This question paper consists of 3 sections: A, B and C. Answer all questions in Section A, 4 questions from Section B and 2 questions from Section C. Non-programmable scientific calculator is allowed.
SectionA
[40 marks]
Answer all questions in this section
1.A student found a torn paper that has a mathematic
equation on it as shown in figure 1.
Examine the equation and try to solve for the value
of a and of b.
[5 marks]
2.Find the range of values of p such that a linear line will not intersect the curve.
[6 marks]
3.Diagram 1 shows a circular sector OAB with centre O and
OAN is a right-angled triangle. Find
a)the length of the arc AB
b)the area of the sector OAB
c)the perimeter of the shaded region.
Diagram 1
[8 marks]
4.A piece of rope shown in figure 2 is 227.5 cm long,
and is cut into 25 pieces that form an arithmetic
progression. Given that the total length of the first
three shortest length of ropes is 4.2 cm, find
a)the difference in length between any two adjacent length of rope
b)the length of the 10th piece from the shortest length of rope.
[7 marks]
5.A curve has a gradient function, where m is a constant. If the stationary point of the curve is (2, 6), find
a)the value of m[3 marks]
b)the equation of the curve.[3 marks]
6.Table 1 shows a frequency distribution of mangoes in weight collected from 60 mango trees in a nearby farm.
a)Calculate the standard deviation of the frequency distribution[4 marks]
b)Without drawing an ogive, determine the median weight of mangoes [4 marks]
in the distribution.
Section B
[40 marks]
Answer four questions from this section
7.Table 2 shows a set of data obtained involving two variables from an experiment. It is known
that x and y are related by an equation and p and q are constants
a)Plot a graph of [4 marks]
b)From the graph, find
i)the values of p and of q
ii)the value of y when x = 1.3
iii)the value of x when y = 7[6 marks]
8.Diagram 2 shows a circle with centre O and another circle with a diameter OQ and centre P. QT is a tangent to both the circles and ORST is a straight line. Given that OP = 3 cm and the length of arc QR is . Find
a) in terms of ,[2 marks]
b)the area of sector QOS,[3 marks]
c)the area of the shaded region.[5 marks]
9.
a)Diagram 3 shows a polygon formed by bending a 150 cm long wire.
i)Show that the area of the polygon,
ii)Find the maximum area for this polygon[5 marks]
b)Given that find the value of at . Hence, find
i)the small change of x, that causes y to increase from 5.25 unit to 5.28 unit,
ii)the rate of change of y at the time when if the rate of change of x is
0.8 unit per seconds [5 marks]
10.
Diagram 4 shows a curve, two straight lines which is perpendicular to the x-axis and.
a)Evaluate the value of a and of b,[2 marks]
b)Determine the roots of the quadratic equation[1 mark]
c)Determine the axis of symmetry of the quadratic equation and hence[1 mark]
d)Calculate the area of the shaded region.[6 marks]
- P (a,b) is a point on the line passing through A(– 1, –2), B(3,0) and PA =
a)Show that a – 2b = 3, and [6 marks]
b)Find the values of a and b.[4 marks]
SECTION C
[20 marks]
Answer two questions from this section.
12.a)A triangle PQR have sides PQ = 4 cm, QR = 5 cm, and PR = 7 cm. Calculate
i)the biggest angle for the triangle,[2 marks]
ii)perpendicular distance Q to the side PR[3 marks]
b)Diagram 5 shows a triangle ABC.
i)Find the [3 marks] ii) If the length of AC and are fixed
whereas the length of AB is reduced,
calculate the length of AB such that
only one triangle ABC can be formed.[2 marks]
13.a)
Table 3 shows the price indexes of items A, B, C and D in 2014 based on year 2000 and their respective weightages. Given that the price of item C in the year 2000 is RM 40 and increases to RM 52 in 2014. If year 2000 is the base year, evaluate the value of m. Hence, find the value of n if the composite index for the year 2014 based on year 2000 is 120 [5 marks]
b)An equation where h and k are constants. A straight line is obtained by plotting a graph of verses x. If the straight line passes
through (0, 3) and (2, 7), find the value of h and of k.[5 marks]
14.a)Given that . Find the value of [4 marks]
b)If . Find, in similar form [6 marks]
15.Diagram 6 shows a curve and a straight line
i)Find the volume generated if the shaded regionis revolved 360o about the x-axis [4 marks]
ii)Find the volume generated if the shaded regionis revolved 360o about the y-axis [4 marks]
iii)The difference in value between the two volumes.[2 marks]
END OF QUESTIONS
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