SPM 2023 Paper 2

Question 5: It is given that (2x + 3) is one of the factors of f(x) = x (5 – 2x) + m, such that m is a constant. (a) Find the value of m. [3 marks](b) By using the method of completing the square, express f(x) in the form, f(x) = a(x – h)2 + … Read more

Question4:(a) Diagram 2 shows the graph of y = tan⁡x + c for 0 ⩽ x ⩽ p, such that c and p are constants.State the value of c and of p. [2 marks](b) For the following questions, give your answer in the simplest fraction form in terms of π radians.(i) Solve the equation 2 … Read more

Question 3:A closed cylindrical tank has a height of h metres and a radius of r metres. The tank can be fully filled with 125/4 π m3 of water. [Use π = 3.142 ](a) Find that the total surface area, in m2, of the tank in terms of π and r. [3 marks](b) The tank … Read more

Question 1: Solve the following simultaneous equations: $$ \begin{gathered} 2 p-q-r=6 \\ p+2 q-4 r=8 \\ 3 p+q-r=2 \end{gathered} $$ [5 marks] Solution:$$ \begin{aligned} &\begin{aligned} & 2 p-q-r=6 \ldots(1)\\ & p+2 q-4 r=8 \ldots(2) \\ & 3 p+q-r=2 \ldots .(3) \end{aligned}\\ &\text { From (2), } p=8-2 q+4 r \ldots \text { (4) } \end{aligned} … Read more