modul 1 - 5 math utk tkt 4

8/11/2019 Modul 1 - 5 Math Utk Tkt 4

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MATHEMATICS F4 EMaS 07 / MODULE 1

2007 Hak Cipta JPNT 2

MODUL BIMBINGAN EMAS

MATHEMATICS ( FORM 4)

MODULE 1PAPER 1

1 Round off 23 881 correct to three

significant figures

A 2 388

B 2 389

C 23 880

D 23 900

2 Round off 0.080281 correct to three

significant 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 2.97 106

D 297 104

5 Express 0.00173 in standard form.

A 1.73 10

B 11.73 10

C 11.73 10

D 1.73 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

48000

8 10

A 6 10

B 10

6 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


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9 4.2 1086.3 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

8

1095.3

D 71095.3

11. 3k(2 k) 5(2k 1) =

A 5k 5

B 5k + 5

C 3k2 4k 5

D 3k2 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(p2) = 3(p +3), then p =

A 13

B 6

C 5D 1

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

A 2

3

B

9

C 7

D 5

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)


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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.x2 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 y 2 + 3 = 7(y 1)


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3. Solve the quadratic equation q =q

q412

4. Solve the quadratic equation5

122 2 m= m

5.

The diagram shows a solid cylinder with

the height of 15 cm. Some parts of the

cylinder which is in the form of a cone has

been taken out.

The height of the cone is 7.5 cm. Given thatthe diameter of the cylinder and the cone

base is 9 cm.

Using = 3.142, calculate the volume of

the remaining solid.


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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 is

combined with one half of a cylinderat a rectangular plane JKLM.

Given that JK = 7 cm, KL = 10 cm

and the height of the prism is 5 cm.

Using =7

22, calculate the volume

of the combined solid.


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8.

9.

In the diagram, a solid cone is taken out from a solid

hemisphere.Given that, the diameter of the hemisphere is 8 cm, and

the diameter of the cone is 4 cm. The height of the cone

is 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. Pdan

Q are the midpoints of sides AD and BC respectively..

Using =7

22, calculate the volume of the remaining

solid.

.

FORMULAE

Volume of a cylinder = r2 h

Volume of a cone =3

1r

2h

Volume of a sphere = 4

r3

Volume of a right prism = cross sectional area length

F

GH

E

AB

CD

Q

P

15 cm

24 cm


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MATHEMATICS F4

MODUL BIMBINGAN EMaS

MATHEMATICS FORM 4

MODULE 2

PAPER 1

1 Given that 8 2

3

p kpk k, express

pin terms ofk.

A8 3

kp

k

B3 8

kp

k

C 5

3 8

kp

k

D 5

8 3

kp

k

2 Given that 4

4

nm

n, thenn=

A 4 4

1

m

m

B 4 4

1

m

m

C 1

1

m

m

D 1

1

m

k

3 Given that 3 b

ba

, then

A 3

1

b

a

B 3

1

ab

a

C 3

1 2 b a

D1 2

ab

a

4 Given that 3

2

sp

s

, expresssin terms

ofp .

A 3

p

B 3

2 1p

C 3

1 2p

D

3

2 1p

5 Given that3

2 m

ppm , expressm in

terms of p.

A13

6

p

p

B13

6p

p

C1

2

p

p

D

1

2

p

p


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

one of the subsets ofPis

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

setsM, NandPsuch that the

univesal set N P.

The shaded region represents the set

A ( ) N P

B ( ) N P

C ( ') N P

D ( ' ) 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

S T and

( ') ( )S n S R , find the values ofx.

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 orD,

represent the set ' 'Y Z

10 It is given that the universal set

xxx ,2511:{ is an integer}.

SetP={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), thenm =

A5

B5

C

5

D5

MP

N

T

RS

5 3x-2

x-17

4

6

X

Y

Z

A B

C

D


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12 Given that 1

2 - 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 + y

2= 15, theny =

A 5

B 10

C 15

D 20

15 Given that2

r+ 1 = r, thenr=

A 1

3

B1

C

D

16 Simplify

21 3

1 25

3m n

A2

B2

C2

9mn

D2

9m n

17 Simplify 4

3 1 2pk p k

A 10k

B 14

k

C 10k

D 5k

18 Simplify

153

23

8 p

mp

.

A2

B m

Cp

D4


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19 Simplify

16 2 2

14 8 4

16.

m n

m n

.

