SPM Mathematics 2023, Paper 2 (Question 3 & 4)

Question 3:
Diagram 2 shows the straight line PQ and point T on a Cartesian plane.

Find the equation of the straight line which is parallel to PQ and passes through point T.
[3 marks]

Solution:
Same gradient for parallel line.
$$\begin{aligned} &\begin{aligned} & \text { Gradient of } \mathrm{PQ}=\frac{4-2}{3-0} \\ & =\frac{2}{3} \\ & y=m x+c, \quad T(1,-1) \\ & -1=\left(\frac{2}{3}\right)(1)+c \\ & c=-\frac{5}{3} \end{aligned}\\ &\text { Equation of the straight line, } \quad y=\frac{2}{3} x-\frac{5}{3} \end{aligned}$$

Question 4:
(a) Diagram 3 shows a partially completed deductive argument.


Complete this argument by writing an appropriate conclusion.
[1 mark]

(b) Encik Jamal is saving to go on a holiday with his friends. Table 2 shows the amount of money in his savings account at the end of each month.


(i) By using induction, write a conclusion for the amount of money in the savings account RMy at the end of month x.    
[2 marks]

(ii) The estimated cost of Encik Jamal’s holiday is RM3 500. Using your answer to b(i), calculate the number of months it will take Encik Jamal to save this amount.
[2 marks]

Solution:
(a) Conclusion : Apple vinegar has a pH value < 7.

(b)(i) 

$$\begin{aligned} 915-600 & =315 \\ 600-315 & =285 \\ y & =315 x+285, \quad x=1,2,3,4,5, \ldots \end{aligned}$$

(b)(ii)
$$\begin{aligned} y & =315 x+285 \\ 3500 & =315 x+285 \\ 315 x & =3500-285 \\ x & =10.21 \\ x & =11 \text { months } \end{aligned}$$