SPM Additional Mathematics (Model Test Paper)
Section B
[40 marks]
Answer any four questions from this section.
Question 7
(a) $\text{Provethat}{\left(\frac{\mathrm{cos}ec\text{}x\mathrm{sec}x}{\mathrm{sec}x\text{}\mathrm{cos}ec\text{}x}\right)}^{2}=1\mathrm{sin}2x$
[3 marks]
(b)(i) Sketch the graph
of y = 1 – sin2x for 0 ≤ x ≤ 2π.
(b)(ii) Hence, using the same axes, sketch a suitable straight line to find the number of solutions to the equation $2{\left(\frac{\mathrm{cos}ec\text{}x\mathrm{sec}x}{\mathrm{sec}x\text{}\mathrm{cos}ec\text{}x}\right)}^{2}=\frac{x}{\pi}$ for 0 ≤ x ≤ 2π.
State the number of soultions.
[7 marks]
Question 8
Diagram 4 shows part of a curve x = y^{2} + 2.
The gradient of a straight line QR is
–1.
Find
(a) the
equation of PQ, [2
marks]
(b) the
area of shaded region, [4
marks]
(c) the
volume of revolution, in terms of π, when the shaded region is rotated through
360^{o} about the yaxis. [4
marks]
Question 9
Use graph paper to answer this question.
Table 1 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are related by
the equation y = hk^{x}^{ + 1}, where h and k are constants.
x

1

2

3

4

5

6

y

4.0

5.7

8.7

13.2

20.0

28.8

Table
1
(a) Based
on table 1, construct a table for the values (x + 1) and log y. [2 marks]
(b) Plot
log y against (x + 1), using a scale of 2 cm to 1 uint on the (x + 1) –axis and 2 cm to 0.2 unit on the
log yaxis.
Hence,
draw the line of best fit. [3
marks]
(c) Use
your graph in 9(b) to find the value of
(i) h.
(ii) k. [5 marks]
Question 10
(a) 20%
of the students in SMK Bukit Bintang are cycling to school. If 9 pupils from
the school are chosen at random, calculate the probability that
(i) exactly
3 of them are cycling to school,
(ii) at
least a student is cycling to school.
[4
marks]
(b) The
volume of 800 bottles of fresh milk produced by a factory follows a normal
distribution with a mean of 520 ml
per bottle and variance of 1600 ml^{2}.
(i) Find
the probability that a bottle of fresh milk chosen in random has a volume of
less than 515 ml.
(ii) If
480 bottles out of 800 bottles of the fresh milk have volume greater that k ml, find the value of k.
[6
marks]
Question 11
In diagram 5, AOBDE,
is a semicircle with centre O and has
radius of 5cm. ABC is a right angle
triangle.
It is given that $\frac{AD}{DC}=3.85\text{and}DC=2.31cm.$
[Use π = 3.142]
Calculate
(a) the
value of θ, in radians, [2
marks]
(b) the
perimeter, in cm, of the segment ADE,
[3
marks]
(c) the
area, in cm^{2}, of the shaded region BCDF. [5
marks]
SPM 2016 Additional Mathematics (Forecast Paper)
Section C
[20 marks]
Answer any two questions from this section.
Question 12
Diagram 6 shows a quadrilateral KLMN.
Calculate
(a) ÐKML,
[2
marks]
(b) the
length, in cm, of KM, [3
marks]
(c) area,
in cm^{2}, of triangle KMN, [3
marks]
(d) a
triangle K’L’M’ has the same
measurements as those given for triangle KLM,
that is K’L’= 12.4 cm, L’M’= 9.5 cm and ÐL’K’M’
= 43.2^{o}, which is different in shape to triangle KLM.
(i) Sketch
the triangle K’L’M’,
(ii) State
the size of ÐK’M’L’.
[2 marks]
Question 13
Table 2 shows the prices, the price indices and the
proportion of four materials, A, B, C
and D used in the production of a
type of bag.
Material

Price (RM) for the year

Price index in the year 2014 based on
the year 2011

Proportion


2011

2014


A

x

7.20

120

7

B

8.00

9.20

115

3

C

5.00

5.50

y

6

D

3.00

3.75

125

8

Table
2
(a) Calculate
the value of x and of y. [2
Marks]
(b) Find
the composite index for the bag in the year 2014 based on the year 2011. [3
Marks]
(c) Given
the cost for the production of the bag in the year 2014 is RM 115, find the
corresponding cost in the year 2011. [2
Marks]
(d) From
the year 2014 to year 2015, the price indices of material B and C increase by 5%,
material A decrease by 10% and material
D remains unchanged.
Calculate
the composite index in the year 2015 based on the year 2011. [3 Marks]