pep f4 ppsmi exam paper

SULIT ppr maths nbk 1449/2

[Lihat Sebelah 1449/2 SULIT

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NAMA : ___________________________________ TINGKATAN : _____________________________

PPSMI ASSESSMENT 2007

MATHEMATICS

Kertas 2

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Kertas soalan ini mengandungi 55 halaman bercetak dan 1 halaman tidak bercetak

1449/2 Matematik Kertas 2 Oktober 2007

jam212

1. Tulis nama dan tingkatan anda pada

ruang yang disediakan. . 2. Kertas soalan ini adalah dalam

dwibahasa. 3. Soalan dalam bahasa Inggeris

mendahului soalan yang sepadan dalam bahasa Melayu

4. Calon dibenarkan menjawab

keseluruhan atau sebahagian soalan sama ada dalam bahasa Inggeris atau bahasa Melayu.

5. Calon dikehendaki membaca arahan di

halaman 2 atau halaman 3.

Pemeriksa Bahagian Soalan Markah

Penuh Markah

Diperoleh1 2 3 4 5 6 7 8 9 10

A

11 12 12 13 12 14 12 15 12

B

16 12 Jumlah

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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 from 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 4 to 7. 9. A booklet of four-figure mathematical tables is provided. 10. You may use a non-programmable scientific calculator. 11. 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 given are the ones commonly used.

RELATIONS 1 am × an = am + n 12 Pythagoras Theorem

c2 = a2 + b2

2 am ÷ an = am − n 13

12

12

xxyym

−−

=

3 (am )n = am n 14

interceptintercept

−−

−=xym

4

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−

=−

acbd

bcadA 11

5 )()()(

SnAnAP =

6 )(1)'( APAP −=

7 Distance = 212

212 )()( yyxx −+−

8

Midpoint, ⎟⎠⎞

⎜⎝⎛ ++

=2

,2

),( 2121 yyxxyx

9 takentimetravelleddistancespeedAverage =

10 data ofnumber

data of sumMean =

11 sfrequencie of sum

frequency) marks (class of sumMean ×=

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SHAPES AND SPACE

1 heightsidesparallelofsum

21 trapeziumof Area ××=

2 Circumference of circle = π d = 2 π r

3 Area of circle = π r 2

4 Curved surface area of cylinder = 2 π r h

5 Surface area of sphere = 4 π r 2

6 Volume of right prism = cross sectional area × length

7 Volume of cylinder = π r 2 h

8 Volume of cone hr 2

31π=

9 Volume of sphere 3

34 rπ=

10 Volume of right pyramid heightareabase

31

××=

11 Sum of interior angles of polygon = (n −2)×180°

12 o360

centreatsubtendedanglecircleofncecircumfere

lengtharc=

13 o360

centreatsubtendedanglecircleofareasector of area

=

14 PAPA'k =,factorScale

15 Area of image = k2 × area of object



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For

Examiner’s Use

Section A [52 marks]

Answer all questions in this section.

1. The Venn diagram in the answer space shows sets P , Q and R such that the universal set ξ = P ∪ Q ∪ R. On the diagrams in the answer space, shade (a) the set P ∩ Q’, (b) the set ( Q ∪ R ) ∩ P.

[3 marks]Answer: (a) (b)

P Q

R

P Q

R

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2(a). Diagram 1 shows a cube with horizontal base TUVW. X is the midpoint of TU.

DIAGRAM 1 Identify and calculate the angle between the line QX and the base TUVW.

[4 marks]Answer:

For Examiner’s

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P Q

RS

W V

UT X

6 cm



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2(b). Diagram 2 shows a right prism with horizontal base PQRS. The right angled triangle MPR is the uniform cross section of the prism.

DIAGRAM 2 Identify and calculate the angle between the plane MSP and the plane MPR.

[4 marks]Answer:

P

Q

R

S

M

N7 cm

6 cm

10 cm

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SOLID GEOMETRY 3.

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Use 4. Solve the quadratic equation 15

32 2

=−y

y .

[4 marks]Answer:

5. Solve the quadratic equation (4n − 1)2 = 4n2. [4 marks]

Answer:

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6. Calculate the value of v and of w that satisfy the following simultaneous linear equations:

3353

=−=−

wvwv

[4 marks]Answer:

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7. Calculate the value of d and of e that satisfy the following simultaneous linear equations:

641

113

=−

=+

ed

ed

[4 marks]Answer:



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CIRCLES 8.

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9(a) Combine the two statements below to form a true statement. Statement I : All even numbers are divisible by 6. Statement II : 3 is a factor of 6. (b) Write two implications based on the following sentence. ∠M and ∠N are vertically opposite angles if and only if ∠M = ∠N. (c) Complete the premise in the following argument. Premise I : If the participants finish the 7km run then they will receive a certificate. Premise II : ________________________________________________________ Conclusion : Ali will not receive a certificate.

[5 marks]Answer: (a)

(b)

(c)

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STRAIGHT LINE 10. In Diagram XX, PQ is a straight line on a Cartesian plane.

DIAGRAM xx (a) Calculate the gradient of the line PQ. (b) Find the equation of the line parallel to the line PQ and passing through the point (−5,1).


