SPM Additional Mathematics (Model Test Paper)


SPM Additional Mathematics (Model Test Paper)

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

Question 9
Use graph paper to answer this question.
Table 1 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are related by the equation y = hkx + 1, where h and k are constants.

x
1
2
3
4
5
6
y
4.0
5.7
8.7
13.2
20.0
28.8
Table 1

(a)    Based on table 1, construct a table for the values (x + 1) and log y.                    [2 marks]
(b)   Plot log y against (x + 1), using a scale of 2 cm to 1 uint on the (x + 1) –axis and 2 cm to 0.2 unit on the log y-axis.
Hence, draw the line of best fit.                                                                           [3 marks]
(c)    Use your graph in 9(b) to find the value of
            (i)     h.
            (ii)   k.                                                                                                                     [5 marks]

Answer and Solution:
(a)
x + 1
2
3
4
5
6
7
log y
0.60
0.76
0.94
1.12
1.30
1.46

(b)



(c)
y = hkx + 1
log y = log h + (x + 1) log k
log y = log k (x + 1) + log h
   ↓         ↓        ↓          ↓
  Y        m         X          c

(i)
log h = y-intercept
log h = 0.26
h = 1.82

(ii)
logk=Gradient of the graph         = 1.460.60 72         =0.172 k=1.486