SPM Additional Mathematics (Model Test Paper)


SPM Additional Mathematics (Model Test Paper)

Section B
[40 marks]
Answer any four questions from this section.


Question 7
(a) Prove that ( cosec xsecx secx cosec x ) 2 =1sin2x    
[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 ( cosec xsecx secx cosec x ) 2 = x π  for 0 ≤ x ≤ 2π.
State the number of soultions.
[7 marks]


Question 8
Diagram 4 shows part of a curve x = y2 + 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 360o about the y-axis.                                                                                                             [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 = hkx + 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 y-axis.
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 mlper bottle and variance of 1600 ml2.
            (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 AD DC =3.85 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 cm2, 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 cm2, 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’= 43.2o, 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, Cand 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]

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