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F4 Maths Ppsmi 2007 P2

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F4 Maths Ppsmi 2007 P2

1. 1. 1 SULIT ppr maths nbk 1449/2 1449/2 NAMA : ___________________________________ Matematik Kertas 2 TINGKATAN : _____________________________ Oktober 2007 1 2 jam 2 PPSMI ASSESSMENT 2007 MATHEMATICS Kertas 2 Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Pemeriksa Bahagian Soalan Markah Markah 1. Tulis nama dan tingkatan anda pada ruang yang disediakan. Penuh Diperoleh . 1 2. Kertas soalan ini adalah dalam 2 dwibahasa. 3 4 3. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam 5 bahasa Melayu A 6 7 4. Calon dibenarkan menjawab 8 keseluruhan atau sebahagian soalan 9 sama ada dalam bahasa Inggeris atau bahasa Melayu. 10 11 5. Calon dikehendaki membaca arahan di 12 12 halaman 2 atau halaman 3. 13 12 B 14 12 15 12 16 12 Jumlah Kertas soalan ini mengandungi 55 halaman bercetak dan 1 halaman tidak bercetak [Lihat Sebelah 1449/2 SULIT
2. 2. SULIT 2 1449/2 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. 1449/2 SULIT
3. 3. 3 SULIT ppr maths nbk 1449/2 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 y2 − y1 m= x2 − x1 3 (am )n = am n 14 y − intercept m=− x − intercept 4 1 ⎛ d − b⎞ A−1 = ⎜ ⎟ ad − bc ⎜ − c a ⎟ ⎝ ⎠ 5 n( A) P ( A) = n( S ) 6 P ( A' ) = 1 − P( A) 7 Distance = ( x2 − x1 ) 2 + ( y2 − y1 ) 2 8 ⎛ x + x y + y2 ⎞ Midpoint, ( x, y ) = ⎜ 1 2 , 1 ⎟ ⎝ 2 2 ⎠ 9 distance travelled Average speed = time taken 10 sum of data Mean = number of data 11 sum of (class marks × frequency) Mean = sum of frequencies [Lihat Sebelah 1449/2 SULIT
4. 4. SULIT 4 1449/2 SHAPES AND SPACE 1 1 Area of trapezium = × sum of parallel sides × height 2 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 1 Volume of cone = π r 2 h 3 9 4 Volume of sphere = π r 3 3 10 1 Volume of right pyramid = × base area × height 3 11 Sum of interior angles of polygon = (n −2)×180° 12 arc length angle subtended at centre = circumference of circle 360o 13 area of sector angle subtended at centre = area of circle 360o 14 PA' Scale factor, k = PA 15 Area of image = k2 × area of object 1449/2 SULIT
5. 5. 5 SULIT ppr maths nbk 1449/2 For Section A Examiner’s Use [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) P R Q (b) P R Q [Lihat Sebelah 1449/2 SULIT
6. 6. SULIT 6 1449/2 For Examiner’s 2(a). Diagram 1 shows a cube with horizontal base TUVW. Use X is the midpoint of TU. P Q S R 6 cm W V T X U DIAGRAM 1 Identify and calculate the angle between the line QX and the base TUVW. [4 marks] Answer: 1449/2 SULIT
7. 7. 7 SULIT ppr maths nbk 1449/2 For Examiner’s Use 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. N 7 cm M 10 cm 6 cm Q R P S DIAGRAM 2 Identify and calculate the angle between the plane MSP and the plane MPR. [4 marks] Answer: [Lihat Sebelah 1449/2 SULIT
8. 8. SULIT 8 1449/2 SOLID GEOMETRY For Examiner’s 3. Use 1449/2 SULIT
9. 9. 9 SULIT ppr maths nbk 1449/2 2 y2 − 3 For Examiner’s Use 4. Solve the quadratic equation = 1. 5y [4 marks] Answer: 5. Solve the quadratic equation (4n − 1)2 = 4n2. [4 marks] Answer: [Lihat Sebelah 1449/2 SULIT
10. 10. SULIT 10 1449/2 6. Calculate the value of v and of w that satisfy the following simultaneous linear For Examiner’s equations: Use v − 3w = 5 3v − w = 3 [4 marks] Answer: 7. Calculate the value of d and of e that satisfy the following simultaneous linear equations: 3d + e = 11 1 d− e=6 4 [4 marks] Answer: 1449/2 SULIT
11. 11. 11 SULIT ppr maths nbk 1449/2 For CIRCLES Examiner’s Use 8. [Lihat Sebelah 1449/2 SULIT
12. 12. SULIT 12 1449/2 For Examiner’s 9(a) Combine the two statements below to form a true statement. Use 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) 1449/2 SULIT
13. 13. 13 SULIT ppr maths nbk 1449/2 For STRAIGHT LINE Examiner’s Use 10. In Diagram XX, PQ is a straight line on a Cartesian plane. y P(−1,3) Q(4,1) O x 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). [4 marks] Answer: (a) (b) [Lihat Sebelah 1449/2 SULIT
