SMK
(P) Treacher Methodist, Taiping
Set 5 -- use as trial
Mathematics Paper
2
Form
5
2
hours 30 minutes
Instruction
: This question paper consists of 2 sections. Section
A and Section B. Answer all
questions in
Section
A and four
questions in Section B. Write all your answers clearly in the spaces
provided, Incomplete
working may cause
you loosing marks. The diagrams in the questions are not drawn to scale unless
stated
otherwise.
Section A (52 marks): Answer all
question in this section.
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1.
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The diagram shows a right prism. The base ABCD is a
horizontal rectangle. Right-angled triangle BCF is the uniform
cross-section of the prism. G is the midpoint of AD.
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Identify and calculate the angle
between the line FG and the plane CDEF.
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[3 marks]
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2.
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Form a general conclusion by induction for the following
series of numbers with a certain pattern.
9(0) + 5 = 5
9(1) + 5 = 14
9(2) + 5 = 23
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3.
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1000002 -
1112 =
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[4 marks]
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4.
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Sketch the graph for the quadratic function y = x2
- 25.
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[5 marks]
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5.
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Round off the following numbers correct to two significant
figures.
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(a) 556 =
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(b) 0.0137 =
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[4 marks]
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6.
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In the graph above, shade the region which satisfies the
inequalities
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y £ x -
4, 2y + x ³ 4 and x
< 5.
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[3 marks]
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7.
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The diagram shows a right prism with right-angled triangle PQR as its
uniform cross-section. Given that 2PQ = QR, calculate
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(a) the length of TR,
(b) the angle between the line PU and the horizontal base.
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[4 marks]
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8.
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Length of call
(minutes)
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Frequency
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3.1 - 3.4
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33
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3.5 - 3.8
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33
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3.9 - 4.2
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47
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4.3 - 4.6
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52
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The frequency table above shows the length of calls, in
minutes, of the outgoing telephone calls of a company in a certain week. Find
(a) the lower limit and upper limit of the last class interval,
(b) the lower boundary and upper boundary of the first class,
(c) the size of the class interval 3.5 -
3.8,
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(d) the modal class.
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[6 marks]
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9.
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In the diagram above, O is the centre of the circle UWV. TU
and TV are two tangents to the circle at point U and point V
respectively. Given that OU = 5 cm and TV = 9 cm, find
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(a) the value of y,
(b) the area of the shaded region.
(Use p = 3.142)
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[6 marks]
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10.
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The table above shows some values of variables p
and q such that p varies directly as the square of q.
(a) Find the relation between p and q.
(b) Calculate the value of
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11.
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The diagram above shows the distance-time graph for the journey of a car. The
graph AB represents the journey of the car from town A to town B.
The graph BC represents the journey of the car from town B to
town C.
(a) State the distance, in km, between town B and town C.
(b) Find the speed, in km h-1, of the car from town B
to town C.
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(c) Calculate the average speed, in km h-1,
of the car from town A to town C.
Section B (48 marks): Answer four question in this section.
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[6 marks]
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12.
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The ogive above shows the distribution of the prices, in Ringgit Malaysia,
of the books sold on a certain day by a bookstore. From the ogive,
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(a) determine
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(i)
(ii)
(iii)
(iv)
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the median,
the first quartile,
the third quartile,
the interquartile range.
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(b) find
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(i)
(ii)
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the total number of books which
cost between RM15 and RM39.
the number of books which cost less than RM23.
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[12 marks]
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13.
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(a)
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Complete the table in the answer space for the equation y
= 9 – x3 by writing down the values of y
when x = –1 and x = 2.
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[2 marks]
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(b)
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By using a scale of 1 cm to 1 unit on the x-axis
and 1 cm to 10 units on the y-axis, draw the graph of y = 9
– x3 for –3 ≤ x ≤ 2.5.
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[4 marks]
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(c)
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From your graph, find
(i) the value of y when x = 2,
(ii) the value of x when y = 30.
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[2 marks]
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(d)
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Draw a suitable straight line on your graph to find the
values of x which satisfy the equation x3 – 9x – 9 = 0 for –3 ≤ x ≤ 2.5.
State these values of x.
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[4 marks]
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Answer:
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(a)
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x
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–3
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–2.5
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–2
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–1
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0
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1
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2
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2.5
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y
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36
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24.63
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17
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9
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8
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-6.63
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(b)
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(c)
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(i) y = __________
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(ii) x = __________
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(d)
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x = __________, __________
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14.
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The diagram shows the quadrilaterals ABCD, EFGH and PQRS.
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(a)
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Transformation U is a reflection in the
line y = x. Transformation V is an
anticlockwise rotation of 90° about
the origin. State the coordinates of the image of
(i) Q under the transformation U,
(ii) G under the transformation VU.
