SPM 2025 Paper 2

Question 15:Sam, a lorry driver, transports x boxes of fruit A and y boxes of fruit B from a farm to a market. The average mass of a box of fruit A is 10 kg and a box of fruit B is 5 kg . The maximum load of the lorry is 70 boxes with … Read more

Question 13:Solution by scale drawing are not accepted.Diagram 13 shows a transparent glass block with a base ABCD on a horizontal plane. AFB is a coloured plane inside the block.It is given that the plane ABE is an isosceles triangle with an area of 9√2 cm2 and ∠BAE = 45o.(a) Show that AB = 6 … Read more

Question 11:Solutions by scale drawing and / or vector is not accepted.Diagram 11 shows the straight lines AEC and DB.It is given that AE : EC = 1 : 2.(a) Find(i) the coordinates of A,(ii) the value of p, if the area of Δ ABC is 48 unit2.[4 marks](b) Point F lies on the same Cartesian … Read more

Question 9:Diagram 9 shows the normal distribution graph of the time taken, in minutes, for a group of students to answer a test with X ~ N(32, 36).(i) A student is selected at random from the group. On the Diagram 9, shade the region that represents the probability of the student answering the test in … Read more

Question 7:Diagram 7.1 shows straight lines PA and AQ which intersect at the point A.It is given that PA is a tangent to the curve y = 8/x, such that h is a constant.(a)(i) Find the value of h.(ii) Hence, determine the coordinates of Q.[4 marks](b) Diagram 7.2 shows part of the curve y = … Read more

Question 5:Solutions by scale drawing are not accepted.Diagram 5 shows two points on a Cartesian plane.(a) $$ \text { Determine } \overrightarrow{A B} \text {. } $$[1 mark](b) $$ \text { Point } C \text { lies on the same Cartesian plane. } $$$$ \text { It is given that } \overrightarrow{O C}=(m+2) \underline{i}+12 \underline{j} … Read more

Question 3:Diagram 3 shows the relation of three sets.(a) Determine gf(2). [1 mark](b) Without finding g-1(x), determine f(x). [2 marks](c) From answer in (b),(i) find f-1(x), (ii) hence, determine the value of x if f-1g(x) = 4gf(2). [3 marks] Answer:(a) $$ \begin{aligned} g f(x) & =4-6 x \\ g f(2) & =4-6(2) \\ g f(2) & … Read more

Question 1:The graph of quadratic function f(x) = x2 – 2x + 6 – m intersects the x-axis at points A and B, such that m is a constant.(a) Find the range of values of m. [2 marks](b)(i) If m = 6, find the range of values of x for f(x) > 8 by using … Read more