQ always constant Y is the locus of a point which moves such that its distance from point S and point Q always constant 16. .. h = 39 – 15 = 12 cm 2 21.

Perimeter = cm7.07222 + 3 cm + 3 cm = 10.4 cm

23.

cmSR

SR

SR

24

6025102510

60

P Q

R S

P

T

8 17 15

h

25 cm

10 cm

15 cm

60 cm

S R

P Q

T

3 cm

1.4 cm

3 cm

0.7 cm

0.7 cm


43

27. – 3 < 5 – x < 4 – 5 < – 5 < – 5

– 8 < – x < – 1 – 8 < – x < – 1 -1 - 1 - 1

8 < x < 1

1 8 36.

x -2 1 2 y -5 1 3

1 – ( - 5) or 3 – 1 = 2 1 – ( - 2) 2 – 1 y = 2x – 1 y = 2( – 2) – 1 = – 5 , y = 2( 1) – 1 = 1, y = 2( 2) – 1 = 3 37

y = – 6 x + 6 – 3 y = 2x + 6 38 x = 9 40. K (– 4, 6) – L (20, – 1) 24, 7 Distance = 25

6

-3 0

P(3,6)

Q(-3,2) S(x,2)

6

2

-3 3 9

24

7 25

modul intermediate math pmr

Documents