Onlinetuition.com SPM Additional Mathematics
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
Question 15:Table 3 shows information related to five cake ingredients J, K, L, M and N used by a baker in his business.Table 3 The composite index for the cost of making the cakes in the year 2020 based on the year 2016 is 136.(a)(i) Find the value of x and of y.(ii) Calculate the … Read more
Question 13:Solution by scale drawing is not accepted.Diagram 6 shows a quadrilateral ABCD such that AC and BD are straight lines.Diagram 6It is given that the area of ∆ABC = 6 cm2 and ∠ABC is obtuse.(a) Find(i) ∠ABC,(ii) the length, in cm, of AC,(iii) ∠BAC [7 marks](b) Given BD = 7.3 cm and ∠BCD … Read more
Question 11:Use a graph paper to answer this question.Table 2 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are related by the equation y= a x b , where a and b are constants.Table 2(a) Based on Table 2, construct a table for the values … Read more
Question 10: ( a )(i) Prove tan A 2 = 1−cosA sinA . ( ii ) Hence, without using calculator, find the value of tan15 o . State your answer in the form p− q , where p and q are constants. (b)( i ) Sketch the graph of y=− 3 2 sinA for 0≤A≤2π. ( ii ) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation ( cot A 2 )( 1−cosA )=− A 2π for 0≤A≤2π. State the number solutions. Solution:(a)(i) Right hand side, 1−cosA sinA = 2 sin 2 A 2 2sin A 2 … Read more
Question 9:Solution by scale drawing is not accepted.Diagram 5 shows the path of a moving point P(x, y). P always moves at a constant distance from point A.Diagram 5B(–1, –2) and R(–5, q) lie on path of point P. The straight line BC is a tangent to the path andintersects the x-axis at point C.Find(a) … Read more
Question 8:Diagram 4 shows a dart’s target board at a dart game booth in a funfair.Diagram 4The booth offers 3 darts per game. The customers have to pay RM5 to play a game. A toy bear will be given to customers who are able to hit the bullseye for the three darts’ throws in a … Read more
Quesion 7:A metal solid is formed by combining a cone and a cylinder with common radius, r cm. The totalsurface area of the solid, A cm2, is given by A=2π( 18 r + r 2 3 ). (a)(i) The solid expands when heated. It is given that the surface area of the solid changes at … Read more