A

B

2

C

58m

D16m

20

3

5r can be written as

A 3 5r

B 5 3

r

C 5r

D 35r

PAPER 2

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

equations:

1

2 11m n

3 4 14m n


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

equations:

2 9x y

3 13x y

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

equations:

15p q

3 18p q


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

equations:

3 2 9d q

2d q

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

equations:

3 12d e

10d e


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6 (a) Complete the following mathematical sentences using the symbol > or < in

the 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 :

Statements1: 6 ( -2) = 3

Statements2: 36 is a perfect square

...............

(c) Write downPremise2 to complete the following arguments:

Premise1 : If ABCDis a rectangle, then ABCDhas two axes of symmetry.

Premise2 : .............................................................................................................

Conclusion: ABCDis 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 'm

Implication1 :.......................................................................................................

Implication2 :..


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(c) Complete the following arguments:

Premise1 : .............................................................................................................

Premise2 :PQRSis a quadrilateral.

Conclusion: PQRShas 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) 8 and 10.03 3 10 ......

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

BCis an equilateral triangle if and only if each of the interior angle of BCis

60o.


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...

..................................................................................................................

(c) Complete the premise in the following argument:

Premise1 :

Premise2 : 90 180 ox

Conclusion : sinxo 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 5 x , then 3 x .

.

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

.

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

which can be written as follow

1(4 2 )

0 (4 2 )

(4 2 )

12 (4 2 )

= ..


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MODULE 3PAPER 1

1 Express2

4

p

p as a single

fraction in its simplest form.

A 11 4

4

B5 4

4

p

C11 4

4

D 5 4

4

p

p

2 Express1 2

5

p p

p p

as a single


A4 9

5

p

B 9

5

p

p

C9

5

p

p

D 95p

p

3 Express6m m

m

as a single


A 3

2

B12 3

C12 3

D 3

4 Express

25 2

4 12

p p as a single


A 1

6p

B

24 2

6

p

C

22 1

6

p

p

D

2

2 16

pp


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5 Express2

3 2

3m as a single


A7 4m

B2

11 4

6

m

m

C 5

6

m

m

D2

11 4

6

m

6 In the diagram below,PQRSTis a

regular pentagon and SUVWXY is a

regular hexagon.

The value of x is

A 18

B 33

C 48

D 60

7 In the diagram below,PQRSTU is a

regular hexagon.

The value ofx 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

15

Q

P

C

Y

R S

T

U V

Wxo

X

x

PQ

S T

U

x

yE

D

C

BA


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9 In the diagram below ,PQRSTU is a

regular hexagon.LTS is a straight

line.

Find the value of x.

A 15B 25

C 35

D 60

10 In the diagram below, ABCDEF is aregular hexagon.GABand GFD is a

straight lines.

The value of x +y is

A 60o

B 90o

C 120o

D 150o

11 Find thex-intercept of the straight line

3y = 4x + 8

A 1

2

B 1

2

C 2

D 2

12 The Following Diagram, MNis a

straight line.

What is the gradient ofMN?

A 2

B 1

2

C2

1

D 2

Ny

M

0 x

9

(- 4,1)

U

QP

S

xO

T

35

L

BA

F

E

D

C

y

Gx


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13 In the Diagram bellow,LM is parallel

toRS.

Find the value of p.

A 1

B 2

C 3

D 4

14 The straight line VW has a

gradient of3

4 and y-intercept

= 12. Find itsx-intercept.

A 16

B 9

C 9

D 16

15 The following diagram shows a

straight line PQ on the Cartesain plane

The gradient of straight line PQ is

A 2

B1

C 1

D 2

16 The following diagram shows a

straight 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


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17 The gradient of the straight line

4x+ 2y = 7 is

A 4

B 2

C 2

D 4

18 Given that 2x+ 3y= 6 is parallel to

mx + 2y= 6,m =

A 4

B3

C3

D 4

19 The following diagram shows astraight lines AB.

If the gradient of AB is 1

, find the

value ofm.

A 10

B 6

C 20

D 26

20 Which of the following points lies on

the straight lines 91

xy ?

A (4, 11)

B (2, 8)

C (2, 8)

D (4, 11)

A(m, 6)

B(10, -2)


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PAPER 2

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

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

(a) (P R)

(b) (P Q ) R.

[ 3marks ]

Answer:

(a) (b)

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

B C .

On the diagram provided in the answer spaces, shade

(a) the set ( ) 'B ,

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

[ 3marks ]

Answer:

(a) (b)

C

A B

CBA

Q

P R

Q

P R


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

set= P Q R .

