SPM 2023 Paper 1

Question 15:Table 1 shows the values of x for the equation $$y+3 \sin \frac{3}{2} x=1$$ (a) Complete the values of y in Table 1.[2 marks](b) For this part of the question, use the graph paper provided on page 96 . You may use a flexible curve rule.Using a scale of 3 cm to π/3 … Read more

Question 14:(a) It is given that $$f(x)=2 x-5 \text { and } g f(x)=\frac{4}{2 x-5}, x \neq h$$ State the value of h. [1 mark](b) Find the value of x when f(x) maps onto itself.  [2 marks](c) Find(i)  g(x), (ii) g(4x-3)(x).[5 marks] Solution:(a)$$ \begin{aligned} g f(x) & =\frac{4}{2 x-5} \\ 2 x-5 & \neq … Read more

Question 13:(a) Express y in terms of x and / or e of(i) 6 ln⁡ y = √5 ln ⁡x,(ii) ln ⁡(x + y2 ) – 3 = 0.[ 4 marks](b) Diagram 9 shows the length of the chord BC at semicircle ABCD.It is given that the length of AD is (x + 2√2)cm and … Read more

Question 12:A farm produce strawberries. The masses of the strawberries, x grams, are normally distributed such that X∼ N[20, (0.5)2].(a) State the mean and the variance of the distribution. [1 mark](b) Diagram 8 shows the standard normal distribution graph for mass of the strawberries. The shaded region represents the probability that the mass of the … Read more

Question 10:Solutions using other then calculus are not accepted.(a) On Sunday, Mus bought a number of spherical balls with radius 5 cm . Some of the balls will be arranged in a single line on a rack with length 2.5 m . On Monday, the volume of each ball decreased uniformly by 20π cm3.Determine the … Read more

Question 8:Listing out all terms of the sequence is not accepted.A cylindrical wooden block is cut into pieces for decoration purposes. Diagram 7 shows the first three pieces that have been cut and the remaining part.The angles of the sectors increase by a constant amount for each subsequent piece. A total of n pieces can … Read more

Question 6: $$\text { (a) Diagram } 5 \text { shows the graph of the function } f(x)=|x-3|+1 \text { for domain }-2 \leqslant x \leqslant 7 \text {. }$$ $$\text { Find the value of the other object of } h \text {. [2 marks]}$$ $$ \text { (b) Given that the functions … Read more

Question 4: $$\text { Diagram } 3 \text { shows point A lies on the circumference of a unit circle. }$$ Express in terms of p and / or q of.(a) tan β,(b) cot (180o + β)[2 marks] Solution:(a)$$ \begin{aligned} \tan \beta & =\frac{\text { Opposite }}{\text { Adjacent }}(\mathrm{TOA}) \\ \tan \beta & =\frac{p}{q} … Read more

Question 1:It is given that four consecutive terms of a sequence are 50, 45, x and y. State the value of(a) y – x if the sequence is an arithmetic progression,(b) y/x if the sequence is a geometric progression.[2 marks] Solution: (a) $$\begin{aligned} & y-x=45-50 \\ & y-x=-5 \end{aligned}$$ (b)$$ \begin{aligned} & \frac{y}{x}=\frac{45}{50} \\ & \frac{y}{x}=\frac{9}{10} … Read more