Mozac Math Module

MATHEMATICS F4 mozac / MODULE 1

PROGRAM BIMBINGAN MATHEMATICS FORM 4

TOPICSOBJECTIV LIN STA QUASUBJECTIV SOL QUA

MODULE 1:E QUESTIONSEAR EQUATIONS INDARD FORMDRATIC EXPRESSIONS

ES QUESTIONSID GEOMETRYDRATIC EQUATION

1


2

MODUL BIMBINGAN

MATHEMATICS ( FORM 4)MODULE 1

PAPER 1

1 Round off 23 881 correct to threesignificant figures

A 2 388

B 2 389

C 23 880

D 23 900

2 Round off 0.080281 correct to threesignificant figures

A 0.08

B 0.080

C 0.0803

D 0.08028

3 Round off 0.0009055 correct to twosignificant figures

A 0.00091B 0.000910

C 0.000906

D 0.00190

4 Express 2970000 in standard form.

A 2.97 10 4

B 297 106

C 2.97 10 6

D 297 10 4

5 Express 0.00173 in standard form.

A 31.73 10B 11.73 10

C 11.73 10

D 31.73 10

6. State 3.07 × 10 6 as a single number

A 307 000

B 3 070 000

C 30 700 000

D 307 000 000

77

480008 10

A 46 10

B 106 10

C 6 × 1010

D 6 × 1012

8. The mass of an atom 6.02 × 10 29 kg.The mass in g, of 100 atoms are

A 6.02 × 10 21

B 6.02 × 10 24

C 6.02 × 10 26

D 6.02 × 10 27


3

9 4.2 × 10 8 −6.3 × 10 7

A 2.1 × 107

B 2.1 × 10 8

C 3.57 × 10 7

D 3.57 × 108

10 87 106.21021.4

A 81061.1

B 71061.1

C 81095.3

D 71095.3

11. 3k(2 – k) −5(2k – 1) =

A −5k −5

B −5k + 5

C −3k 2 −4k−5

D −3k 2 −4k + 5

12. 3(h – 1 ) + 4(1 – 2h) =

A h + 3

B −5h + 3

C −5h + 1

D 1

13. Given that m – 3 = 2, then m =

A – 5

B – 1

C 1

D 5

14. Given that 2(p ─2) = 3(p +3), then p =

A – 13

B – 6

C – 5

D – 1

15 Given that 12 = 2h – 3(2h – 2), then h =

A −23

B −29

C −27

D −25

16. x 2 −5x + 6 =

A (x + 6)(x – 1)

B (x + 1)(x+6)

C (x – 3)(x – 2)

D (x – 3)(x + 2)

17. x 2 −x −6 =

A (x + 6)(x – 1)

B (x + 1)(x + 6)

C (x – 3)(x – 2)

D (x – 3)(x + 2)


4

18. x 2 + 7x + 6 =

A (x + 6)(x – 1)

B (x + 1)(x+6)

C (x – 3)(x – 2)

D (x – 3)(x + 2)

.19. x 2 −5x−6 =

A (x −6)(x + 1)

B (x + 1)(x+6)

C (x – 3)(x – 2)

D (x – 3)(x + 2)

20. (4y – 1) 2 – 4y 2 =

A (3y – 1)(4y – 1)

B (2y – 1)(6y – 1)

C (y – 1)(12y – 1)

D (2y + 1)(6y + 1)

PAPER 2

1. Solve the quadratic equation5

42 x= x

2. Solve the quadratic equation y2 + 3 = 7(y – 1)


5

3. Solve the quadratic equation q =q

q412

4. Solve the quadratic equation5

122 2 m= −m

5.

The diagram shows a solid cylinder withthe height of 15 cm. Some parts of thecylinder which is in the form of a cone hasbeen taken out.The height of the cone is 7.5 cm. Given thatthe diameter of the cylinder and the conebase is 9 cm.

Using= 3.142, calculate the volume ofthe remaining solid.


6

6

7.

