SPM Mathematics (Model Test Paper)



SPM Mathematics (Model Test Paper)

Section B
 [48 marks]
Answer any four questions from this section.

12 (a) Complete Table 1 in the answer space for the equation y = 2x2 − 8x + 1.
 [2 marks]

(b) For this part of the question, use the graph paper provided. You may use a flexible curve rule. By using a scale of 2 cm to 1 unit of the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 2x2 − 8x + 1 bagi 0 ≤ x ≤ 6.  [4 marks]                                                                                                                                        
(c) From your graph, find
(i)      the value of y when x = 3,   
             (ii)   the value of x when y = 2,                                                                                  [2 marks]

(d)   Draw a suitable straight line on your graph to find all the values of x which satisfy the equation 2x2 − 4x − 11 = 0 for 0 ≤ x ≤ 6. State the values of x.                               [4 marks]
    
Answer:
(a)                                           
x
0
0.5
1
2
3
4
5
5.5
6
y
1
−2.5
−5
−7
−5
1


25

Table 1
Answer and solution:
(a)
x
5
5.5
y
11
17.5

(b)

(c)(i)
From the graph, when x = 3, y = −5

(c)(ii)
From the graph, when y = 2, x = 4.15

(d)
y = 2x2 − 8x + 1 ---- (1)
2x2 − 4x − 11 = 0
0 = 2x2 − 4x – 11 ---- (2)
(1)   minus (2),
The suitable straight line is y = −4x + 12

x
0
2
y
12
4

From the graph, x = 3.6