SPM Mathematics (Model Test Paper)


SPM Mathematics (Model Test Paper)
 
Section A
 (52 marks)
Answer all questions in this section.


1. The Venn diagram in the answer space shows sets E, and G such that the universal set, ξ = E F G .
  On the diagrams in the answer space, shade
( a ) E ' G ' ( b ) ( E F ) ' G '
[3 marks]
Answer
Answer and solution:
(a)
(b)


2.   Calculate the value of x and of that satisfy the following simultaneous linear equations:
  x + 6 y = 12 2 3 x + 2 y = 6
[4 marks]
Answer and solution:
x + 6 y = 12 x = 12 6 y ( 1 ) 2 3 x + 2 y = 6 ( × 3 ) 2 x + 6 y = 18 ( ÷ 2 ) x + 3 y = 9 ( 2 )
 
Substitute (1) into (2),
12 – 6y + 3y= 9
–3y = –3
y= 1
Substitute y = 1 into (1),
x = 12 – 6(1)
x = 6 


3.    
   Diagram 1  

Diagram 1 shows a square ABCD and a right-angled triangle PQR with equal area.
Based on the information, find the value of x.
Hence, find the perimeter, in cm, of the square ABCD. [4 marks]  

Answer and solution:

( 3 x + 2 ) 2 = 1 2 ( 4 x + 8 ) 4 x 9 x 2 + 12 x + 4 = 8 x 2 + 16 x x 2 4 x + 4 = 0 ( x 2 ) ( x 2 ) = 0 x = 2
Perimeter of the square ABCD
= (3x + 2) × 4
= [3(2) + 2] × 4
= 32cm

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