14. 14. SULIT 14 1449/2 STRAIGHT LINE For Examiner’s 11. Diagram xx shows KL , ML and MN are straight lines on a Cartesian plane. Use N is on the y-axis. KL is parallel to MN, ML is parallel to the y-axis and LO = ON. y M K N x L O 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. [5 marks] Answer: (a) (b) 1449/2 SULIT
15. 15. 15 SULIT ppr maths nbk 1449/2 For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use [Lihat Sebelah 1449/2 SULIT
16. 16. SULIT 16 1449/2 For Section B Examiner’s Use [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) Q P R (ii) Q P R 1449/2 SULIT
17. 17. 17 SULIT ppr maths nbk 1449/2 Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m For Examiner’s’ 12(b) In Diagram xx, OJKL is a parallelogram and O is the origin. Uses y J(3,6) K(6,h) x O L 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) [Lihat Sebelah 1449/2 SULIT
18. 18. SULIT 18 1449/2 For Sets-3m / Straight lines-5m / Lines & Planes In 3D-4m Examiner’s Use 12(c) Diagram xx shows a cuboid with a horizontal base PQRS. W V 6 cm T U S R 8 cm P 6 cm Q DIAGRAM xx Calculate the angle between the plane VPQ and base PQRS. [4 marks] Answer: 1449/2 SULIT
19. 19. 19 SULIT ppr maths nbk 1449/2 Maths reasoning-6m / Circles-6m For Examiner’s’ 13(a) (i) State whether the following statement is true or false. Uses (a) 2 and 25 are perfect squares (b) 62 = 12 or 3 − 8 = −2 (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: [Lihat Sebelah 1449/2 SULIT
20. 20. SULIT 20 1449/2 For Maths reasoning-6m / Circles-6m Examiner’s Use 13(b) In Diagram xx, O is the centre of a circle with diameter KON. KO is the diameter of the circle KJOH . L M J 30° K N O H DIAGRAM xx KON = 14 cm and ∠ MON = 30°. 22 Using π = ,calculate 7 (i) the perimeter, in cm, of the whole diagram, (ii) the area, in cm2, of the shaded region. [6 marks] Answer: (i) (ii) 1449/2 SULIT
21. 21. 21 SULIT ppr maths nbk 1449/2 Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m For Examiner’s’ 9 7 Uses 14(a) Solve the quadratic equation x 2 − = 3 − x . 2 2 [4 marks] Answer: [Lihat Sebelah 1449/2 SULIT
22. 22. SULIT 22 1449/2 For Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m Examiner’s Use 14(b) Calculate the value of x and of y that satisfy the following simultaneous linear equations: 1 x + y = 17 4 1 x− y =3 3 [4 marks] Answer: 1449/2 SULIT
23. 23. 23 SULIT ppr maths nbk 1449/2 Quad Eqn-4m / Linear Eqn-4m / Solid Geometry-4m For Examiner’s 14(c) Diagram xx shows a solid right pyramid with a square base. Use 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: [Lihat Sebelah 1449/2 SULIT
24. 24. SULIT 24 1449/2 For Statistics-12m Examiner’s Use 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] 1449/2 SULIT
25. 25. 25 SULIT ppr maths nbk 1449/2 Answer: For Examiner’s (a) Use Time(minutes) Frequency Cumulative Frequency 5−9 10−14 TABLE xx (b) Refer graph on page xx. (c)(i) (ii) [Lihat Sebelah 1449/2 SULIT
26. 26. SULIT 26 1449/2 Graph for Question 15 For Examiner’s Use 1449/2 SULIT
27. 27. 27 SULIT ppr maths nbk 1449/2 Statistics-12m For Examiner’s 16. The data in Diagram xx show the height, in cm, of a group of 40 pupils. Use 152 167 168 177 178 174 172 173 176 154 162 173 163 155 167 164 160 175 171 178 159 174 168 176 171 169 156 166 172 153 179 174 160 158 169 151 154 167 164 154 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] [Lihat Sebelah 1449/2 SULIT
28. 28. SULIT 28 1449/2 For Answer: Examiner’s Use (a) Height(cm) Lower Upper Frequency Boundary Boundary 145 − 149 150 − 154 TABLE xx (b) (c) Refer graph on page xx. (d) 1449/2 SULIT
29. 29. 29 SULIT ppr maths nbk 1449/2 Graph for Question 16 For Examiner’s Use [Lihat Sebelah 1449/2 SULIT
30. 30. SULIT 30 1449/2 END OF QUESTION PAPER For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use For Examiner’s Use 1449/2 SULIT