Paper 2 Modul Baru

8/6/2019 Paper 2 Modul Baru

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1. LINEAR EQUATION I , II (PAPER 2)

1 Calculate the value ofp and q that satisfy the following simultaneous linear equations.2p q = 418p 4q = - 4 [ 4 marks]

2 Calculate the value ofkandfthat satisfy the following simultaneous linear equations.

3k+ f= 12kf= 4 [ 4 marks ]

3 Calculate the value ofx andy that satisfy the following simultaneous linear equations.

x- 4y = 73x + y = 8 [ 4 marks ]

4 Calculate the value ofrands that satisfy the following simultaneous linear equations.

2r 4s = 63r+ s = 9

[ 4 marks]

5 Calculate the value ofv and w that satisfy the following simultaneous linear equations.

2v2

3w = 5

4v + w = 6 [ 4 marks ]

2. PERIMETERS AND AREAS OF CIRCLES ( Paper 2 )

1 In Diagram 1, BDE is an arc of circle with centre A and BFCis a semicircle.

DIAGRAM 1

ABC is a right angle triangle. Using T=7

22, calculate

(a) the perimeter, in cm of the shaded region

(b) the area, cm2,of the shaded region. [7 marks

7 cm45

0

AB

C

D

E

FG


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2 In Diagram 2, ABC and DEFare arcs of two different circles with centre O. AOE is a right angletriangle.

DIAGRAM 2

Given that OC= CD= 7 cm.

Using T =7

22, calculate

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

(b) the area, in cm2

,of the shaded region. [7 marks]

3 In Diagram 3, EHFis an arc of circle with centre O and OIFis a semicircle. ABCD and AFOE aretwo squares.

DIAGRAM 3

Given that AE= 7 cm and DE= 9cm.

Using T =7

22, calculate

(a) the perimeter, in cm, ofOEHFIO region,

(b) the area, in cm2

of the shaded region. [7marks]

F

O 30

0

A

BC

D E

OF

G

H

I


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4 In Diagram 4, AEC is an arc of circle with centre O and ODCis a semicircle.

DIAGRAM 4

ABCO is a rombus. Using T =7

22, calculate

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

(b) the area, in cm2, of the shaded region. [7 marks]

5 In Diagram 5, AGC is an arc of circle with centre D, DEB is an arc of circle with centre A, andDFB is an arc of circle with centre C.

DIAGRAM 5

ABCD is a rombus with area 24.5 cm2

.Using T =7

22, calculate

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

(b) the area,in cm2

,of the shaded region. [7 marks]

A B

C

E

GO

D

1500

7 cm

14 cm

G

A

D

7 cm

EF30

B


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3. Solid Geometry (Paper 2)

1. Diagram 1 shows a solid formed by joining a right pyramid and a half cylinder.

DIAGRAM 1

The height from Eto the plane ABCD is 6 cm. Calculate the volume, in cm3, of the solid.

[Use7

22!T ] [4 marks]

2. Diagram 2 shows a solid formed by joining a cuboid ABCDEFGHand a right prism FGHEJKLI.

The trapezium GHIL is the cross section of the prism.

DIAGRAM 2

The height of point L from the plane ABCD is 5 cm.

Calculate the volume, in cm3, of the solid.

[Use7

22!T ] [4 marks ]

3. Diagram 3 shows a solid formed by joining a hemisphere and a cylinder.

Diagram 3

Calculate the volume, in cm3, of the solid. [Use

7

22!T ]

[4 marks]

AB

C

D

E

7 cm 10 cm

AB

C

D

E

FG

H

IJ

KL

7 cm

5 cm

2 cm

4 cm

12 cm

5 cm


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4. Diagram 4 shows a solid formed by removing a right circular cone from a hemisphere which has a

diameter of 14 cm.

DIAGRAM 4

Given that the vertex of the cone touches the surface of the hemisphere.

Calculate the volume, in cm3, of the solid.

[Use7

22!T ] [4 marks ]

5. Diagram 5 shows a solid formed by removing a cylinder from a right prism.

DIAGRAM 5

If the diameter of the cylinder is 7 cm and the volume of the remaining solid is 861 cm3,

Calculate the length of the prism.

[Use7

22!T ] [4 marks ]

4. QUADRATIC EXPRESSIONS AND EQUATIONS ( Paper 2)

1. Solve the equation 3x2 = 5 ( 1 4x ) + 2 [ 4 marks ]

2. Solve the quadratic equation2

3

25m

m!