M L

KJ

In the diagram , a hemisphere is joint to the base ofa right cone

Given that , the radius of the hemisphere and the base ofthe cone is 3.5 cm , and the height of the cone is 14 cm.

Using =7

22, calculate the volume of the combined

solid.

The diagram shows a right prism iscombined with one half of a cylinderat a rectangular plane JKLM.

Given that JK = 7 cm, KL = 10 cmand the height of the prism is 5 cm.

Using =7

22, calculate the volume

of the combined solid.


8.

9.

In the diagram, a solid cone is taken out from a solidhemisphere.Given that, the diameter of the hemisphere is 8 cm, andthe diameter of the cone is 4 cm. The height of the coneis 6 cm.

Calculate the volume of the remaining solid

. ( Use =7

22).

In the diagram, a solid hemisphere with diameter PQ wastaken out from the solid cuboid with a square base. P danQ are the midpoints of sides AD and BC respectively..

Using =722

, calculate the volume of the remaining

solid..

Volume of a cylinder = r 2

Volume of a cone =31

Volume of a sphere =34r

Volume of a right prism = cr

F

GH

E

A B

CD

QP

15 cm

24 cm

FORMULAE

h

r 2 h

3

7

oss sectional area × length


PROGRAM BIMBINGAN MATHEMATICS FORM 4

TOPICSOBJECTIV LIN REA IND SET

SUBJECTIV SIM MET

MODULE 2:E QUESTIONSEAR EQUATIONS IIRRANGING FORMULAE IEXS

ES QUESTIONSULTANEOUS EQUATIONSHEMATICAL REASONING

1


2

MODUL BIMBINGAN

MATHEMATICS FORM 4MODULE 2

PAPER 1

1 Given that8 2

3

p k

pk k , express

p in terms of k.

A8 3

k

pk

B3 8

kp

k

C5

3 8

k

pk

D5

8 3

k

pk

2 Given that44

nm

n, then n =

A4 41

mm

B4 41

mm

C1

1

mm

D1

1

mk

3 Given that 3 b

ba

, then

A3

1

b

a

B3

1

a

ba

C3

1 2

b

a

D1 2

ab

a

4 Given that3

2s

ps

, express s in terms

of p.

A3p

B3

2 1p

C3

1 2 p

D3

2 1p

5 Given that3

2 mppm , express m in

terms of p.

A13

6pp

B13

6pp

C1

2pp

D1

2pp


3

6 Given that {2,3,5,6,7,9}P , then

one of the subsets of P is

A {2,3,5,7}

B {1,2,3,5,7}

C {2,3,4,5,6}

D {5,6,7,8,9}

7 The following diagram shows the

sets M, N and P such that the

univesal set M N P .

The shaded region represents the set

A ( ) M N P

B ( ) M N P

C ( ') M N P

D ( ' ) M N P

8 The diagram below is a Venn

diagram which shows the number of

element in set R, set S and set T.

Given that the universal set R S T and

( ') ( ) n S n S R , find the values of x.

A 7

B 8

C 9

D 10

9 The diagram below is a Venn diagram

with the universal set X Y Z .

Which of the regions, A, B, C or D,

represent the set ' 'X Y Z

10 It is given that the universal setxxx ,2511:{ is an integer}.

Set P ={x : x is multiple of 3} and setQ = {x : x is a prime number}.Find set ( P Q )’.

A {11, 13, 17, 19, 23 }

B { 11, 14, 16, 20, 22, 25 }

C { 12, 15, 18, 21, 24 }

D { 12, 14, 16, 18, 20, 22, 24 }

11 Given that 2m – 7 = 4(2 – m), then m =

A25

B52

C25

D52

MP

N

T

RS

5 3x-2

x-17

4

6

X

Y

Z

A B

CD


4

12 Given that 12 - w = 43

, then w =

A –6

B –2

C 2

D 6

13 Given that 3k – (k – 1) = 9, then k =

A 1

B 2

C 4

D 5

14 Given that y +y2

= 15, then y =

A 5

B 10

C 15

D 20

15 Given that2r

+ 1 = r, then r =

A13

B14

C34

D43

16 Simplify21 2 3

1 25

3 m pm np

A 2

6np

B 2

9np

C2

9mnp

D4

2

9m np

17 Simplify 43 1 2pk p k

A 5 10p k

B 3 14p k

C 3 10p k

D 2 5p k

18 Simplify

16 53

23

8m p

mp

.

