SPM 2022 Paper 1

Question 8: (a) Diagram 3 shows the standard normal distribution graph.On Diagram 3, shade the region(s) to represent P(|Z| ≥ a). [1 mark](b) Diagram 4 shows the standard normal distribution graph which is divided into three equal parts.State(i) the vakue of k,(ii) the mode for part A.[2 marks] Answer: (a) (b)(i) k = 0.431(b)(ii) Mode for … Read more

Question 13:(a) Diagram 9 shows angle θ on a Cartesian plane.(i) On Diagram 9, label the position of θ.(ii) State the value of tan (-θ) in terms of p and q. [2 marks](b) Solve the equation 2 cos x = √3 cot x for 0o ≤ x ≤ 360o. [3 marks](c) $$ \text { It … Read more

Question 11:Diagram 7 shows triangle ABC.$$ \text { It is given that } B C=(2+x) \mathrm{cm}, A D^2=1+\sqrt{2} \text { and } A B D \text { is a straight line. } $$$$ \text { Show that } x=\frac{1+5 \sqrt{2}}{49} \mathrm{~cm} \text {. } $$[5 marks] Answer:$$ \begin{aligned} B D & =\sqrt{(2+x)^2-(2-x)^2} \\ & =\sqrt{8 … Read more

Question 5:$$ \text { The coordinates of points } P \text { and } Q \text { are }(2,3) \text { and }(q, 2 q) \text { respectively. } $$$$ \text { Given that } \overrightarrow{P Q} \text { is a unit vector. } $$$$ \text { Using the vectors’s triangle law, find the possible … Read more

Question 1:Diagram 1 shows the mapping of function f, such that p is a constant.(a) State the object which has no image. [1 mark](b) Find the value of p. [2 marks] Answer:(a) x = 6(b) $$ \begin{aligned} \frac{3 p}{6-2} & =9 \\ 3 p & =36 \\ p & =12 \end{aligned} $$ Question 2: (a) Express … Read more