[4 marks ]

3. Solve the equation3

1

62

2

!kk

[4 marks ]

4. Solve the equation 52

43 2!

x

xx[4 marks ]

5. Solve the equation2

712 2

pp ! [4 marks ]

12 cm

8 cm

10 cm


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5. SETS ( Paper 2 )

1 The Venn diagram in the answer space shows sets

, Q andR such that the universal set,

= PQR. On the diagrams in the answer space, shade

(a) the set PQ R'(b) the set ( Q R )'P

[3 marks]Answer:

(a)

(b)

2 The Venn diagram in the answer space shows sets P, Q and R. Given that universal set, = PQR.. On the diagrams in the answer space, shade

(a) the set Q R

(b) the set (PQ )' R[ 3 marks ]

Answer :

(a)

(b)

PQ

R

RP

Q

P

QR

P

QR


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

= AB C . On the diagrams in the answer space, shade

(a) (A B) C

(b) ( B C )' A[ 3 marks ]

Answer :

(a)

(b)

4 The Venn diagram in the answer space shows sets P, Q and R. Given that universal set, = P Q R. On the diagrams in the answer space, shade

(a) the set Q R'

(b) the set P QR[ 3 marks ]

Answer:

(a)

(b)

A

B

C

A

B

C

P Q R

P

Q R


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

= ABC. On the diagrams in the answer space, shade

(a) AC

(b) (A C) B[ 3 marks ]

Answer:

(a)

(b)

6. Mathematical Reasoning (Paper 2)

1 (a) State whether the following sentence is a statement or non-statement.

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

(c) Complete the premise in the following argument:Premise 1 : All pentagons have five sides.Premise 2 :

Conclusion : ABCDE has five sides.

(5 marks)2 (a) State whether each of the following statement is true or false.

(i) 16 z 2 = 4 or 42 = 16.

(ii) The elements of set P= {8,10,12} is divisible by 2 and the elements of set

Q = {41,49,51} is a prime number.

(b) Write down Premise 2 to complete the following argument:

Premise 1 : Ifm is smaller than zero, then m is a negative number.Premise 2 :

..

Conclusion : 4 is a negative number.

(c) Write down two implications based on the following sentence:(5 marks)

A

C

B

A

C

B

2p + 2q = 5

p = 6 if and only ifp2= 36

2k< 1 if and only if k < 0


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3 (a) Write the converse of the statement below. State whether the converse is true or false.

(a) Complete the premise in the following argument.Premise 1 :

Premise 2 : p is not divisible by 2.

Conclusion : p is not a multiple of 4.

(b) Write a conclusion based on the information below.T1 = 40 (1 + 1)(5)

T2 = 40 (2 + 1)(5)

T3 = 40 (3 + 1)(5)

(5 marks)

4 (a) Fill in each of the boxes below with the symbol or so as to form true statement.

(i) A B A(ii) A A B

(b) Combine the following two statements to form a true statement.

(i) 9 is an even number.(ii) 9 > 7.

(c) Complete the premise in the following argument.Premise 1 : All quadrilaterals are polygons.

Premise 2 :

........Conclusion : A rectangle is a polygon.

(5 marks)

5 (a) Rewrite the statement below by using the quantifier all or some so that the meaning of the

statement does not change.

No odd number is divisible by 2

(b) Write a conclusion based on the premises below.Premise 1 : If the cube of the number is negative, then the number is negative.Premise 2 : x3 = 27

Conclusion :

.

(c) Complete the premise in the following argument.Premise 1 : If a polygon has n sides, then the sum of all its interior angles is equal to

(n 2) v 180o.Premise 2 :

..Conclusion : The sum of all the interior angles of the polygon ABCDE is equal to

(5 2) v 180o.(5 marks)

If Ay , then y BA


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7. THE STRAIGHT LINE ( Paper 2)

1 Diagram 1 shows a straight line PQ and straight line

S drawn on a Cartesian plane. PQ is

parallel to

S.

DIAGRAM 1

Finda) gradient of line PQ .b) equation of line RS .c) x-intercept of line RS. [5 marks]

2 In diagram 2,NQ is parallel to OP.

DIAGRAM 2

The equation of straight line PQR is 3y - 2x = 6. PointNlies on the x-axis and point Q lies on the

y-axis.Find

(a) value of k

(b) equation of lineNQ [5 marks]

3 In the diagram 3, straight line RSis parallel to PQ.

DIAGRAM 3

y

P(1, 0)

Q (3, 4)

O xS 2,6

y

P(-4,1)

Q

R(6, k)

NO x

P

Q (2, -3)

R

S

y

x0


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Given that the equation of the lineRSis 32

1! xy . Find

(a) equation of line PQ.

(b) x-intercept of line PQ. [5 marks]

4 In the diagram 4 , PQ is parallel to MN and OQ = QN.

DIAGRAM 4

The equation of the linePQ is 93 ! yx

(a) x-intercept of line PQ.

(b) equation of the straight lineMN. [5 marks]

5 In the diagram 5, O is the origin, point Q lies on the x-axis and point R lies on the y-axis. Straight

line PQ is parallel to straight line RSand the gradient of the line QR is 4.

