Spm Trial Paper 2 4m6z3f

SULIT 1449/2 Mathematics Paper 2 2010

1 2 hours 2

SRI SEDAYA SCHOOL SUBANG JAYA SPM TRIAL EXAMINATION 2010

Form Four

MATHEMATICS Paper 2 Two hours and thirty minutes DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO

INFORMATION FOR CANDIDATES

7.

1.

This question paper consists of 2 sections: Section A and Section B.

2.

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

3.

Write your answer in the space provided in the question paper.

4.

Working steps must be written clearly..

6.

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

You may use a non-programmable scientific calculator.

This question paper consists of 21 printed pages including this front page

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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 2 a m ÷ a n = a m−n 3 ( a m ) n = a mn 1  d − b −1   4 A = ad − bc  − c a  n( A) 5 P ( A) = n( S ) 6 P ( A' ) = 1 − P ( A) 7 8 9 10 11 12 13 14

Distance =

( x1 − x 2 ) 2 + ( y1 − y 2 ) 2

 x1 + x 2 y1 + y 2  ,  Midpoint, ( x, y ) =  2   2 distance travelled Average speed = time takenl sum of data Mean = number of data sum of (class mark × frequency) Min = sum of frequencie s Pythagoras Theorem c2 = a2 + b2 y − y1 m= 2 x 2 − x1 y - intercept m= − x - intercept

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SHAPES AND SPACE 1 2 3 4 5 6 7 8 9 10 11 12 13

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1 Area of trapezium = × sum of parallel sides × height 2 Circumference = πd = 2πr Area of circle = πr2 Curved surface area of cylinder = 2πrh Surface area of sphere = 4πr2 Volume of right prism = cross sectional × length Volume of cylinder = πr2h 1 Volume of cone = πr2 h 3 4 Volume of sphere = πr3 3 1 Volume of right pyramid = × base area × height 3 Sum of interior angles of a polygon = (n - 2) × 180o arc length angle subtended at centre = circumfere nce of circle 360  area of sector angle subtended at centre = area of circle 360  PA' PA 2 Area of image = k × area of object.

Scale factor , k =

3

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 (Q ∪ R )’ ∩ P, (b) the set Q ∩ ( P ∪ R ). [3 marks] Answer : (a)

(b)

2. Solve the quadratic equation

7 − 3k 2 = −k 4 [4 marks]

Answer :

4

3. Calculate the value of m and the value of n which satisfy the following simultaneous equations. m – 3n = 5 3m – n = 3 [4 marks] Answer:

4. Diagram 1 shows a right prism. Trapezium ABCD is the uniform cross-section of the prism.

DIAGRAM 1 Calculate the angle between the plane CDEF and the plane ADEH. [3 marks] Answer :

5

5. In Diagram 2, the straight line PQ is parallel to the straight line OR where O is the origin. The point P lies on the x-axis and the point Q lies on the y-axis.

DIAGRAM 2 3 Given that the gradient of the straight line QR is − , find 2 (a) the value of u, (b) the gradient of the straight line PQ, (c) the equation of the straight line PQ. [5 marks] Answer : (a)

(b)

(c)

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6. Diagram 3 shows three sectors OPQ, ORS and OTU with the same centre O. POU, OQR and 1 OTS are straight lines and OQ = OR. 2

DIAGRAM 3 OR = 7cm, ∠POQ = ∠TOU and ∠QOT = 45° . Using π =

22 ,calculate 7

(a) the perimeter, in cm, of the whole diagram, (b) the area, in cm2 , of the shaded region. [6 marks] Answer : (a)

(b)

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7. (a) State whether each of the following statements is true or false. (i) -3 > 4 or -3 < - 4 3

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(ii) 81 4 = 27 and 81 2 = 9. (b) Write down Premise 1 to complete the following argument. Premise 1: …………………………………………………………………………………... Premise 2: Hwei Minn is a student in the engineering class. Conclusion: Hwei Minn ed the SPM examination. (c) Write down two implications based on the following sentence: 3 125 = 5 if and only if 3 125 + 3 = 8 Implication 1: ………………………………………………………………………………... Implication 2: ………………………………………………………………………………… [5marks] Answer: (a) (i) ……………………………………………………………………………………………… (ii) …………………………………………………………………………………………….. (b) Premise 1: ………………………………………………………………………………………. ……………………………………………………………………………………… Implication 1: …………………………………………………………………………………... Implication 2: ……………………………………………………………………………………

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 2 6  5 m  1 0  and matrix N = n   such that MN =   8. Given that matrix M =   4 5 − 4 2  0 1 (a) Find the value m and of n. (b) Hence, using matrices, find the value of x and y that satisfy the following simultaneous linear equations: 2x + 6y = 6 4x + 5y = 4 [7 marks] Answer: (a)

(b)

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9. Diagram 4 shows 10 labeled cards in two boxes.

DIAGRAM 4 A card is picked at random from each of the boxes. By listing the outcomes, find the probability that (a) both cards are labeled with a number, (b) one card is labeled with a number and the other card is labeled with a consonant. [5 marks] Answer: (a)

(b)

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10. Diagram 5 shows the speed-time graph of a particle for a period of t seconds.

