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, F and G such that the universal set, ξ=EFG.
      On the diagrams in the answer space, shade
(a) E 'G' (b) ( EF )' G'
                                                                                                                [3 marks]
Answer
Answer and solution:
(a)

(b)


2.      Calculate the value of x and of y that satisfy the following simultaneous linear equations:
      x+6y=12 2 3 x+2y=6        
[4 marks]
Answer and solution:
x+6y=12 x=126y(1) 2 3 x+2y=6 ( ×3 )2x+6y=18 ( ÷2 )x+3y=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:
( 3x+2 ) 2 = 1 2 ( 4x+8 )4x 9 x 2 +12x+4=8 x 2 +16x x 2 4x+4=0 ( x2 )( x2 )=0 x=2

Perimeter of the square ABCD
= (3x + 2) × 4
= [3(2) + 2] × 4
= 32cm