Onlinetuition.com SPM Additional Mathematics
Question 10 (10 marks):(a) Prove that 2 tan x cos2 x = sin 2x.(b) Hence, solve the equation 4 tan x cos2 x = 1 for 0 ≤ x ≤ 2π.(c)(i) Sketch the graph of y = sin 2x for 0 ≤ x ≤ 2π.(c)(ii) Hence, using the same axes, sketch a suitable straight line … Read more
Question 8 (10 marks):Diagram 5 shows a triangle ABC. The straight line AE intersects with the straight line BC at point D. Point V lies on the straight line AE. It is given that BD → = 1 3 BC → , AC → =6 x ˜ and AB → =9 y ˜ . ( a ) Express in terms of x ˜ … Read more
Question 6 (6 marks):Diagram 4 shows a cylindrical container with the length of 20 cm placed on the floor against the wall. W is the point on the edge of the base of the container. It is given that the distance of point W is 2 cm from the wall and 1 cm from the … Read more
Question 4 (7 marks):Diagram 2 shows part of a rectangular wall painted with green, G, blue, B and purple, P subsequently.The height of the wall is 2 m. The side length of the first coloured rectangle is 5 cm and the side length of each subsequent coloured rectangle increases by 3 cm.It is given that … Read more
Question 1 (5 marks):Solve the following simultaneous equations:x – 3y = 1,x2 + 3xy + 9y2 = 7Solution: x−3y=1……………….( 1 ) x 2 +3xy+9 y 2 =7……………….( 2 ) From ( 1 ):x=3y+1……………….( 3 ) Substitute ( 3 ) into ( 2 ): ( 3y+1 ) 2 +3( 3y+1 )y+9 y 2 =7 9 y 2 +6y+1+9 y 2 … Read more
Question 23 (4 marks):A set of data consists of 2, 3, 4, 5 and 6. Each number in the set is multiplied by m and added by n, where m and n are integers. It is given that the new mean is 17 and the new standard deviation is 4.242.Find the value of m and … Read more
Question 20 (4 marks):Table 1 shows the distribution of marks for 40 students in an Additional Mathematics test. The number of students for the class interval 40 – 59 is not stated.Table 1(a) State the modal class.(b) Puan Zainon, the subject teacher, intends to give a reward to the top ten students. Those students who … Read more
Question 17 (3 marks):It is given that ∫ 5 ( 2x+3 ) n dx= p ( 2x+3 ) 5 +c , where c, n and p are constants.Find the value of n and of p.Solution: ∫ 5 ( 2x+3 ) n dx= ∫ 5 ( 2x+3 ) −n dx = 5 ( 2x+3 ) −n+1 … Read more
Question 15 (4 marks):It is given that cos α = t where t is a constant and 0o ≤ α ≤ 90o.Express in terms of t(a) sin (180o + α),(b) sec 2α.Solution: (a) sin( 180 o +α ) =sin180cosα+cos180sinα =0−sinα =−sinα =− 1− t 2 (b) sec2α= 1 cos2α = 1 2 cos 2 α−1 … Read more
Question 11 (4 marks):The quadratic function f is defined by f(x) = x2 + 4x + h, where h is a constant.(a) Express f(x) in the form (x + m)2 + n, where m and n are constants.(b) Given the minimum value of f(x) is 8, find the value of h.Solution: (a)f(x) = x2 + … Read more