A2p

B2mp

C8

mp

D 4

8mp


5

19 Simplify

16 2 2

14 8 4

16.

m n

m n

.

A54m

n

B24m

n

C58m

n

D516m

n

2035r can be written as

A 3 5r

B 5 3r

C 35r

D 35r

PAPER 2

1 Calculate the value of m and of n that satisfy the following simultaneous linearequations:

12 11

2m n

3 4 14m n


6

2 Calculate the value of x and of y that satisfy the following simultaneous linearequations:

2 9x y

3 13x y

3 Calculate the value of p and of q that satisfy the following simultaneous linearequations:

12 5

2p q

3 18p q


7

4 Calculate the value of d and of q that satisfy the following simultaneous linearequations:

3 2 9d q

6 2d q

5 Calculate the value of d and of e that satisfy the following simultaneous linearequations:

3 12d e

2 10d e


8

6 (a) Complete the following mathematical sentences using the symbol “ > ” or “ < ” inthe empty box to form

(i) a true statement

-4 4

(ii) a false statement

(-2)3 -4

(b) Combine the following pair of statements to form a true statement :

Statements 1: 6 ÷ ( -2) = 3

Statements 2: 36 is a perfect square

……………………………………..……………………………………….............

(c) Write down Premise 2 to complete the following arguments:

Premise 1 : If ABCD is a rectangle, then ABCD has two axes of symmetry.

Premise 2 : .............................................................................................................

Conclusion : ABCD is not a rectangle.

7 (a) State whether the following statement is true or false.

' 3 ( 5) 15 and 8 6'

…………………………………………………………………………………….

(b) Write down two implications based on the following sentence.

'5 10m if and only if 2'm

Implication 1 :.......................................................................................................

Implication 2 :…………………………………………………………………..


9

(c) Complete the following arguments:

Premise 1 : .............................................................................................................

Premise 2 : PQRS is a quadrilateral.

Conclusion : PQRS has a sum of interior angles equal to 360o.

8 (a) Explain why '3 ( 5) 8' is a statement.

……………………………………………………………………………………..

(b) Complete the following statement using a quantifier to make the statement true.

‘……………………. odd numbers are multiples of 7 `.

(c) Make a conclusion using inductive reasoning for the number sequence 10, 28, 82,

244, ……… which can be written as follows:

210 3 1

328 3 1

482 3 1

5244 3 1

… = …… ………………………………………………

9 (a) State whether each of the following statements is true or false:

(i) 3 64 4 …………………………………………….

(ii) 5 8 and 10.03 3 10 …………………………………………......

(b) Write down two implications based on the following sentence.

ABC is an equilateral triangle if and only if each of the interior angle of ABC is

60o.


10

...………………………………………………………………………………

……..................................................................................................................

(c) Complete the premise in the following argument:

Premise 1 : ……………………………………………………………………

Premise 2 : 90 180 o ox

Conclusion : sin xo is positive.

10 (a) Determine whether the following is a statement and give a reason for your answer.

' 2 3 5 1 '

………………………………………………………………………………………

(b) Complete the following statement using ‘and’ or ‘or’ so that the statement is false.

’60 is a multiple of 12 ……………. 20 is a factor of 30’.

(c) State the converse of each of the following implications and state its truth value

(i) If 5x , then 3x .

……………………………………………………………………………….

(ii) If y = 7, then y + 2 = 9

……………………………………………………………………………….

(d) Make a conclusion using inductive reasoning for the number sequence -2, 0, 4, 12,

……… which can be written as follow

12 (4 2 )

20 (4 2 )

34 (4 2 )

412 (4 2 )

… = …… ..………………………………………………

PROGRAM BIMBINGAN MATHEMATICS

FORM 4

TOPICSOBJECTIV ALG POL THE

SUBJECTIV SET THE

MODULE 3:E QUESTIONSEBRAIC FRACTIONSYGONSSTRAIGHT LINE

ES QUESTIONSSSTRAIGHT LINE

1

2

MODUL BIMBINGAN


PAPER 1

1 Express3 2

4p

p p

as a single

fraction in its simplest form.

