Onlinetuition.com SPM Mathematics
Question 7:Diagram 3 shows the straight lines PR, SQ, QT and ST drawn on a Cartesian plane. It is given that PR and ST are parallel and SQ = QT – 10 units.Diagram 3Find the equation of the straight line PR. [4 marks]Solution: Q=( x, 8 ) SQ=10 [ x−( −2 ) ] 2 + 8 … Read more
Question 6:(a) State whether the following sentence is a statement or not a statement. [1 mark] 2 x 2 +3y (b) Write down two implications based on the following statement: [2 marks] Matrix ( a b c d ) does not have the inverse if and only if ad−bc=0. (c) Make a general conclusion by induction for the sequence of the numbers 3, 38, 133, 318 which follows … Read more
Question 4:Diagram 2 in the answer space shows a rectangle door with the height of 2.5 m and the width of 1 m. The distance between P and Q is 1.2 m.(a) On Diagram 2 in the answer space, mark the angle between the door and the wall. [1 mark](b) Hence, calculate the angle of … Read more
Question 2:Radziah bought (2x – 17) dictionaries with the price of RM12x each. She paid RM4 104 for all the dictionaries.Calculate the number of dictionaries that she bought. [4 marks]Solution:Number of dictionaries = 2x – 17Total purchase = 410412x(2x – 17) = 4104x(2x – 17) = 3422×2 – 17x – 342 = 0(2x + 19)(x … Read more
Question 1:(a)Diagram 1 is a Venn diagram showing set W and set X, such that the universal set, ξ = W U X.Diagram 1State the relation between set W and set X. [1 mark].(b) It is given that set P = {x : x is a multiple of set 4}, set Q = {x : … Read more
Question 15 (12 marks):You are not allowed to use graph paper to answer this question.(a) Diagram 11.1 shows a solid prism with a rectangular base JKLM on a horizontal plane. The surface MQRSTL is the uniform cross section of the prism. Triangle STU and PQR are horizontal planes. Edges PJ, RS and UK are vertical. PQ = TU = 3 cm.Diagram 11.1Draw to full scale, the elevation … Read more
Question 13 (12 marks):(a) Diagram 9.1 shows point P (5, 1) on a Cartesian plane.Diagram 9.1Transformation T is a translation ( 4 −3 ) Transformation S is an enlargement about the centre (–5, 2) with a scale factor 2.State the coordinates of the image of point P under the following transformations:(i) T2,(ii) TS.(b) Diagram 9.2 shows geometrical shapes KLMNP, KSRQP and KTUVW drawn on … Read more
Question 11 (6 marks):Diagram 8 shows sectors OABC and ODE with the common centre O respectively.Diagram 8Calculate(a) the perimeter, in cm, of the whole diagram,(b) the area, in cm2, of the shaded region.Solution:(a) Perimeter of the whole diagram =OP+PE+Arc DE+DC +Arc CBA+AO =10+5+( 50 o 360 o ×2× 22 7 ×15 )+5 +( 230 o 360 o ×2× 22 7 ×10 )+10 =30+ 275 21 + 2530 … Read more
Question 9 (5 marks):Diagram 7 shows a distance-time graph for the journey of a car from Kuala Lumpur to Ipoh.(a) State the duration of time, in minutes, the driver stopped and rest at Tapah.(b) Calculate the speed, in kmh-1, of the car from Kuala Lumpur to Tapah.(c) Calculate the average speed, in kmh-1, of the … Read more
Question 7 (6 marks):Diagram 6 shows two parallel straight lines, JK and LM, drawn on a Cartesian plane.The straight line KM is parallel to the x-axis.Diagram 6Find(a) the equation of the straight line KM,(b) the equation of the straight line LM,(c) the value of k.Solution:(a)The equation of the straight line KM is y = 3(b) Given, equation of JK: 2y=4x+3 y=2x+ 3 2 Thus, m JK =2 m … Read more