2007 MidTerm Johor (Math_P2)

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SULIT 1449/2 1449/2 Matematik Kertas 2 Mei 2007 2½ jam PEPERIKSAAN 2 TAHUN 2007 MATEMATIK TINGKATAN LIMA Kertas 2 Dua jam tiga puluh minit  _______________ ___ JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU  _______________________________________________________________________  _ Kertas soalan ini mengandungi 21 halaman bercetak  NAMA : _  TINGKA T AN : __________ ____  Kod Pemeriksa Bahagian Soalan Markah Penuh Markah Diperoleh A 1 4 2 4 3 4 4 3 5 4 6 5 7 6 8 5 9 6 10 5 11 6 B 12 12 13 12 14 12 15 12 16 12 Jumlah 1. Tuli s nama dan tingkatan pada ruang disediakan. 2. Ker tas soal an in i adalah dal am Bahasa  Inggeris. 3. Cal on dike hend aki membaca arahan di halaman 2.

Transcript of 2007 MidTerm Johor (Math_P2)

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SULIT 1449/2

1449/2

Matematik 

Kertas 2

Mei

2007

2½ jam

PEPERIKSAAN 2

TAHUN 2007

MATEMATIK TINGKATAN LIMA

Kertas 2

Dua jam tiga puluh minit

 _____________________________________________________________ 

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

 _______________________________________________________________________ 

 _ Kertas soalan ini mengandungi 21 halaman bercetak 

 NAMA : _______________________________ 

TINGKATAN : _______________________________ 

 Kod Pemeriksa

Bahagian Soalan Markah

Penuh

Markah

Diperoleh

A

1 4

2 43 4

4 3

5 4

6 5

7 6

8 5

9 6

10 5

11 6

B

12 12

13 12

14 1215 12

16 12

Jumlah

1. Tulis nama dan tingkatan pada ruang 

disediakan.

2. Kertas soalan ini adalah dalam Bahasa

 Inggeris.

3. Calon dikehendaki membaca arahan di

halaman 2.

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INFORMATION FOR CANDIDATES

1. This question paper consists of two sections: Section A and  Section B.

2.  Answer all questions in Section A and  four questions in Section B.

3. Write your answers clearly in the spaces provided in the question paper.4. Show your working. It may help you to get marks.

5.  If you wish to change your answer, neatly cross out the answer that you have done.

Then write down the new answer.

6. The diagrams in the questions provided are not drawn to scale unless stated.

7. The marks allocated for each question and sub part of a question are shown in

brackets.

8.  A list of formulae is provided on pages 3 to 4.

9. You may use a non-programmable scientific calculator.

10. This question paper must be handed in at the end of the examination.

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MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols givenare the ones commonly used.

RELATION

1 nmnm aaa +=×

2 nmnm aaa −=÷

3 ( ) mnnm aa =

4    

  

 −

−−

=−

ac

bd 

bcad  A

11

5)(

)()(

S n

 An A P  =

6 )(1)( `  A P  A P  −=

7 Distance = ( ) ( ) 2

21

2

21  y y x x −+−

8 Midpoint, ( )  

 

 

 

  ++=

2

,

2

, 2121  y y x x y x

9 Average speed = distance travelled

time taken

10 Mean = sum of data

number of data

11 Mean = sum of (class mark × frequency)

sum of frequencies

12 Pythagoras Theorem,222

bac +=

1312

12

 x x

 y ym

−−

=

14 −=m  y-intercept  x-intercept

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SHAPES AND SPACE

1 Area of trapezium = ×2

1sum of parallel sides × height

2 Circumference of cirle = r d  π  π   2=

3 Area of cirle = 2r π  

4 Curved suurface area of cylinder = rhπ  2

5 Surface area of sphere = 24 r π  

6 Volume of right prism = cross sectional area × length

7 Volume of cylinder = hr 2π  

8 Volume of cone = hr 2

3

1π  

9 Volume of sphere =3

3

4r π  

10 Volume of right pyramid = ×3

1base area × height

11 Sum of interior angles of a polygon = ( ) °×− 1802n

12 arc length = angle subtended at centre

circumference of cirle 360º

13 area of sector = angle subtended at centre

area of circle 360º

14 Scale factor, k , = PA

 PA'

15 Area of image = ×2k  area of object

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SECTION A

[ 52 marks]Answer all questions in this section.

