Onlinetuition.com SPM Additional Mathematics
Question 5:Table 1 shows the deviation from the mean mark scored by Nora in a monthly test. The deviation from the mean mark for Sejarah has been left out.Table 1It is given that her mean mark for all the 9 subjects is 60.Find(a) the median mark, [4 marks](b) the standard deviation. [3 marks]Solution:(a) Mean mark=60 450+m … Read more
Question 4:Diagram 2 shows the curve y = 4x – x2 and tangent to the curve at point Q passes point P.Diagram 2(a) Show that h = 3. [4 marks](b) Calculate the area of the shaded region. [4 marks]Solution:(a) y=4x− x 2 dy dx =4−2x At point Q( h, 4h− h 2 ) dy dx =4−2h Equation of tangent at Q y− … Read more
Question 3:Diagram 1 shows a sector POA with centre O.It is given that the length of arc PB is 2.56 cm. [Use π = 3.142]Calculate(a) ∠ POB in radians, [2 marks](b) the area, in cm2, of the shaded region. [4 marks]Solution:(a) s=rθ 2.56=10θ θ=0.256 radian (b) Area of OBP = 1 2 r 2 θ = 1 2 … Read more
Question 2:Express 2n + 2 – 2n + 1 + 2n – 1 in the form p(2n – 1), where p is a constant.Hence, solve the equation 8(2n + 2 – 2n + 1 + 2n – 1) = 5( 2 n 2 ). [6 marks]Solution: 2 n+2 − 2 n+1 + 2 n−1 =( … Read more
Question 1:Solve the simultaneous equations x + 2y = 1 and 3 x − 2 y =5. Give you answer correct to three decimal places. [5 marks]Solution: x+2y=1 x=1−2y ………… (1) 3 x − 2 y =5 × xy, 3y−2x=5xy ………… (2) Substitute (1) into (2): 3y−2( 1−2y )=5y( 1−2y ) 3y−2+4y=5y−10 y 2 10 y 2 +2y−2=0 5 y 2 +y−1=0 a=5, b=1, c=−1 y= … Read more
Question 13 (10 marks):Table 2 shows the information related to four ingredients, J, K, L and M, used in the production of a type of energy drinks.The production cost for this energy drinks is RM47600 in the year 2017.(a) If the price of ingredient K in the year 2013 is RM4.20, find its price in … Read more
Question 10 (10 marks):Diagram 7 shows the straight line 4y = x – 2 touches the curve x = y2 + 6 at point P. Find(a) the coordinates of P,(b) the area of the shaded region,(c) the volume of revolution, in terms of π, when the region bounded by the curve and the straight line … Read more
Question 7 (10 marks): ( a ) Prove sin( 3x+ π 6 )−sin( 3x− π 6 )=cos3x ( b ) Hence, ( i ) solve the equation sin( 3x 2 + π 6 )−sin( 3x 2 − π 6 )= 1 2 for 0≤x≤2π and give your answer in the simplest fraction form in terms of π radian. ( ii ) sketch the graph of y=sin( 3x+ π 6 )−sin( 3x− π 6 )− 1 2 for 0≤x≤π. Solution: ( a ) Left hand side, … Read more
Question 5 (7 marks):Mathematics Society of SMK Mulia organized a competition to design a logo for the society.Diagram 3 shows the circular logo designed by Adrian. The three blue coloured regions are congruent. It is given that the perimeter of the blue coloured region is 20π cm.[Use π = 3.142]Find(a) the radius, in cm, of … Read more
Question 3 (6 marks):Solution by scale drawing is not accepted.Diagram 1 shows a triangle OCD.Diagram 1(a) Given the area of triangle OCD is 30 units2, find the value of h.(b) Point Q (2, 4) lies on the straight line CD.(i) Find CQ : QD.(ii) Point P moves such that PD = 2 PQ. Find … Read more