SPM Trial Paper 2021 (Selangor) – Paper 1

Question 15:Diagram 6 shows a triangle ABC. Given that the area of triangle ABC is 21 cm2 and ∠BAC is obtuse angle.Diagram 6Find(a) ∠BAC, [3 marks](b) the length of BC, in cm, [2 marks](c) the length of the perpendicular line from A to BC. [3 marks] Solution:(a) Area of Δ= 1 2 absinC 21= 1 2 ( … Read more

Question 14:(a) Solve the equation 3 sin⁡ 2x = 4 cos⁡x for 0∘ ≤ x ≤ 360∘. [4 marks](b) Solve the simultaneous equations 2 cos⁡ (x – y) = √3 and 2 cos ⁡(x + y) = 1, where x and y are both acute angles. [4 marks] Solution:(a) 3sin2x=4cosx 3(2sinxcosx)=4cosx 6sinxcosx=4cosx 6sinxcosx−4cosx=0 2cosx( 3sinx−2 … Read more

Question 12:(a) Find the number of ways to arrange each word SAKU and SAKA if no repetition is allowed. Are the number of arrangement that formed are the same?Explain. [3 marks](b) Two boats are used to cross a river with each boat only able to carry 7 passengers. There are 9 adults and 4 children … Read more

Question 10:(a) Given the gradient of the tangent to the curve y = x2 (3 + px) is -3 when x = -1.Find the value of p. [2 marks](b) Volume, V cm3, of a solid is given by V=8π r 2 + 2 3 π r 3 , r is the radius. Find the approximate … Read more

Question 9:Diagram 4 shows a circle ADBC, with centre O and diameter 12 cm while sector ADC with the centre A and radius AD = 10 cm.Diagram 4By using π = 3.142,find(a) ∠BAC in radians, (2 marks)(b) area, in cm2, of the shaded region. (3 marks) Solution:(a) By using the cosine rule, 6 2 = 10 2 + 6 … Read more

Question 8: Diagram 3 shows a parallelogram OABC. Point P is the midpoint of AB and the  ratio of  QP → : OP → =2:5. Given that  OA → =3 i ˜ +4 j ˜  and  OC → =6 i ˜ + j ˜ Diagram 3 Express in the terms of  i ˜  and  j ˜ , (a)  OP →  (1 mark) (b)  AQ →  (3 marks) Solution:(a) OP → = OA → + AP →  =3 … Read more

Question 7:Solutions by scale drawing is not accepted.Diagram 2Diagram 2 shows a trapezium ABCDE where BC is the height of the trapezium ABCDE.Find(a) the value of k, (2 marks)(b) the coordinates of point C. (4 marks) Solution:(a) m AB = m ED 4−3 7−4 = 0−( −1 ) k−0 1 3 = 1 k k=3 … Read more

Question 5:(a) Given a geometric progression with terms a, ar, ar2, ar3, … , arn-2, arn-1 and the sum of first n terms is Sn. Derive the formula for the sum of the first n terms, Sn for the geometric progression when |r| < 1. [3 marks](b) Hence, find the value of n for which the … Read more

Question 3:(a) Find the value of p and q for the equation (√2 – 1)(p + q√2) = 5 – √8. [3 marks](b) Find the value of p which satisfies the following equation: 3 log p pq + 3 log q pq +2=5p [3 marks] Solution:(a) ( 2 −1 )( p+q 2 )=5− 8 p+q … Read more

Question 1: Given g( x )= 2x−5 3x−p , x≠q (a)(i) Express p in terms of q and find g-1 (x) in term of p. (a)(ii)   Given  g n−1 ( x )= px−5 3x−2 , x≠k , determine the value of n by comparing the g-1 (x) above with the given gn-1 (x). Next, find the value … Read more