1 Solve the equation  y + 1 =5

)1(22

+ y .

[ 4 marks]

 Answer :

2 Calculate the value of  p and of q that satisfy the following simultaneous linear equations:

3 p + 2q = 4

2 p + 5q = 12− [ 4 marks]

 Answer :

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IAGRAM 3

M

U

T

S

6cm

8c

cm

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3

Diagram 1 shows a cuboid. The base TUVW is a horizontal rectangle. M is themidpoint of TW . Calculate the angle between the line QM and the base TUVW .

[4 marks]

 Answer :

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DIAGRAM 1

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4 On the graph in the answer space, shade the region which satisfies the three

inequalities 2 y < x + 12 ,  y ≥ 6 − 2 x and  x < 3.[ 3 marks ]

   Answer : y 2 y = x + 12

x0

y + 2x = 6

5 Diagram 2 shows a solid cylinder with radius 14 cm and height 16 cm. A conewith diameter 20 cm and height 12 cm is taken out of the solid.

DIAGRAM 2

Calculate the volume, in cm3 , of the remaining solid. (Use π   =

7

22) [4 marks]

 Answer:

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6   y

 

0

In Diagram 3 , O is the origin and OABC is a parallelogram,(a) find the coordinates of  B,(b) find the equation of the straight line AB and hence, state its y-intercept.

[ 5 marks]

 Answer:

(a)

(b)

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 x

DIAGRAM 3

 B

C(6,3)A(-2, 5)

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7

 

Diagram 4 shows EOGF is a semicircle with centre O. It is given that

OG = 10 cm,  EJO and GHO are two equal semicircles. Using π   =7

22, calculate

 

(a)  perimeter of shaded region,

(b) area of the shaded region.

[6 marks]

 Answer :

(a)

(b)

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10

   F 

   H  

 E   O 10cm  G

  J DIAGRAM 4

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8 (a) State whether each of the following statement is true or false

(i) 25 = 10 or 2

5= 2.5

(ii) –5 × (–2) = 10 and –5 > –2

(b) Complete the conclusion in the following argument :

Premise 1 : All regular pentagons have five sides of equal length.

Premise 2 : PQRST is a regular pentagon.

Conclusion : …………………………………………….

(c) Write down the two implications based on the following statement:

n is an even number if and only if n is divisible by 2.

 [5 marks]

 Answer :

(a) (i) …………………..

(ii) …………………..

(b) Conclusion : …………………………………………………………….

(c) Implication 1 : …………………………………………………………..

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

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9

 

Diagram 5 shows a distance-time graph for the journey of a car from C to E andthen returned to C .

(a) Find the distance, in km, from D to E .

(b) Calculate the length of time, in hours, of the car from D to E .

(c) Calculate the average speed, in kmh -1, of the car for the whole journey.

[6 marks]

 Answer :

(a)

(b)

(c)

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0 5 10 15 20 25 30 35 40 45 50

1

2

3

4

5

6

7

8

9

 D

 E 

Time (minutes)

DIAGRAM 5

Distance(km)

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10 (a) It is given that    

  

 −

−=  

 

  

 −

−52

43

52

43M  . Find the matrix M .

 

(b) Using matrices, calculate the values of  x and y that satisfy the followingsimultaneous linear equations:

3 x – 4 y = –55 y – 2 x = 8

[6 marks]

 Answer :

(a)

(b)

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11 It is given that the matrix G =    

  

 k 1

34

(a) Find the value of  k if G does not have an inverse matrix.