A11 4

4p

p

B5 44

pp

C11 4

4p

p

D5 4

4p

p

2 Express1 2

5p p

p p

as a single


A4 95pp

B6 9

5p

p

C2 9

5p

p

D6 9

5p

p

3 Express3 6

2m m

m m

as a single


A3

2

B12 3

2m

m

C12 3

2m

m

D6 3m

m

4 Express23 5 2

4 12p p

p

as a single


A1

6p

p

B24 2

6p

p

C22 1

6p

p

D22 1

6p

p


3

5 Express2

3 22 3

mm m

as a single


A 2

7 46m

m

B 2

11 46mm

C 2

2 56m

m

D 2

11 46mm

6 In the diagram below, PQRST is aregular pentagon and SUVWXY is aregular hexagon.

The value of x is

A 18

B 33

C 48

D 60

7 In the diagram below, PQRSTU is aregular hexagon.

The value of x is

A 30o

B 40o

C 50o

D 60o

8 In the diagram below, ABCDE is a

regular pentagon.

The value of x + y is

A 134

B 144

C 154

D 180

15o

Q

P

C

Y

SR S

T

U V

Wxo

X

xo

PQ

R

S T

U

xo

yoE

D

C

BA


4

9 In the diagram below , PQRSTU is aregular hexagon. LTS is a straightline.

Find the value of x.

A 15

B 25

C 35

D 60

10 In the diagram below, ABCDEF is aregular hexagon. GAB and GFD is astraight lines.

The value of x + y is

A 60o

B 90o

C 120o

D 150o

11 Find the x-intercept of the straight line3y = 4x + 8

A 12

B12

C 2

D 2

12 The Following Diagram, MN is astraight line.

U R

QP

S

xO

T350

L

BA

F

E D

C

yo

Gxo

What is the gradient of MN ?

A 2

B12

C2

1

D 2

Ny

M

0 x

9

(- 4,1)


5

13 In the Diagram bellow, LM is parallelto RS.

Find the value of p.

A –1

B –2

C –3

D –4

14 The straight line VW has a

gradient of34

and y-intercept

= 12. Find its x-intercept.

A 16

B 9

C 9

D 16

15 The following diagram shows astraight line PQ on the Cartesain plane

The gradient of straight line PQ is

A 2

B21

C 21

D 2

16 The following diagram shows astraight line PQ.

The equation of the straight line PQ is

A 4x + 3y = 24

B 4x 3y = 24

C 4x 3y =24

D 4x + 3y = 24

y

x

y = –2x+3

2y = px – 5

L

R

S

M


6

17 The gradient of the straight line4x + 2y = 7 is

A 4

B 2

C 2

D 4

18 Given that 2x + 3y = 6 is parallel tomx + 2y = 6, m =

A34

B43

C43

D34

19 The following diagram shows astraight lines AB.

If the gradient of AB is21

, find the

value of m.

A 10

B 6

C 20

D 26

20 Which of the following points lies on

the straight lines 921

xy ?

A (4, 11)

B (2, 8)

C (2, 8)

D (4, 11)

A(m, 6)

B(10, -2)


7

PAPER 2

1 Venn Diagram in answer space shows the sets P, Q and R. Given that the universal set,

= PQ R . On the diagram in the answer space, shade the region that represents:

(a) ( P R )

(b) ( PQ ) R.

[ 3 marks ]

Answer :

(a) (b)

2 The Venn diagram in the answer space shows sets A, B and C. Given that the universal setA B C .

On the diagram provided in the answer spaces, shade

(a) the set ( ) 'A B ,

(b) the set ( A B ) ( B C ).

