SEKOLAH MENENGAH KEBANGSAAN DESA TUN HUSSEIN ONN JALAN JELATEK, 54200 KUALA LUMPUR
PROGRAM E-PEMACU LATIHAN PENGUKUHAN MATEMATIK TINGKATAN 5 TINGKATAN : 5A /5C /5D 1
1 1 Diagram 1 shows the graph of y = −2 x − 3, y = −x + 1 and y = −4 x − 3.
Diagram 1 1 1 Shade the region that satisfies y > − x − 3, y ≤ −x + 1 and y > − x − 3. 2 4 [3 marks]
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Solve the quadratic equation
2x(x + 4) = x + 6. 3 [4 marks]
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Diagram 2 shows a right prism with right-angled triangle PQR as its uniform cross-section and rectangle PQTS as its base. V is the midpoint of RU.
Diagram 2 (a) Identify the angle between the line VT and the plane PSUR. (b) Calculate the angle between the line VT and the plane PSUR. [3 marks]
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In Diagram 4, OPQ is a sector of a circle with centre O and RSTU is a semicircle with centre R. PSRUO is a straight line.
Diagram 4 It is given that PO = 45 cm, RS = 7 cm and ∠POQ = 48°. 22 Use π = 7 , and give the answer correct to two decimal places. Calculate (a) the area, in cm2, of the shaded region. (b) the perimeter, in cm, of the shaded region. [6 marks] 5
Diagram 6 shows a composite solid comprises of a cylinder and a hemisphere.
Diagram 6 Given that the diameter of the hemisphere is 6 cm, calculate the volume, in cm3, of the solid. 22 (Use π = 7 ) [4 marks] 6
(a) Complete Table 8 in the answer space for the equation y = −2x2 + 4x − 8. [2 marks] (b) For this part of the question, use the graph paper provided. You may use a flexible curve rule. By using a scale of 2 cm to 1 unit of the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = −2x2 + 4x − 8 bagi −1 ≤ x ≤ 5. [4 marks] (c) From your graph, find (i) the value of y when x = 2.5, (ii) the value of x when y = −6.5, [2 marks]
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(d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation −2x2 + 9x − 2 = 0 for −1 ≤ x ≤ 5. State the values of x. [4 marks]
(a) x
−1
−0.5
y
−14 −10.5
0
1
2
3
−6
−14
4
4.5
5
−24 −30.5 −38
Table 8
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(a) Diagram 9 shows two points A and B on a Cartesian plane.
Diagram 9 4 Transformation V is the translation 1. Transformation W is an anticlockwise rotation of 90° about the centre (0, 0). (i) State the coordinates of the image of point A under transformation W. (ii) State the coordinates of the image of point B under the following transformation: (a) V2 (b) VW [7 marks]
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(b) Diagram 10 shows three quadrilaterals ABCD, JKMN and PQRS on a Cartesian plane.
Diagram 10 JKMN is the image of ABCD under transformation E. PQRS is the image of JKMN under transformation F. (i) Describe in full the transformation: (a) E (b) F (ii) Given that quadrilateral PQRS represents a region of area 46.8 cm2, calculate the area, in cm2, of the region represented by the shaded region. [5 marks] 8
(a) Table 3 shows the score obtained and the number of trials performed by a player in a game. Score 1 2 3 4 5 Number of trial × 4 18 3 12 15 score Table 3 (i) Calculate the total number of trials. (ii) Find the mode of score. [3 marks] (b) Table 3 shows the distribution of price of the books. Price (RM) Frequency 1−5 27 6 − 10 31 11 − 15 42 16 − 20 43 21 − 25 50 26 − 30 49 31 − 35 37 36 − 40 14 Table 3 (i) Construct a cumulative frequency table for the above data. [3 marks] (ii) (a) By using the scales of 2 cm to RM5 on the horizontal axis and 2 cm to 20 books on the vertical axis, draw an orgive for the data. [4 marks] (b) From the orgive, find the interquartile range. [2 marks]
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