SPM Additional Mathematics (Model Test Paper)


SPM Additional Mathematics (Model Test Paper)

Section C
[20 marks]
Answer any two questions from this section.

Question 12
Diagram 6 shows a quadrilateral KLMN.

Calculate
(a)KML, [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 ∠L’K’M’= 43.2o, which is different in shape to triangle KLM.
(i) Sketch the triangle K’L’M’,
(ii) State the size of ∠K’M’L’. [2 marks]


Answer and Solution:
(a)
sinKML 12.4 = sin 43.2 o 9.5 sinKML= sin 43.2 o 9.5 ×12.4 sinKML=0.8935 KML= 63.32 o  

(b)
∠KLM = 180o – 43.2o – 63.32o = 73.48o
KM2 = 9.52 + 12.42 – 2(9.5)(12.4) cos 73.48o
KM2 = 244.01 – 66.99
KM2 = 177.02
KM = 13.30 cm

(c)
KM2 = MN2+ KN2– 2(MN)(KN) cos ∠KNM
13.302 = 5.42 + 9.92– 2(5.4)(9.9) cos ∠KNM
176.89 = 127.17 – 106.92 cos ∠KNM
cosKNM= 127.17176.89 106.92 KNM= 117.71 o
 
Area of triangle KMN
= 1 2 ( 5.4 )( 9.9 )sin 117.71 o =23.66 c m 2
  
(d)(i)


(d)(ii)
∠K’M’L’ = 180o – 63.32o = 116.68o


Question 13
Table 2 shows the prices, the price indices and the proportion of four materials, ABC 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]

Answer and Solution:

(a)
I= P 1 P 0 ×100 I= P 2014 P 2011 ×100 120= 7.20 x ×100 x=6.00 y= 5.50 5.00 ×100 y=110

(b)
Composite index for bag in the year 2014 based on the year 2011, I ¯ = IW W I ¯ = ( 120 )( 7 )+( 115 )( 3 )+( 110 )( 6 )+( 125 )( 8 ) 7+3+6+8 I ¯ = 840+345+660+1000 24 I ¯ =118.54

(c)
I ¯ = P 2014 P 2011 ×100 118.54= 115 P 2011 ×100 P 2011 =97.01

(d)
< Composite index for the bag in the year 2015 based on the year 2011, I ¯ = IW W = ( 120×0.9 )( 7 )+( 115×1.05 )( 3 )+( 110×1.05 )( 6 )+1000 24 = 756+362.25+693+1000 24 =117.14


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