The equation of the lineRSis 042 ! yx

(a) equation of straight lineQR.

(b) Find the equation of the straight linePQ and hence, state its x-intercept.

[5 marks]

NQ

M

O x

P

y

Q

R

y

P( 10-,2 )

S

O x

DIAGRAM 5


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8. Statistics ( Paper 2)

1. The data in Diagram 1 shows the donation in RM which donated by 40 families

40 24 17 30 22 26 35 19

23 28 33 33 39 34 39 28

27 35 45 21 38 22 27 3530 34 31 37 40 32 14 2820 32 29 26 32 22 38 44

DIAGRAM 1

( a ) Using the data given and a class interval of RM 5, complete Table 1.

( 4 marks )

Donation ( RM ) Frequency Cumulative Frequency

11 15

16 - 20

TABLE 1

( b ) Forthispartofthe question,use a graph paper.

By using a scale of 2 cm to RM on the x axis and 2 cm to 5 families on the y - axis, drawan ogive based on the data in the table.

( 6 marks )

( c ) From your ogive in ( b ), find

(i) the third quartile

(ii) Thus, explain briefly the meaning of the third quartile.( 2 marks )

2. Table 2 below shows the frequency table for the lengths of 160 pencils which were used by a groupof students

Length ( mm) Frequency CumulativeFrequency

UpperBoundaries

90 99 2

100 -109 6

110 -119 16120 129 24

130 -139 35

140 -149 42

150 -159 21

160 169 10

170 -179 4

TABLE 2


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( a ) Based on the above data, state the modal class ( 2 marks )

( b ) ( i ) Construct a cumulative frequency table for the above data.

( ii ) Using a scale of 2 cm to10 mm on the x axis abd 2 cm to 20 pencils on the y axis

draw an ogive based on Table 2.

Hence, use the ogive to estimate

( a ) mean length

( b) interquatile range( 10 marks )

3. Table 3 shows the score and the number of trials done by a player in a game.

Score 1 2 3 4 5 6 7

Number of trial score 3 14 15 16 20 18 7

TABLE 3

( a) ( i ) Calculate the total trials done by the player

( ii ) Find the score mode( 4 marks )

( b ) Forthispartofthe question,use a graphpaper.

Height of the durian trees Frequency

85 89 4

90 94 12

95 - 99 22

100 104 33

105 109 62

110 114 43

115 119 18

120 - 124 6

TABLE 4Using a scale of 2cm to 5 cm on the horizontal axis dan 2 cm kepada 20 durian trees on thevertical axis.

(i ) Construct a cumulative frequency table base on Table 4 ( 2 marks )

( ii ) Draw an ogive for the above data. ( 4 marks )

( c ) Use your ogive in ( b ) to estimate the interquatile range ( 2 marks )


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4. The marks obtained by 30 students in mathematics test are show below

54 64 52 55 63 45 73 88 32 72

51 58 95 78 58 41 59 67 95 5880 43 62 47 78 37 46 65 68 86

(a) Copy and complete the following frequency table, using equal class interval

( 5 marks )( b ) From the above table,

( i ) state the modal class

(ii) estimate the mean mark

( 4 marks )

( c ) Forthispartofthe question,use a graph paper

Using a scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 1 student on the vertical

axis, construct a histogram from the above table( 3 marks )

5. Table 5 shows the frequency distribution of heights of 96 Year One Students

Height ( cm ) Midpoint Frequency

90 - 94 4

95 - 99 10

100 104 26

105 - 109 24

110 114 17

115 - 119 9

120 - 124 4

125 - 129 2

TABLE 5

( a ) ( i ) Copy and complete Table 5

(ii ) Hence, calculate the mean height of the students

( 4 marks )

Mark Frequency Midpoint

30 - 39


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3. Diagram 3 shows a right prism. The base ABCis a hori ! ontal equilateraltriangle. The triangle

DEF is the uniform cross section ofthe prism. N and P are midpoints of AC and BC respectively.

Mis vertically above N.

Identify and calculate the angle between the MP and the base ABC. ( 4 marks )

4. Diagram 4 shows a cuboid. The base PQRS is a hori! ontal square. Mis the midpoint of ST and N

is the midpoint of PQ.

Identify and calculate the angle between the line MQ and the base PQRS ( 4 marks )

5. Diagram 5 shows a cuboid. The base ABCD is a hori! ontal rectangle. Mis the midpoint of AB.

Identify and calculate the angle between the plane M

"#

and the plane CDHG ( 4 marks )

Diagram 5

Diagram 3

Diagram 4

NQ

S


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10. Graphs Of functions

1 (a) Complete the following table for the question .4

xy !

x -4 -2.5 -1 -0.5 0.5 1 2 3.2 4

y 1 1.6 8 -8 -4 -1.25 -1

[ 2 marks ]

(b) Forthispartofthe question,use the graphpaperprovidedonpage 2 . Youmayuse a

flexible curve rule.By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 2 units on they-axis, draw the

graph ofx

y4

! for -4 x 4.

