2.5 Graph of Functions (II), SPM Paper 2 (Long Questions)


Question 5:
(a) The following table shows the corresponding values of x and y for the equation y = 24 x
  
x
–4
–3
–2
–1
1
1.5
2
3
4
y
–6
k
–12
–24
24
n
12
8
6
Calculate the value of k and n.
 
(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph of  y = 24 x  for –4 ≤ x ≤ 4.
 
(c) From your graph, find
(i) The value of when x = 3.5,
(ii) The value of when y = –17.
 
(d) Draw a suitable straight line on your graph to find the value of x which satisfy the equation 2x2 + 5= 24 for –4 ≤ x ≤ 4.
 
Solution:
(a)
y = 24 x when x = 3 , k = 24 3 = 8 when x = 1.5 , n = 24 1.5 = 16

(b)



(c)
(i) From the graph, when x = 3.5, y = 7
(ii) From the graph, when y = –17, x = –1.4

(d)
 

y = 24 x -------------- (1) 2 x 2 + 5 x = 24 ------ (2) ( 2 ) ÷ x , 2 x + 5 = 24 x -------- (3) ( 1 ) ( 3 ) , y ( 2 x + 5 ) = 0 y = 2 x + 5

The suitable straight line is y = 2x + 5.
Determine the x-coordinate of the point of intersection of the curve and the straight line = 2x + 5.
 
x
0
3
y = 2x + 5
5
11
From the graph, = 2.5

Question 6:
(a) Complete the table in the answer space for the equation y= 36 x   by writing down the values of y when x = 3 and x = 8.

(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 1cm to 1 unit on the x-axis and 1cm to 1 unit on the y-axis, draw the graph of y= 36 x  for 2 ≤ x ≤ 14.

(c) From your graph, find
(i) the value of y when x = 2.6,
(ii) the value of x when y = 4.

(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation 36 x +x14=0  for 2 ≤ x ≤ 14.

Answer:
x
2
2.4
3
4
6
8
10
12
14
y
18
15
9
6
3.6
3
2.6

Solution:
(a)
y= 36 x when x=3 y= 36 3 =12 when x=8 y= 36 8 =4.5

(b)


(c)
(i) From the graph, when x = 2.6, y = 13.6
(ii) From the graph, when y = 4, x = 9

(d)
y= 36 x  ........... ( 1 ) 0= 36 x +x14 ........... ( 2 ) ( 1 )( 2 ): y=x+14

The suitable straight line is y = x + 14.

x
2
12
y = x + 14
12
2
From the graph, x = 3.4, 10.6.

Leave a Reply

Your email address will not be published. Required fields are marked *