[ 3 marks ]

Answer :

(a) (b)

C

A B

CBA

Q

P R

Q

P R


8

3 The Venn diagram shows the elements of set P, Q and R. Given that the universalset = P Q R .

List the elements of set : -

(a) P Q R(b) P Q R '

Answer :

(a)

[ 3 marks ]

(b)

4 The Venn diagram in the answer space shows set P, Q dan R..

On the diagram provided in the answer spaces, shade

(a) P Q

(b) ( )Q R P

[ 3 marks ]Answer :

(a)

(b)

P

R

Q

R

QP

.6

.2

.1

R

QP

.3

.7

.5

.8.4


9

5 In the following diagram, O is the origin, point K and point P lies on the x-axis and pointN lies on the y-axis. Straight line KL is parallel to straight line NP and straight line MN isparallel to the x-axis. The equation of straight line NP is 2 18 0x y

(a) State the equation of the straight line MN.

(b) Find the equation of the straight KL and hence, state the coordinate of the point K.

[5 marks]

M

K

L(4,7)

O

y

xP

N


10

6 The following diagram shows, O is the origin. Point D lies on the x-axis and point B lies

on the y-axis. Point B is the midpoint of AC and the gradient of BD is 45

.

(a) Calculate the value of k.

(b) Find the equation of the straight BD.

(c) Find the x-intercept of the straight line BD.

[5 marks]

A(−3, k)

xO

B

C (3 , 2)

4

D

y


11

7 The following diagram shows, O is the origin. Point B and C lies on the x-axis andpoint A and D lies on the y-axis. AB is parallel to CE. The equation of the straightline BE is y + 2x + 12 = 0

(a) Find the x-intercept of the straight line AB.

(b) Find the equation of straight line CE and hence, state the coordinates of thepoint D.

[5 marks]

y

x0

A4

CB

D

E (−3, −6)

y + 2x + 12 = 0


12

8 The following diagram shows, O is the origin. The straight line RT is parallel to they-axis and OQ = OS.

Given the straight line ST is 2x – y – 4 = 0.

Find

(a) the equation of the straight line PR

(b) the coordinates of R.

[5 marks]

O

S

Tx

R

Q

P

y


13

9 The following graph shows, PQ, QT and RS is a straight lines. PQ and RS is parallel.Point R lies on the QT and O is the origin.

Given the straight line ST is y = 3x + 12.

Find

(a) the equation of the straight line RS,

(b) the y-intercept of the straight line QRT.[5 marks]

T (12, -1)

S

R (5, 6)

Q

PO

x

y


FORM 4

TOPICSOBJECTIV LIN PRO CIR GRASUBJECTIV STA

MODULE 4:E QUESTIONSEAR INEQUALITIESBABILITYCLESPHS OF FUNCTIONS I

ES QUESTIONSTISTICS

1

PAPER 1

1 The solution

A 6x

B 3x

C 3x

D 6x

2 List all integ

inequalities

A 2x

B 6x

C 2 x

D 2 x

3 The solution

A 4n

B 4n

C 4n

D 4n

4 List all the inwhich satisf

6m and 1

A 5

B 4, 5

2

MODUL BIMBINGAN

MATHEMATICS FORM 4MODULE 4

for 6 3 18x x is

ers x that satisfy the1

42

x and 1 5 9x .

8

8

for 1 2 72n

n is

teger values of my both the inequalities5 2 7.m

C 5, 6

D 4, 5, 6

5 List all the integer values of qwhich satisfy both the inequalities

2 1 17q and3

18.2q

A 9, 10, 11

B 9, 10, 11, 12

C 8, 9, 10, 11

D 8, 9, 10, 11, 12

6 It is given that set K is {0, 1, 2, 4, 5,

7, 11, 15, 19, 21, 27}. A number is

choosen at random from the

elements of set K.

Find the probability that the number

chosen is a prime number.

A4

11

B5

11

C6

11

D7

11


3

7 A beg contains 4 red pens, 2 black

pens and a number of blue pens. A

pen is chosen at random from the

beg.

The probability of choosing a black

pen is 18

.

Find the probability of choosing a

blue pen.

