**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*=*hk*^{x}^{ + 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)

(ii)

(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*=

*hk*

^{x}^{ + 1}

log

*y =*log*h*+ (*x*+ 1) log*k*log

*y =*log*k*(*x*+ 1) + log*h*Y = log

*y**m = log k*

*X =*(*x*+ 1)

c = log hc = log h

**(i)**

log

*h*=*y*-interceptlog

*h*= 0.26

*h***= 1.82**

**(ii)**

$\begin{array}{l}\mathrm{log}k=\text{Gradient of the graph}\\ \text{}=\frac{1.46-0.60}{7-2}\\ \text{}=0.172\\ k=1.486\end{array}$