[ 5 marks ]

(c) From your graph, find(i) the value ofy when x = 1.8

(ii) the value ofx when y = 3.4[ 2 marks ]

(d) Draw a suitable straight line on your graph to find all the values ofx which satisfy the

equation 324

! xx

for -4 x 4.

State the value ofx.

[ 3 marks ]

2 (a) Table 1 shows values ofx andy which satisfy the equation .342 2 ! xxy

x -2 -1 0 1 2 3 4 4.5 5

y k 3 -3 -5 -3 m 13 19.5 27

Table 1Calculate the value ofkand ofm.

[ 2 marks]

(b) Forthispartofthe question,use the graphpaperonpage 4 . Youmayuse a flexible curve

rule.By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on they-axis,

draw the graph of .342 2 ! xxy for -2 x 5.

[ 4 marks]

(c) From your graph, find

(i) the value ofy when x = -1.5

(ii) the values of x when y = 0.

(d) Draw a suitable straight line on your graph to find a value of x which satisfies the equation

0232 2 ! xx for -2 x 5.[ 3 marks]


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3 (a) Complete Table 2 in the answer space for the equation 32 2 ! xxy .

x -2 -1 -0.5 1 2 3 4 4.5 5

y 7 -2 -2 3 12 33

Table 2[ 3 marks]

(b) Forthispartofthe question,use the graphpaperprovidedonpage 6 . Youmayuse a

flexible curve rule.

By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units ony-axis, draw the graph

of 32 2 ! xxy for -2 x 5.

[4 marks]

(c) From your graph, find(i) the value ofy when x = 3.6(ii) the value ofx when y = 37

[2 marks]

(d) Draw a suitable straight line on your graph to find the value ofx which satisfy the equation1032 2 ! xx for -2 x 5.

State these values ofx.[3 marks]

4 (a) Complete Table 3 in the answer space for the equation .583 ! xxy

x -3 -2 -1 0 1 2 3 3.5 4

y 2 12 5 -3 19.9 37

Table 3

[ 3 marks]

(b) Forthispartofthe question,use the graphpaperprovidedonpage 8 . Youmayuse aflexible curve rule.

By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on y-axis, draw the graph

of 583

! xxy for -3 x 4.

[4 marks]

(c) From your graph, find(i) the value of y whenx = -1.4

(ii) the value of x wheny = 25

[ 2 marks]

(d) Draw a suitable straight line on your graph to find the value ofx which satisfy the equation

01123 ! xx for -3 x 4.State these values ofx.

[ 3 marks]


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5 (a) Complete Table 5 in the answer space for the equation2273 xxy ! .

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

y -36 -6 3 9 6 -12

Table 5[ 3 marks ]

(b) Forthispartofthe question,use the graph paperprovidedonpage 10 . Youmayuse a

flexible curve rule.

By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on y-axis, draw the graph

of2273 xxy ! for -3 x 5.

[ 4 marks ]

(c) From your graph, find(i) the value of y when x = 1.3

(ii) the value ofx when y = -25

[ 2 marks ]

(d) Draw a suitable straight line on your graph to find the value ofx which satisfy the equation

01332 2 ! xx for -3 x 5.State these values of x.

[ 3 marks ]


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11. T ansformation ( Paper 2)

1. (a) Transformation Tis a translation

5

4. Transformation Ris a reflectionin the y-axis

Transformation V is a reflectionin the x = 3.

State the coordinates ofthe image of point (1, 3) under each ofthe following transformations :

(i) T (ii) TR

(iii) VT [4marks]

(b) Diagram 1 shows three quadrilaterals,$

BC%

,&

FGHandIJK'

drawn on a Cartesian plane.

&

FGH is the image ofABC%

underthe transformation W. IJKL is the image of EFGH underthe

transformation U.

(i) Describe in fullthe transformation :(a) W,(b) U.

(ii) Itis given that quadrilateral EFGH represents a region of area 24.5 m2. Calculate thearea, in m

2, ofthe region represented by the quadrilateralIJK

(

.

[8 marks]

Answer :

(a) (i)

(ii)

(iii)

(b) (i)

(ii)

(c)

x0

AB

CDE

F

G)

K

I

J

0

DIAGRAM 1


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2. Diagram 2 shows three quadrilaterals,ABC1

, EFGHandAIJK drawn on a Cartesian plane.

(a) Transformation Pis a reflection in the line x = 2.Transformation Q is a clockwise rotation of90

0aboutthe centre A.