List the elements of set : -

(a) P Q R

(b) P Q R '

Answer :

(a)

[ 3marks ]

(b)

4 The Venn diagram in the answer space shows setP, QdanR..

On the diagram provided in the answer spaces, shade

(a) P Q

(b) ( )Q R P

[ 3marks ]

Answer:

(a)

(b)

P

Q

R

QP

.6

.2

QP

.3

.7

.5

.8.4


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5 In the following diagram,O is the origin, point Kand pointPlies on the x-axis and pointNlies on the y-axis. Straight lineKL is parallel to straight line NPand straight lineMNis

parallel to the x-axis. The equation of straight lineNPis 2 18 0x y

(a) State the equation of the straight lineMN.

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

[5marks]

M

K

L(4,7)

O

y

xP

N


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6 The following diagram shows,O is the origin. Point D lies on thex-axis and pointBlies

on they-axis. PointB is the midpoint ofACand the gradient ofBD is 4

5.

(a) Calculate the value ofk.

(b) Find the equation of the straightBD.

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

[5marks]

A(3,k)

xO

B

C(3 , 2)

4

D

y


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7 The following diagram shows,O is the origin. Point B andClies on the x-axis andpointA andD lies on they-axis. ABis parallel to CE. The equation of the straight

lineBEisy + 2x + 12 = 0

(a) Find the x-intercept of the straight lineAB.

(b) Find the equation of straight lineCEand hence, state the coordinates of thepointD.

[5marks]

y

x0

A4

CB

D

E(3,6)

y+ 2x + 12 = 0


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

Given the straight lineSTis 2xy 4 = 0.

Find

(a) the equation of the straight linePR

(b) the coordinates ofR.

[5marks]

O

S

Tx

R

Q

P

y


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9 The following graph shows,PQ,QTand RSis a straight lines. PQand RSis parallel.PointR lies on theQTand O is the origin.

Given the straight lineSTisy = 3x+ 12.

Find

(a) the equation of the straight lineRS,

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

T(12, -1)

S

R(5, 6)

Q

P

O x

y


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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 1

8.

Find the probability of choosing a

blue pen.

A 1

B 3

8

C 5

8

D 3

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 is 1

0.

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 is 1

3. 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 2

3

B

C11

D11

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

is 1

2. Find the total number of coins

in the handbag.

A 6

B 12

C 15

D 18


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11 Which of the following graphs

represents 1

y ?

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


represents y= 2 x3 ?

14

The equation of the graph shown

in the above diagram is

x

y

O

x

y

O

x

y

O

x

y

O

x

y

O

x

y

O

9

-3

0

2

B

0

2

0

2

D

x

y

0

2

y

x

2

O


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A y = x3

+ 2

B y = x 3 2

C y = x 3 + 2

D y =x32


represents 2

y ?

A

B

C

D

16 In the diagram below,PST is a

tangent to the circle centreO, at

point S.

Find QOS

A 36

B 72

C 108

D 126

17 In the diagram below,DEis a

tangent to the circle ABCD atD.ACEis a straight line.

The value ofx is

A 30

B 40

C 70

D 110

x

y

O2

2

y

xO

2

x

y

O

2

x

y

O

T

P

Q

S

O

54o

80

xC

200

B


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18 In the diagram below,RSis a tangent

to the circle atS and PQRis a

straight line.

The value ofx is

A 20

B 25

C 30

D 40

19 In the diagram below,PQRis a

tangent to the circle with centreO atQ.

The value of x is

A 40

B 50

C 65

D 115

20 In the diagram below,PQRis atangent to the circle QSTW atQ.

The value of x is

A 68

B 62

C 60

D 58

x

0

P

65

Q

R

100P

P

x

O

118

x

S

T

W

60

P Q R


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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.

[4marks ](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 correct

to 2 decimal places.[4marks ]

(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 onx-axis and 2 cm to 1 participant on the y-

axis, draw the histogram for the data.[4marks ]

Answer:(a)

Class Interval Frequency Midpoint

1 - 5

6 - 10

(b) (i)

(ii)


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(c) Refer graph on page27.

Graph for Question 1


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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.[1marks ]

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

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

(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 thex-axis and 2 cm to 5 cars on the y-axis,draw an ogive for the data.

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


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Answer:

(a)

(b) (i)

Speed (kmj-1

) Frequency Upper

Boundary Midpoint

CumulativeFrequency

3539 0

4044 4

4549 5

50

54 7

5559 9

6064 6

6569 5

7074 4

(ii) Mean speed =

(c) Refer graph on page10

Median =


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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 3534 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 the

table in the answer space.

[3marks ]

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

[3marks ]

(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 onx-axis and 2 cm to 1 pupil on they-axis,draw fequency polygon for the data.

[5marks ]

(d) Based on the fequency polygon in ( c), stateone piece of information about the

donations.