DIAGRAM 5 (a) State the length of time, in s, when the particle moves with uniform speed. (b) Calculate the rate of change of speed, in ms-2, in the first 4 seconds. (c) Calculate the value of t, if the total distance traveled in t seconds is 306m. [6 marks] Answer: (a)

(b)

(c)

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11. Diagram 6 shows a solid cylinder with radius 16 cm and height 42 cm. A cone with radius 5 cm and height 14 cm is taken out of the solid.

DIAGRAM 6 22 Using π = ,calculate the volume in cm 3 of the remaining solid. 7 [4marks] Answer:

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Section B [48 marks] Answer any four questions in this section. 12. (a) Diagram 7 shows two points, J and K, on a Cartesian plane.

DIAGRAM 7  2  Transformation T is the translation   .Transformation R is a clockwise rotation of 90 ̊about the  − 3 centre (2, 1). (i) State the coordinates of the image of point J under transformation R. (ii) State the coordinates of the image of point K under (a) TR (b) RT [5 marks] (b) Diagram 8 shows 3 triangles, KLM, PQR and PST, drawn on a Cartesian plane.

DIAGRAM 8 ∆PQR is the image of ∆KLM under transformation V. ∆PST is the image of ∆PQR under transformation W. (i) Describe in full transformation : (a) V, (b) W. (ii) Given that the area of ∆PTS is 135 cm2, calculate the area, in cm2 of region represented by the shaded region. [7 marks]

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Answer: (a)

(i)

(ii) (a)

(b)

(b)

(i) (a)

(b)

(ii)

13. (a) Complete Table 1 in the answer space for the equation y = 4x2 – 5x -7 by writing down 14

the values of y when x = -1 and x = 2.5. [2marks] (b) For this part of the question, use the graph paper provided. You may use a flexible curve rule. By using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph of y = 4x2 – 5x -7 for -2.5 ≤ x ≤ 3. [4 marks] (c) From your graph, find (i) the value of y when x = -1.5, (ii) the value of x when y = 22. [2 marks] (d) Draw a suitable straight line on your graph to find a value of x which satisfies the equation 4x2 + 2x -2 = 0 for -2.5 ≤ x ≤ 3. State these values of x. ( show how you get the straight line equation) [4marks] Answer : (a)

TABLE 1 (b) Refer graph. (c) (i)

y = ……………………………………………….

(ii)

x = ……………………………………………….

(d) x = ……………………………………………………

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14 (a) The data in Diagram 9 shows the masses (in g) of 40 eggs used in an experiment.

DIAGRAM 9 (a) Based on the data in Diagram 9 and by using a class interval of 5, complete the Table 2 in the answer space. [4 marks] (b) Based on the Table 2 in (a), calculate the estimated mean mass of the eggs. each student. [3 marks] (c) For this part of the question, use the graph paper provided. By using a scale of 2 cm to 5 g on the x-axis and 2cm to 1 egg on the y-axis , draw a frequency polygon for the data. [4 marks] (d) Based on the frequency polygon in (c), state the modal class. [1 mark] Answer : (a) Class interval 35 - 39 40 - 44

Midpoint 37

Frequency 2

TABLE 2 (b)

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(c) Refer graph.

(d)

15. You are not allowed to use graph paper to answer this question. (a) The diagram 10(a) shows two prisms ed together at the vertical plane BMQG. The base

AFGNKB is a rectangle lying on a horizontal table. ABCDE and BKLM are the uniform cross sections of the respective prisms. AE and BMC are vertical edges of the same length. EJID and IHCD are inclined planes. MLPQ is a horizontal plane. ED = CD and DI is 6cm vertically above the base of the solid.

DIAGRAM 10 (a) Draw to full scale, the plan of the solid. [3 marks] Answer :

17

(a)

(b) A triangular prism is ed to the solid in Diagram 10(a) at the horizontal plane PQML. The 18

combined solid is a shown in the Diagram 10 (b). LMR is the uniform cross section of the triangular prism. RM = RL and RS is 2cm vertically above the plane PQML.

DIAGRAM 10 (b)

Draw to full scale, (i) The elevation on a vertical plane parallel to ABK as viewed from X. [4 marks] (ii) The elevation on a vertical plane parallel to KN as viewed from Y. [5 marks]

Answer : 19

(b) (i)

(ii)

16. A (54°S, 5°W), B (54°S, 25°E), C and D are four points on the earth’s surface. AC is a diameter 20

of a parallel or latitude and D is due north of A. (a) Find the longitude of C. [2 marks] (b) Calculate the shortest distance, in nautical miles, from A to C. [3 marks] (c) Calculate the distance of AB, in nautical miles, measured along the common parallel of latitude. [3 marks] (d) A plane took off from A due north at a speed of 550 knots and took 6 hours to reach D. Find the latitude of D. [4 marks] Answer : (a)

(b)

(c)

END OF QUESTION PAPER

Prepared by, _________________ (Ms Tan Suk Wan)

Checked by,

Approved by,

___________________ (Ms Tee Swee Lee)

________________ (Mrs Tan See Miin)

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