State the coordinates ofthe image of point I underthe following tansformations :

(i) P (ii) Q (iii) Q2

[ 4 marks]

(b) QuadrilateralABC2

is the image ofEFGHunder a transformation V and quadrilateralsAIJKis

the image

ofABC3

under a transformation W. Describe in fullthe transformation

(i) V (ii) W

(c) Itis given that quadrilateral EFGH represents a region of area 32.5 cm2. Calculate the area,

in m2, ofthe region represented by the quadrilateral AIJK.

[8 marks]

Answer :

(a) (i)

(ii)

(iii)

(b) (i)

(ii)

(c)

x

y

0

A

B

C

D 4

G

F

E

K I

J

Diagram 2


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3. Diagram 3 shows three triangles,ABC, DEF and GEH, drawn on a Cartesian plane.

(a) Transformation T is a translation

2

3 .

Transformation V is a reflection in the line y = 3.

State the coordinates ofthe image of pointB underthe following transformations:

(i)

Translation T(ii) Combined transformations TV ? 3 marksA

(b) The triangleDEFis the image ofABCunder a transformation P. The triangle GEH is theimage of DEFunder a transformation Q. Describe in fullthe transformation

(i) P (ii) Q

(c) Itis given that triangle ABC represents a region of area 12 m2. Calculate the area, in

m2, ofthe region represented by the shaded region.

? 9 marksAAnswer:

(a) (i) .

(ii)

(b) (i)

(ii)

(c)

x

y

0

A

B

C

D

E

F

G 5

RAJAH 3


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4. Diagram 4 shows four pentagons,ABCDE,FGDHI,JK6

MNand O7

QRS drawn on a Cartesan

plane.

(a) Transformation Tis a translation

1

4 . Transformation Uia a reflection in the line y =x. State

the coordinates ofimage of point S underthe following transformations :

(i) T (ii) TU

[3 marks]

(b) The pentagon FGDHIis the image ofABCDEunder a transformation V. The pentagonJK8 MNis the image ofFGDHIunder a transformation U. Describe in fullthe transformation

(i) V (ii) U(iii) a single transformation which is equivalentto the combined transformation UV

[7 marks]

(c) Itis given that O9

QRSis the image of ABCDE under an enlargement with centre (6, 3) and

scale factor 3. Ifthe area ofO9

QRS represents a region of 167.4 m2, calculate the area, in

m2, ofthe pentagonABCDE.

[2 marks]

Answer:

(a) (i)

(ii)

(b) (i)

(ii)

(iii)

(c)

x

y

0

AB

C

D

E

F

G

@

K

I

J

Diagram 4

A

MN

OP

Q

R

B


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5. Diagram 5 shows three triangles, ABC, DEF and DHG, drawn on a Cartesan plane.

.

(a) Transformation T is a translation

3

5

Transformation V is a reflection in the line y =x .

State the coordinates ofthe image of point A underthe following transformations :

(i) Translation T (ii) combined transformation VT ? 3 marksA

(b) The triangleDEF is the image ofABC under a transformation P. The triangleDHGis

the image ofDEF under a transformation Q. Describe in fullthe transformation :

(i) P (ii) Q

(C) Itis given that quadrilateral EHGF represents a region of area 88.5 cm2. Calculate the

area, in cm2, of the region represented by the triangle DEF.

? 9 marksAAnswer:

(a) (i)

(ii)

(b) (i)

(ii)

(c)

x

y

0

A

B

CD

E

F

G

C

Diagram 5


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12. Matrices ( Paper 2)

1. Q is a 22 matrix where

!

10

01

43

56Q

(a) Find the matrix Q(b) Write the following simultaneous linear equations as a matrix equation.

6u 5v = -8

-3u + 4v = 7Hence, calculate the values ofu and v using matrices.

[ 6 marks ]

2. (a) Given that .10

01

6

12

23

161

!

pkfind the values ofkandp.

(b) Using matrices, calculate the values ofx andy that satisfy the following simultaneous

linear equations :

!

13

9

23

16

y

x

[ 6 marks ]

3. Given P=

23

35and Q =

m6

64

(a) Find the value of m where PQ =

20

02

(b) State the inverse matrix ofP

(c) Using matrices, calculate the values ofu and v that satisfy the following simultaneouslinear equations :

!

02

2335

vu

[ 6 marks ]

4. Given that matrixQ =

23

6 h

(a) Find the value of h, ifQ does not have an inverse matrix.

(b) Given that h = 3(i) state the inverse matrix ofQ

(ii) Using matrices, calculate the values ofx and y that satisfy the following simultaneouslinear equations :

!

10

21

23

6

y

xh

[ 6 marks ]


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5. Given that matrixP=

k3

42

(a) Find the value ofk, if determinant of matrix P= 0(b) Given k= 5

(i) state the inverse matrix ofP(ii) Using matrices, find the values ofu and v that satisfy the following simultaneous

linear equations :

!