[1marks ]

Answer:

(a)

Class Interval Midpoint Frequency

2125 23 5

2630

(b)

(c) Refer graph on page12

(d)


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MODULE 5PAPER 1

1. Given that n

m3

5 , then n

A5

B3

5

C 31

5

D13

5

2 Given that 110

nnt

, then t=

A1

102

B10

12 n

C10

1n

D10

1n

3Given that

121

p, then p =

A3

2

B2

3

C5

2

D2

5

4 Given thata

b3 = b, then b =

A b =a1

3

B b =a

a

1

3

C b =a1

3

D b =a

a

1

5. Diberi de

dm

3, maka e

Ad

m

3

B23d

m

C

d

m

3

2

D

2dm


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6 In the diagram,Pis a point on the arc of

sector of a unit circle and with the origin

O as the centre.

Calculate the value of.

A 100 0

B 110 0

C 135 0

D 1550

7 In the diagram, QRSis a straight lineandPQ = PR .

Find the value of cos m

0

.

A - 0.3313

B - 0.5216

C - 0.5225

D - 0.8526

8. In the diagram,ABCis a straight line

and cos x0

=13

5.

Find the value of cos y0

.

A13

24

B13

12

C13

10

D13

5

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

Given that cos13

5PQR .

Calculate the value of tan .QSP

y

xO

P(0.7.0.7)

Q R S

R

63

m

D

C

B

A

y

x

P

Q

R

10 cm

S


42/50



A 5

B5

C 5

D 5

10 The diagram shows graph ofy = cosx

The value of p is

A 90o

B 180o

C 270o

D 360o

11 Given that cosy 0 = 1805.0 and

0 0 y 0 360 0 Thepossible 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 the

flag 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 pole

with the height of 16 m. Points P andQ are on the horizontal line, 20 m

apart.

Calculate the angle of elevation of R

from P.

A 38 40

B 41 59

C 48 1

D 51 20

P

5.42 m

A

0

1

-1

xp

PQ

R


43/50



14 In the diagram,Pand Q are two pints on

a horizontal plane, and PT is a vertical

pole.

Given thatPQ= 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, Mand Q are two points

on the horizontal field, while LKM is avertical pole

The angle of elevation of point L fromtitikQ 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 represent

two towers on the horizontal ground.Given that the angle of depression of R

from S is .180

Calculate the distance between the two

towers.

A 76.94

B 80.90

C 26.29

D 25.00

17 The diagram shows a cuboid with

horizontal rectangle PQRS as the base.

R

V

W

T

P

QM

N

U

S

Q

T

20 m

Q

S

R

50 m

75 m

P

Q

L

K

M 20 m


44/50



MandNthe midpoints of PQand TU

respectively.Name the angle between the plane of

WPQ and plane ofPQUT

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. M

andN are the midpoints ofQR andPS.

Vertex Vis right above of the point M.

Name the angle between the planePVS

and the planePQRS.

A VMN

B VNM

C VPQD VSQ

20 The diagram shows a pyramid with the

vertical rectangular base, ABCD. Theplane ABP is a horizontal plane.

Name the angle between line PC and

plane ABCD.

A

CPB

B

CPA

C PCD

D

PCA

F

K

J

H

G

E

Q

S

M

P

B

CD

A


45/50



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 KNand the plane HLMN.

[4marks]

M

N H

J

L

6 cm

12 cm

8 cm


46/50



2 Diagram below shows a cuboid with horizontal base TUVW.

Identify and calculate the angle between the plane PRVand the plane QRVU.

[4marks]

P Q

U

R

S

T

WV

5 cm

12 cm

4 cm


47/50



3 Diagram below shows a right prism with a horizontal square base ABCD. The rectangle

planeADPQis vertical and the rectangle plane PQRSis horizontal. TrapeziumABRQ is auniform cross-section of the prism with MandN are midpoints ofAB andDC respectively.

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

Calculate the angle between the plane ABSand the plane ABCD.

[3marks]

M

A

B

CD

Q R

P

N

S

16 cm


48/50



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

semicircles.

Using =7

22, calculate

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

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

[6marks]

7 cm 120

O


49/50


1

5 Diagram below shows a semicirclePQR with centre Oand sectorTRS with centreT. P is

the midpoint ofOR.

.

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

Using =7

22, calculate



[6marks]

P

Q

R

S

TO


50/50


6 Diagram below shows a sectorOPQ with centreO. AOBRis semicircle withAOBas its

diameter andPO = 2 OA.

OB = 7 cm , POB = 45 dan AOR = 120.

Using =7

22, calculate



[6marks]

B

P

O A

R

Q

modul 1 - 5 math utk tkt 4

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