Onlinetuition.com SPM Mathematics
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
Question 5 (4 marks):Solving using matrix method is not allowed in this question.Diagram 5 shows a rectangular fish pond with the perimeter of 62 m.It is given that the length of the fish pond is 3 times its width.Calculate the length, in m, of the fish pond.Solution:Given y + 4 = 3xy = 3x – 4 … Read more
Question 3 (4 marks):Diagram 3 shows a garden path with a rectangular shape. There are 8 similar circular stepping stone built in the path. Given the area of the path is 32 m2, find the diameter, in m, of one piece of stepping stone.Solution: Given the area of the path =32 m 2 =320000 cm 2 x( x+4 )=320000 x … Read more
Question 1 (3 marks):(a) It is given that set E = {perfect square numbers} and set F = {9, 16, 25}.Complete the Venn diagram in the answer space to show the relationship between set E and set F.Answer:(b) The Venn diagram in Diagram 1 shows the sets X, set Y and set Z.The universal set, ξ = X U Y … Read more