19

16

53

42

v

u

[ 6 marks ]

13. Gradient and Area under a Graph (Paper 2)

1 Diagram 1 shows the distance-time graph of a car from the airport to town G.

(a) Find the distance, in km, of the town G from the airport.

(b) Find the total period, in minutes, that car stop during the journey to town G.

(c) Find the average speed of the car, in km h-1 in the last 15 minutes.

[ 6 marks ]

2 Diagram 2 shows the distance-time graph of a particle for a period of 20 seconds.

(a) Find the total distance traveled.

(b) Calculate the total period that the particles stops.

(c) Calculate the average speed of the particles for the whole journey in ms-1.

Time (min)

Distance ( km )

60

40

0 40 85 100 DIAGRAM 1

Time ( s )

Distance(m)

0

40

15 18 20DIAGRAM 2


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3 Diagram 3 shows the speed-time graph of a particle for a period Tseconds.

Find,(a) the distance in m, travelled at constant speed.

(b) the rate of change of speed, in m s- 2, in the first 3 seconds.

(c) the value ofT, given that total distance travelled for a period Tseconds is 171 m.[ 6 marks ]

4 Diagram 4 shows speed-time graph of a particle for a period of 15 seconds.

Given the total distance travelled is 168 m. Calculate

(a) the value ofv, in ms-1.

(b) the average speed, of ms -1, in the first 11 seconds.

(c) deceleration, in ms-2, in the last 4 seconds.

[ 6 marks]

Speed ( ms-1

)

Time (s)0 3 7 T

14

20

Speed (ms -1 )

Time (s)0 5 15

v

DIAGRAM 3

DIAGRAM 4


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5 Diagrams 5 shows the speed-time graph ofthe movement of a particle for a period T seconds.

(a) Calculate the rate of change of speed, in ms-2

, in the first 4 seconds.

(b) State the length oftime, in seconds, that particle moves with uniform speed.

(c) Calculate the value of Tifthe total distance travelled is 368 m.[ 6 marks]

Probability II

1. Diagram shows seven cards labelled with letters in box Eand boxF.

A card is picked at random from box E and then a card is picked at random from box F.

By listing the sample space of allthe possible outcomes ofthe event, find the probability

that

(a)both cards are labelled with same letters(b) only one ofthe cards is labelled with the letterP are picked.

Time(s)

Speed ( ms-1

)

20

12

8

04 18 T

DIAGRAM 5


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2. Diagram shows the cards in box A and box B.

A card is picked at random from box A and then a card is picked at random from box B.By listing the sample space of all the possible outcomes of the event, find the probabilitythat

(a) a card labelled X or a card with number 8 is picked(b)both cards are labelled with number

3. Diagram shows four cards labelled with letters in box M and three numbers in box N.

A card is picked at random from box M and then a card is picked at random from box N.By listing the sample space of all the possible outcomes of the event, find the probabilitythat

(a) a card with a vowel and a card with a two-digit numbers are picked(b) a card with a consonant or a card with an odd number are picked

4. A coin is tossed and a dice is rolled simultaneously. By listing the sample space of all thepossible outcomes of the event, find the probability that,

(a) a tail and an even number are obtained(b) a head or a number greater than four are obtained

5. Seven cards bearing the letters the word SCIENCE are well shuffled and placed in abox. Two cards are picked at random from the box, one after the other and are not

replaced.Calculate the probability that

a) the first card bears the letter E and the second card does not bears the letter Eb) both card bear the same letter


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6. Diagram shows 8 labelled in two boxes.

A card is picked at random from 1 and then a card is picked at random from box 2.By listing all the possible outcomes, find the probability that,

(a) two cards with consonant are picked(b) a card with a vowel and a card with a number are picked

7. Diagram shows a board numbered 1, 3, 6 and 9.

A student throw a dart at random onto a board and then he tossed a coin.

By listing all the possible outcomes, find the probability that,

(a) perfect square and a head are obtained,(b) multiple of 6 or tail are obtained

8. Diagram shows seven labelled in two boxes.

A card is picked at random from each of the boxes.

(a) List the sample space,(b) Find the probability that,

(i) both cards are labelled with a number,(ii) one card is labelled with a letter and the other card is labelled with a number.


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9. Diagram shows two boxes, A and B, containing numbered balls which are all of the samesize. A ball is taken out randomly from box A, and another one is taken out from box B.

(a) List down all possible outcomes,(b) Find the probability that,

(j) both balls are labelled with prime numbers,(ii) a ball is labelled with even number or a multiple of three.

10. Four cards which are labelled from 5 to 8 are placed in a box. Two cards are drawn atrandom.

By listing all the possible outcomes, find the probability of

(a) choosing cards with 5 and 7,(b) choosing cards with number 6 or 8.