(b) Given that k = 2,

(i) find the inverse matrix for G.

(ii) Hence, using matrices, calculate the value of d and the value of e

which satisfy the matrix equation:

   

  

 k 1

34   

  

 e

d =   

 

  

 4

21

[6 marks]

 Answer :

(a)

(b) (i)

(ii)

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Section B

[48 marks]

 Answer any four questions from this section.

12 (a) Complete Table 1 in the answer space for the equation 3112 2 ++−=  x x y  

 by writing down the values of y when 1= x and 6= x .

[2 marks]

 (b)  For this part of the question, use the graph paper provided. You may use a

 flexible curve ruler.

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the

   y- axis, draw the graph of  31122 ++−=  x x y for −1 ≤ x ≤ 7.

[4 marks]

(c) From your graph, find

(i) the value of  y when x = 3.5

(ii) the values of  x when y = 0.

[3 marks]

(d ) Draw a suitable straight line on your graph to find all the values of  x

which satisfy the equation 0982 2 =++−  x x for −1 ≤ x ≤ 7.

State these values of  x.[3 marks]

 Answer :

(a)

TABLE 1

(c) (i)   y = …………

(ii)  x = …………………

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 x −1 0 1 2 3 4 5 6 7

 y − 10 3 17 18 15 8 −18

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(d)  x = ……………………..

13 (a) Transformation P is a clockwise rotation about point (1,1) while the

transformation Q is a translation    

  

 − 3

4.

State the coordinates of the image of point T , ( 2,3 ) under transformation

(i) Q2.

(ii) QP.[4 marks]

(b) Diagram 6 shows quadrilaterals, ABCD, PQRS and EFGH , drawn

on a Cartesian plane.

 

DIAGRAM 6

 PQRS  is the image of  ABCD under the transformation V and  EFGH  is

the image of  PQRS  under the transformation W.

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-12 -10 -8 -6 -4 -2 2 4 6 8 F 

 E 

G H 

Q P 

 DC 

 B A

 y

 xO

 R

6

4

2

- 2

- 4

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(ii) (a)

(b)

14

DIAGRAM 8

The quadrilateral AGFE is the image of the quadrilateral ABCD under the

transformation V . The quadrilateral HJKE is the image of the quadrilateral AGFE 

under the transformation W .(i). Describe in full the transformation:

(a) V

(b) W

(ii) Given that quadrilateral ABCD represents a region of area 24.5 cm2,

calculate the area of the quadrilateral AGFE .

[7 marks] Answer :

(b) (i) (a)

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 K 

 J 

 H  F  E 

 D C 

 B

G

 A

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(b)

 

(ii)

15 The data in Diagram 9 shows the age (years) of 40 residents in a village.

49 65 91 50 78 52 58 69

68 32 64 68 95 63 40 73

79 57 72 39 61 45 84 5253 83 71 70 95 76 85 70

71 49 88 55 63 77 49 81DIAGRAM 9

(a) Based on the data in Diagram 9 and by using a class interval of 10, completeTable 2 provided in the answer space. [4 marks]

(b) Based on table in (a), calculate the estimated mean age of the residents.

[3 marks]

(c) For this part of the question, use the graph paper provided.

By using a scale of 2 cm to 10 years on the horizontal axis and2 cm to 1 resident on the vertical axis, draw the histogram based on the

data.

[3 marks]

(d) State one piece of information obtained based on the histogram in (c).

[2 marks] Answer :(a)

Age(years) Frequency Midpoint

31 − 40

41 − 50

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(iii) the number of students who qualified for the final if 38 minutes is

the qualifying time.

[5 marks]

 Answer :

(a)

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Time (minutes) Frequency Upper  

Boundary

Cumulative

Frequency

25 – 29 0

30 – 34 5

35 – 39 8

40 – 44 11

45 – 49 21

50 – 54 22

55 – 59 10

60 – 64 3

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