A14

B38

C58

D34

8 Kartini buys three boxes of diskette.

Each box has 180 diskette in it. All

of the diskettes are put inside a

container. The probability of

choosing a spoilt diskette is1

90.

How many of the diskette are not

spoilt?

A 531

B 534

C 537

D 538

9 In a class, nine students know how to

swim. If a student is chosen at

random from the class, the

probability that the student knows

how to swim is13

. Six students who

do not know how to swim then join

the class. If a student is now chosen

at random, calculate the probability

that the student does not know how

to swim.

A 23

B58

C3

11

D8

11

10 The table below shows the number

of different coins in a handbag. The

frequency column is incomplete.

Coin Frequency

5 sen 3

10 sen

20 sen 5

50 sen 4

If a coin is drawn at random from the

handbag, the probability that it is a

coin with a value of less than 20 sen

is12

. Find the total number of coins

in the handbag.

A 6

B 12

C 15

D 18


4

11 Which of the following graphs

represents 1y

x ?

A

B

C

D

12

The equation of the graph shown in

the above diagram is

A 2 9y x

B 2 9y x

C 2 9y x

D 2 9y x

13 Which of the following graphsrepresents y = 2 – x3 ?

14

The equation of the graph shownin the above diagram is

x

y

O

x

y

O

x

y

O

x

y

O

x

y

O

x

y

O

9

-3

A

x

y

0

−2

B

x

y

0

2

C

x

y

0

−2

D

x

y

0

2

y

x

─2

O


5

A y = x 3 + 2

B y = x 3 ─2

C y = ─x 3 + 2

D y = ─x 3 ─2

15 Which of the following graphs

represents 2yx

?

A

B

C

D

16 In the diagram below, PST is atangent to the circle centre O, atpoint S.

Find QOS

A 36

B 72

C 108

D 126

17 In the diagram below, DE is atangent to the circle ABCD at D.ACE is a straight line.

The value of x is

A 30

B 40

C 70

D 110

x

y

O−2

2

y

xO

2

x

y

O

2

x

y

O

T

P

Q

S

O

54o

800

xo

A

CE

D

200

B


6

18 In the diagram below, RS is a tangentto the circle at S and PQR is astraight line.

The value of x is

A 20

B 25

C 30

D 40

19 In the diagram below, PQR is atangent to the circle with centre O atQ.

The value of x is

A 40

B 50

C 65

D 115

20 In the diagram below, PQR is atangent to the circle QSTW at Q.

The value of x is

A 68

B 62

C 60

D 58

xºQ R

S

40º

P

65º

Q

R

S

100ºP

P

xºO

118º

x º

S

T

W

60 º

P Q R


7

PAPER 2

1 Data in table below shows the ages, in years, of 30 participants in a game on a FamilyDay.

3 14 18 12 18 23

12 24 7 13 22 13

16 13 19 27 6 16

24 29 9 13 25 8

11 20 17 15 14 17

(a) Based on the data in the table and by using a class interval of 5, complete thetable 1 in the answer space.

[4 marks ](b) Based on your table in (a)

(i) State the modal class,

(ii) Calculate the estimated mean age of the data and give your answer correctto 2 decimal places.

[4 marks ]

(c) For this part of the question, use the graph paper provided on page 7

By using a scale of 2 cm to 5 years on x-axis and 2 cm to 1 participant on the y-axis, draw the histogram for the data.

[4 marks ]

Answer:(a)

Class Interval Frequency Midpoint

1 - 5

6 - 10

(b) (i)

(ii)


9

2 Table below shows the speed, in kmj -1, of 40 cars which moving on a road .

Speed (kmj-1) Frequency

35-39 0

40-44 4

45-49 5

50-54 7

55-59 9

60-64 6

65-69 5

70-74 4

Based on the table,

(a) state the modal class.[1 marks ]

(b) (i) Complete the table on the answer space.

(ii) Calculate the estimated mean of speed.[6 marks ]

(c) For this part of the question, use the graph paper provided on page 10You may use a flexible curve rule.