16. EARTH AS A SPHERE (Paper 2)

1 P,Q andR are three points on the surface of the earth.P,Q andR lie on the same parallel

of latitude 770N, such that PR is the diameter of the parallel of latitude. The longitude ofP

is 700 Ewhile the longitude ofQ is 200 E.

(a) State the location ofR.[3 marks]

(b) Calculate the shortest distance, in nautical miles, between Pand R,measured along the

earths surface.[3 marks]

(c) Calculate the shortest distance, in nautical miles, betweenPand Q,measured along the

parallel of latitude. [3 marks]

(d) Given that an aeroplane flew from Q to the South Pole at an average speed of 600 knots,calculate the time of flight fromQ to the South Pole.

[3 marks]


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2 P,Q and R are three points on the surface of the earth. PQ is the diameter of the parallel

of latitude 50r N. R is 5400 nautical miles due south to Q. The longitude of R is 75r W.

(a) Calculate the latitude ofR . ?2 marksA(b) Calculate the longitude ofP. ?2 marksA

(c) Calculate the distance,in nautical miles, between Pand Q measured along the parallel oflatitude. ?3 marksA

(d) An aeroplane flew from Pto Q using the shortest route measured along the earthssurface and the flew due south to R at an average speed of 850 knots. The aeroplane

took off from P at 0715 hours. Calculate the time the aeroplane arrived at R.

?5 marksA

3 P )58,35( WS QQ , Q )24,35( ES QQ , R and V are four points on the surface of the earth. PRis the diameter of the earth and V is 3060 nautical miles due north ofQ.

(a) Calculate the longitude ofR. [2 marks]

(b) Calculate the longitude ofV. [3 marks]

(c) Calculate the distance, in nautical miles, from P due east to Q, measured along thecommon parallel of latitude. [4 marks]

(d) An aeroplane took off fromPat 0800 hours and flew due east to Q and then due north

to V. If the average speed for the flight is 600 knots, find the time the aeroplane arrived

at V.

[3 marks]

4 )50,0( WF QQ , G dan H are three points on the surface of the earth. GH is the diameter of

the parallel of latitude NQ

30 and G is due north of F.

(a) State the latitude of G. [1 marks]

(b) State the location ofH. [2 marks]

(c) Calculate the shortest distance, in nautical miles, between G and H,measured along the

earths surface. [3 marks]

(d) An aeroplane took off from F due north to G and then due east to H. Given the

average speed of the aeroplane is 500 knots, calculate

(i) the total distance of the flight, in nautical miles,

(ii) the total time taken for the whole flight to the nearest minute.[6 marks]


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5 MRWSQWNP and),45,(38),45,60( QQQQ arefour points on the surface of the earth.

PRis the diameter of the parallel of latitude and M is due north toR.

(a) State the longitude ofR.

[2 marks]

(b) The point Tis due east to Pand the distance betweenPand Tmeasured along the

common parallel of latitude is 4500 nautical miles. Calculate the longitude ofT.

[4 marks]

(c) Given that the distance between Rand Mmeasured along the surface of the earth is1500 nautical miles, calculate the latitude ofM.

[3 marks]

(d) An aeroplane took off fromM toPthrough the North Pole at an average speed of 700

knots. Calculate the time taken for the flight.

[3 marks]

16: Plans and Elevation ( Paper 2 )

1. (a) The Diagram 1 (i) shows a solid object made up of a cuboids and a prism with basesOMTWand WVUTon a horizontal plane. Given that KL =NW= 1 cm

l

DIAGRAM 1 (i)

Draw full scale, the elevation of the solid object on a vertical plane toOWVas viewed

from X.

[3 marks]

4 cm

3 cm

3 cm

H I

JK L

M

N

O

P

R

U

V4 cm

T

W

X

2 cm


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(b). The solid shown in the Diagram 1 (ii) is combination of Diagram 1 (i) and a half-cylinder

HZUM. HIZUTMand JRTUare vertical surfaces; MEUVO is horizontal surfaces. GiventhatNW= KL= 1 cm

DIAGRAM 1 (ii)

Draw full scale,

( i ) the plan of the solid, [4 marks]

(ii) the elevation of the solid on a vertical plane parallel to VUas viewed from Y.[5marks]

2. (a) The Diagram 2 (i) shows a solid object made up of a cuboids and a prism with basesABGHand BCFG on a horizontal plane. Given that JN= KM= 1 cm and JI= KL = 2cm.

X DIAGRAM 2 (i)

Draw full scale, the elevation of the solid object on a vertical plane to ABC as viewedfrom X.

