SPM Additional Mathematics 2018, Paper 1 (Question 17 – 19)


Question 17 (4 marks):
( a ) Given P= log a Q, state the  conditions of a. ( b ) Given  log 3 y= 2 log xy 3 , express  y in terms of x.

Solution:
(a)
a > 0, a ≠ 1

(b)
log 3 y= 2 log xy 3 log xy y log xy 3 = 2 log xy 3 log xy y=2 y= ( xy ) 2 y= x 2 y 2 1 x 2 = y 2 y y= 1 x 2


Question 18 (3 marks):
Diagram 8 shows the graph y = a (xp)2 + q, where a, p and q are constants. The straight line y = –8 is the tangent to the curve at point H.

Diagram 8

(a) State the coordinates of H.
(b) Find the value of a.


Solution:
(a)
Coordinate x of H = 1+7 2 = 6 2 =3 Thus, coordinates of H=( 3,8 ).

(b)
y=a ( xp ) 2 +q y=a ( x3 ) 2 +( 8 ) y=a ( x3 ) 2 8 ……… ( 1 ) Substitute ( 7,0 ) into ( 1 ): 0=a ( 73 ) 2 8 0=16a8 16a=8 a= 1 2


Question 19 (3 marks):
Faizal has a rectangular plywood with a dimension 3x metre in length and 2x metre in width. He cuts part of the plywood into a square shape with sides of x metre to make a table surface.
Find the range of values of x if the remaining area of the plywood is at least (x2 + 4) metre2.

Solution:



Area of plywood – area of square ≥ (x2 + 4)
3x(2x) – x2x2 + 4
6x2x2x2 ≥ 4
4x2 ≥ 4
x2 – 1 ≥ 0
(x + 1)(x – 1) ≥ 0
x ≤ –1 or x ≥ 1
Thus, x ≥ 1 (length is > 0)




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