P(−1,3)

Q(4,1)

y

xO

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STRAIGHT LINE 11. Diagram xx shows KL , ML and MN are straight lines on a Cartesian plane. N is on the y-axis. KL is parallel to MN, ML is parallel to the y-axis and LO = ON.

DIAGRAM xx The equation of MN is 3x + 4y = 20. (a) Find the equation of LM. (b) Find the equation of KL and state its y-intercept.


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y

xO

K

L

M

N



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Section B [48 marks]

Answer any four questions from this section. Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m 12(a) The Venn diagram in the answer space shows sets P, Q and R such that the universal set ξ = P ∪ Q ∪ R. On the diagram in the answer space, shade (i) the set P ∩ Q’, (ii) the set (P ∪ Q ) ∩ R’.

[3 marks]Answer: (i) (ii)

P Q R

P Q R



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Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m 12(b) In Diagram xx, OJKL is a parallelogram and O is the origin.

DIAGRAM xx Find (i) the value of h, (ii) the equation of the straight line KL, (iii) the coordinate of point C.

[5 marks]Answer: (i) (ii) (iii)

For Examiner’s’

Uses

J(3,6) K(6,h)

O Lx

y

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Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m 12(c) Diagram xx shows a cuboid with a horizontal base PQRS.

DIAGRAM xx Calculate the angle between the plane VPQ and base PQRS.

[4 marks]Answer:

P Q

RST U

VW

6 cm

6 cm

8 cm



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Maths reasoning-6m / Circles-6m 13(a) (i) State whether the following statement is true or false. (a) 2 and 25 are perfect squares (b) 62 = 12 or 283 −=− (ii) Write two implications from the following sentence “ k2 > 49 if and only if k > 7.” (iii) Complete the premise in the following argument Premise 1 : If m = 3 , then 6 × m = 18. Premise 2 : _____________________ Conclusion : m ≠ 3.

[6 marks]Answer: (i)(a)

(b)

(ii)

(iii) Premise 2:

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Maths reasoning-6m / Circles-6m 13(b) In Diagram xx, O is the centre of a circle with diameter KON. KO is the diameter of the circle KJOH .

DIAGRAM xx KON = 14 cm and ∠ MON = 30°.

Using 722

=π ,calculate

(i) the perimeter, in cm, of the whole diagram, (ii) the area, in cm2, of the shaded region.

[6 marks]Answer: (i) (ii)

30°O K

L M

N

H

J



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Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m

14(a) Solve the quadratic equation xx273

292 −=− .

[4 marks]Answer:

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Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m 14(b) Calculate the value of x and of y that satisfy the following simultaneous linear equations:

331

1741

=−

=+

yx

yx

[4 marks]Answer:



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Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m 14(c) Diagram xx shows a solid right pyramid with a square base. A cuboid with a square base is taken out from the pyramid.

DIAGRAM xx Calculate the volume , in cm3 , of the remaining solid.

[4 marks]Answer:

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Statistics-12m 15. The data in Diagram xx shows the time taken by 60 pupils to go school on a particular day.

38 25 16 22 30 27 18 33 20 24 23 26 23 12 15 29 12 21 18 13 11 13 17 19 11 17 28 5 24 26 23 15 13 9 18 28 28 21 29 25 19 11 34 11 13 21 13 23 31 20 19 32 24 27 18 25 15 15 22 30

DIAGRAM xx

(a) Based on the data in Diagram xx and using a class interval of 5 minutes, complete Table xx in the answer space.

[4 marks]

(b) For this part of the question, use the graph paper provided on page xx. By using a scale of 2 cm to 5 minutes on the x-axis and 2 cm to 5 pupils on the y-axis, draw an ogive for the data.

[6 marks]

(c) From your ogive in (b), (i) find the median, (ii) hence, using the time taken, in minutes, and the number of pupils, explain briefly the meaning of the median.

[2 marks]



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Answer: (a)

Time(minutes) Frequency Cumulative Frequency5−9

10−14

TABLE xx (b) Refer graph on page xx. (c)(i) (ii)

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Graph for Question 15 For

Examiner’s Use



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Statistics-12m 16. The data in Diagram xx show the height, in cm, of a group of 40 pupils.

152 167 168 177 178 174 172 173176 154 162 173 163 155 167 164160 175 171 178 159 174 168 176171 169 156 166 172 153 179 174160 158 169 151 154 167 164 154

DIAGRAM xx

(a) Based on the data in Diagram xx and by using a class interval of 5 cm, complete Table xx in the answer space.

[3 marks]

(b) Based on the Table xx in (a), calculate the estimated mean height. [3 marks]

(c) For this part of the question, use the graph paper provided on page xx. By using a scale of 2 cm to 5 cm on the horizontal x-axis and 2 cm to 1 pupil on the vertical axis, draw a histogram for the data.

[5 marks]

(d) Based on the histogram in (c), state one information relating height with number of pupils.

[1 mark]

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For

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Answer: (a)

Height(cm) Lower Boundary

Upper Boundary

Frequency

145 − 149 150 − 154

TABLE xx (b) (c) Refer graph on page xx. (d)



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Graph for Question 16

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END OF QUESTION PAPER

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pep f4 ppsmi exam paper

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