[3 marks]

4 cm

3 cm3 cm

3 cm

1 cm

H I

JK L

M

N

O

P

R

U

V4 cm

T

W Y

Z

D

E

2 cm

A

H

BC

F

G

NJ

MK

L

I

4 cm

4 cm

5 cm


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2. (b) The Diagram 2 (ii) shows a solid consisting of a cuboids BCMKGFNJ, a right angle

prism AMLHGI and a quarter-cylinderCDPFEQ. CMNF and LBGI are on the samevertical plane. The base ABCDEFGH is on a horizontal plane. It is given that PC =

QF= CD = FE= 2 cm.

Y

DIAGRAM 2 (ii)

Draw full scale,

( i ) the plan of the solid, [4 marks]

(iii) the elevation of the solid on a vertical plane parallel to DEas viewed from Y.[5marks]

3. (a) The Diagram 3 (i) shows a solid object made up of a cuboids and a prism with bases

GHIJ on a horizontal plane. Given that AD = AC = BE = BF = 3 cm.

DIAGRAM 3 (i)

Draw full scale, the elevation of the solid object on a vertical plane to GHas viewedfrom Y.

[3 marks]

A

B

CD

FE

G H

IJ

Y

5 cm

5 cm

5 cm

5 cm

A

H

BC

F

G

NJ

MK

L

I

4 cm

4 cm

P

2cm

Q

D

E


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(b) The Diagram 3 (ii) shows a solid object made up of a cuboids, pyramid and a prismwith bases GHIJ and HPOIon a horizontal plane. Given that HL = 3 cm, MP= 2 cm

and HP= 1 cm.

Diagram 3 (ii)Draw full scale,

( i ) the plan of the object, [4 marks]

(iv) the elevation of the solid on a vertical plane parallel to PO as viewed fromX.[5marks]

4. (a) The Diagram 4 (i) shows a solid consisting of a cuboids GHIFAKJland a right angle

prism ABGECD. AEDG and EKHD are on the same vertical plane. The baseBCDG and

GHIFis on a horizontal plane. It is given that

DIAGRAM 4 (i)

Draw full scale, the elevation of the solid object on a vertical plane to BCas viewed fromX.

[3 marks]

A

B

CD

FE

G H

IJ

KN

L

M

P

O

X

2 cm

3 cm

5 cm5 cm

5 cm

L

J

K

I

H

D

A

B

C

E

F

G

2 cm

4 cm

4 cm

4 cm

3 cm

X


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(b) The Diagram 4 (ii) shows a solid object made up of a cuboids with bases GHIF, and twoprism with bases BCDG and QPHNon a horizontal plane. It is given that IH= PQ = 2 cm.

DIAGRAM 4 (ii)Draw full scale,

( i ) the plan of the object, [4 ma rks]

(ii) the elevation of the solid on a vertical plane parallel to PHIas viewed from Y.[5marks]

5. (a) The Diagram 5 (i) shows a solid object with bases BCJFA on a horizontal plane. KLMand GHI is right angle triangle. Given that LG = 2 cm.

DIAGRAM 5 (i)

Draw full scale, the elevation of the solid object on a vertical plane to AB as viewed fromY.

[3 marks]

L

JK

I

H

D

A

B

C

E

F

G

2 cm

4 cm

4 cm

3 cm

M

P

Q

N

Y

K M Q

A

L

G

I

H

F

N P

B C J

4 cm 3 cm

4 cm

Y 4 cm


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(b) The solid shown in the Diagram 5 (ii) is combination of Diagram 5 (i) and a halfcylinderBDCLEN. LNPJCB is vertical surfaces; BJFA is horizontal surfaces. GiventhatLG = 2 cm

DIAGRAM 5 (ii)

Draw full scale,

( i ) the plan of the object, [4 marks]

(v) the elevation of the solid on a vertical plane parallel to BCJas viewed fromX.[5marks]

INEQUALITIES

1. On the graph in the answer space, shade the region which satisfies the three inequalities3 12,y xe 2 4y xu and 2x .

[3 marks]

Answer:

K M Q

A

L

G

I

H

F

N

P

B

C

J

4 cm 3 cm

4 cm

D

E

X

4 cm

3 12y x!

2 4y x!

Ox

y


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2. Pada graf di ruang jawapan, lorekkan rantau yang memuaskan ketiga-tiga ketaksamaan

y 2x+ 12 , y < 12 and x 6 .

[3 markah]

3. On the graph in answer space, shade the region which satisfies the three inequalitiesy x + 6, y 2x 4 and x>1.

y

6

0 2 6 x

4

x

y

0

122 ! xy

6!x

y = x + 6

y = 2x 4


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4. On the graph in answer space, shade the region which satisfies the three inequalitiesy x + 10, y < x and y > 1.

y

0

5. On the graph in answer space, shade the region which satisfies the three inequalitiesy 2x + 8, y x and y < 8.

yy = 2x + 8

y = x

y = x + 10

y = 1

0 x

Paper 2 Modul Baru

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