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[4 marks]
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(b)
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Quadrilateral EFGH
is the image of quadrilateral ABCD under a transformation L
and quadrilateral PQRS is the image of quadrilateral EFGH
under a transformation M. Describe in full,
(i) transformation L,
(ii) transformation M.
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[4 marks]
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(c)
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Given that the area of
quadrilateral ABCD is 16 cm2.
Find the area of the quadrilateral PQRS.
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[4 marks]
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15.
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The following diagram shows four points, P, Q,
R and X, on the surface of the earth. P lies on
longitude of 74°W. QR is the
diameter of the parallel of latitude of 53°N.
X lies 5880 nautical miles due south of P.
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(a)
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Find the position of R.
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[3 marks]
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(b)
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Calculate the shortest distance, in nautical miles, from
Q to R, measured along the
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surface of the earth.
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[2 marks]
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(c)
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Find the latitude of X.
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[3 marks]
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(d)
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An aeroplane took off from P and flew due west to
R along the parallel of latitude
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with an average speed of 560
knots.
Calculate the time, in hours, taken for the flight.
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[4 marks]
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Answer:
(a)
(b)
(c)
(d)
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16.
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The diagram above shows a solid consisting of a right prism and a cuboid
joined at the plane EFGH. The trapezium FGLK is the uniform
cross-section of the prism. The base ABCD is on a horizontal plane.
The rectangle IJKL is an inclined plane. KF and LG are
vertical edges. Draw at full scale
(a) the plan of the solid,
(b) the elevation of the solid onto a vertical plane parallel to
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(i)
(ii)
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BC as viewed from X,
AB as viewed from Y.
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[12 marks]
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Answers:
1.
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tan ÐFGD
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=
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15
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8
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ÐFGD
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=
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61°55'
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2. Conclusion : All the numbers in
the series can be expressed by
9(n) + 5, n = 0, 1, 2,
...
3. 110012
4.
5. (a)
560 (b) 0.014
6.
7. (a) 13 cm
(b) 10°53'
8. (a) Lower limit = 4.3, upper limit = 4.6
(b) Lower boundary = 3.05, upper
boundary = 3.45
(c) 0.40
(d) 4.30 - 4.60
9. (a) 60.95°
(b) 18.402 cm2
10.
(b) (i) 10
(b) (ii) 32
11. (a) 350 km
(b) 23.33 km h-1
(c) 37.5 km h-1
12. (a) (i) RM25.3
(ii) RM21.9
(iii) RM28.7
(iv) RM6.8
(b) (i) 28
(ii) 8
13.
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(a)
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x
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–3
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–2.5
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–2
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–1
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0
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1
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2
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2.5
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y
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36
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24.63
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17
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10
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9
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8
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1
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-6.63
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x
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=
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–1,
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y
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=
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9 – (–1)3
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=
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10
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x
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=
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2,
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y
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=
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9 – (2)3
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=
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1
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(b)
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(c)
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(i)
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When
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x
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=
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2,
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y
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=
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1
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(ii)
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When
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y
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=
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30,
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x
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=
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–2.76
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(d)
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y
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=
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9 – x3
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....... (1)
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x3 – 9x – 9 = 0
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....... (2)
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Equation (1) + Equation (2)
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y
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=
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–9x
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From the graph,
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x
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=
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–1.2, –2.2
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14. (a) (i) Q'(1, 0)
(ii) G'(2,
3)
(b) (i) L is a
translation (4, -2)
(ii) M
is an enlargement with a scale factor of 2 about the centre (-10, 7).
(c) Area of PQRS = 22
´ 16 = 64 cm2
15.
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(a)
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Q is due east of P.
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Longitude of Q
Longitude of R
Latitude of R
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= 74° -
33°
= 41°W
= 180° - 41°
= 139°E
= 53°N
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Thus, the position of R is (53°N, 139°E).
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(b)
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The shortest distance from Q to R is the
distance measured along arc QNR via the North Pole.
ÐQOR = 180° - 2 ´
53° = 74°
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The shortest distance from Q
to R
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= 74 ´ 60
= 4440 nautical miles
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(c)
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P and X are two points on the same
meridian and the distance between P and X is 5880 nautical miles.
Let ÐPOX = q.
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Hence, q × 60
q
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= 5880
= 98°
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Thus, latitude of X = 98° - 53° = 45°S
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(d)
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Obtuse ÐPO1R
= 180° - 33° = 147°
Distance between P and R measured along the parallel of
latitude 53°N
= 147 ´ 60 ´ cos 53°
= 5308.01 nautical miles
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Time taken for the flight
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=
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5308.01
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= 9.48 hours
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560
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16. (a)
(b)
(c)