By using a scale of 2 cm to 5 kmj-1 on the x-axis and 2 cm to 5 cars on the y-axis,draw an ogive for the data.

From the ogive, find the median.[5 marks]


10

Answer:

(a)

(b) (i)

Speed (kmj-1) Frequency UpperBoundary Midpoint Cumulative

Frequency

35–39 0

40–44 4

45–49 5

50–54 7

55–59 9

60–64 6

65–69 5

70–74 4

(ii) Mean speed =

(c) Refer graph on page 10

Median =


12

3 Data in table below shows the donations, in RM, collected by 40 pupils.

49 26 38 39 41 45 45 43

22 30 33 39 45 43 39 31

27 24 32 40 43 40 38 35

34 34 25 34 46 23 35 37

40 37 48 25 47 30 29 28

(a) Based on the data in the table and by using a class interval of 5, complete thetable in the answer space.

[3 marks ]

(b) Based on the table in (a), calculate the estimated mean of the donation collectedby a pupil.

[3 marks ]

(c) For this part of the question, use the graph paper provided on page 12

By using a scale of 2 cm to RM 5 on x-axis and 2 cm to 1 pupil on the y-axis,draw fequency polygon for the data.

[5 marks ]

(d) Based on the fequency polygon in (c), state one piece of information about thedonations.

[1 marks ]

Answer:

(a)

Class Interval Midpoint Frequency

21 – 25 23 5

26 – 30

(b)

(c) Refer graph on page 12

(d)


13




FORM 4

TOPICSOBJECTIV REA TRI ANG

SUBJECTIV PER LIN

MODULE 5:E QUESTIONSRRANGING FORMULAE IIGONOMETRYLES OF ELEVATION AND DEPRESSIONS

ES QUESTIONSIMETERS AND AREAS OF CIRCLESES AND PLANES IN 3-DEMENSIONS

1


2

MODUL BIMBINGAN


PAPER 1

1. Given thatn

nm3

5 , then n

Am25

B13

5m

Cm31

5

D13

5m

2 Given that 110

ntnt

, then t =

A1

102 n

B10

12 n

C10

1n

D10

1n

3 Given that21

421

p

, then p =

A32

B23

C52

D25

4 Given thatab3 = b, then b =

A b =a1

3

B b =a

a13

C b =a21

3

D b =a

a21

5. Diberi de

dm

3, maka e

Ad

m3

B 23dm

Cd

m3

2

D3

2dm


6 In the diagram, P is a point on the arc ofsector of a unit circle and with the originO as the centre.

Calculate the value o

A 100 0

B 110 0

C 135 0

D 155 0

7 In the diagram, QRSand PQ = PR .

Find the value of cos

A - 0.3313

B - 0.5216

C - 0.5225

D - 0.8526

8. In the diagram, ABC is a straight line

and cos x 0 =13

5.

y

O

P(−0.7.0.7)

Q R

R

63º

B

A

y º

3

f .

is a straight line

m 0 .

Find the value of cos y 0 .

A13

24

B13

12

C1310

D13

5

9 In the diagram, PSR is a straight line,and PS = 10 cm.

Given that cos135

PQR .

Calculate the value of tan .QSP

x

S

m º

D

C x º

P

Q

R

10 cm

S


4

A35

B25

C35

D25

10 The diagram shows graph of y = cos x

The value of p is

A 90o

B 180o

C 270o

D 360o

11 Given that cos y 0 = 1805.0 and

0 0 y 0 360 0 The

possible values of y are :

A 79.6 , 259.6

B 100.4 , 190.4

C 190.4 , 259.6

D 100.4 , 259. 6

12 In the diagram, the flag pole is vertical.Given that the angle of elevation of theflag A from P is 350 .

Find, in m, the height of the pole.

A 0.13

B 3.79

C 3.80

D 7.74

13 In the diagram, QR is a vertical polewith the height of 16 m. Points P andQ are on the horizontal line, 20 mapart.

Calculate the angle of elevation of Rfrom P.

A 38° 40´

B 41° 59´

C 48° 1´

D 51° 20´

P

5.42 m

A

0o

1

y

-1

xp

PQ

R


5

14 In the diagram, P and Q are two pints ona horizontal plane, and PT is a verticalpole.

Given that PQ = 20 m and the angle ofelevation of T from Q is 32 . Theheight of the pole is

A 10.6 m

B 12.5 m

C 17 m

D 32 m

15 In the diagram, M and Q are two pointson the horizontal field, while LKM is avertical pole

The angle of elevation of point L fromtitik Q is 65○ and the angle of elevationof point K from Q is s 30○.

Calculate, in m , length of LK.

A 14.15

B 25.55

C 31.34

D 54.44

16 In the diagram, PR and QS representtwo towers on the horizontal ground.Given that the angle of depression of Rfrom S is .180

Calculate the distance between the twotowers.

A 76.94

B 80.90

C 26.29

D 25.00

17 The diagram shows a cuboid withhorizontal rectangle PQRS as the base.

R

V

W

T

P

QM

N

US

P Q

T

20 m

Q

S

R

50 m

75 m

P

Q

L

K

M 20 m

MATHEMATICS F4 EMaS 07 / MODULE 5

© 2007 Hak Cipta JPNT 6

M and N the midpoints of PQ and TUrespectively.Name the angle between the plane ofWPQ and plane of PQUT

A WPT

B WMN

C WQS

D WQU

18 The diagram shows a right prism with a

horizontal rectangular base, EFGH.

Name the angle between the plane FHJ

and the plane GHJK.

A FJG

B FJK

C FHG

D FHK

19 The diagram shows a pyramid with ahorizontal rectangular base PQRS. Mand N are the midpoints of QR and PS.Vertex V is right above of the point M.

Name the angle between the plane PVSand the plane PQRS.

A VMNB VNMC VPQD VSQ

20 The diagram shows a pyramid with thevertical rectangular base, ABCD. Theplane ABP is a horizontal plane.

Name the angle between line PC andplane ABCD.

A ∠ CPBB ∠ CPAC ∠ PCDD ∠ PCA

F

K

J

H

G

E

P Q

N

S

V

R

M

P

B

CD

A

MATHEMATICS F4 EMaS 07 / MODULE 5

© 2007 Hak Cipta JPNT 7

PAPER 2

1 Diagram below shows a right prism. The base HJKL is a vertical rectangle. The rightangled triangle NHJ is the uniform cross section of the prism.

Identify and calculate the angle between the line KN and the plane HLMN.[4 marks]

M

N H

J

K

L

6 cm

12 cm

8 cm


8

2 Diagram below shows a cuboid with horizontal base TUVW.

Identify and calculate the angle between the plane PRV and the plane QRVU.[4 marks]

P Q

UR

S

T

W V

5 cm

12 cm

4 cm


9

3 Diagram below shows a right prism with a horizontal square base ABCD. The rectangleplane ADPQ is vertical and the rectangle plane PQRS is horizontal. Trapezium ABRQ is auniform cross-section of the prism with M and N are midpoints of AB and DC respectively.

QR = PS = 8 cm and QA = PD = 10 cm.

Calculate the angle between the plane ABS and the plane ABCD.[3 marks]

MA

B

CDQ R

P

N

S

16 cm


10

4 Diagram below shows a sector OQRS with centre O. OQ and OS are diameters of twosemicircles.

Using =7

22, calculate

(a) the perimeter, in cm, of the whole diagram

(b) the area, in cm2 , of the shaded region

[6 marks]

7 cm 120o

O

Q S


11

5 Diagram below shows a semicircle PQR with centre O and sector TRS with centre T. P isthe midpoint of OR.

.

OP = 5 cm, QR = 6 cm and 60oRTS .

Using =7

22, calculate



[6 marks]

P

Q

R

S

TO


12

6 Diagram below shows a sector OPQ with centre O. AOBR is semicircle with AOB as itsdiameter and PO = 2OA.

OB = 7 cm , POB = 45° dan AOR = 120°.

Using =7

22, calculate



[6 marks]

B

P

O A

R

Q

Mozac Math Module

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