SPM 2016

Question 15 (12 marks):You are not allowed to use graph paper to answer this question.(a) Diagram 15.1 shows a pyramid with rectangular base ABCD on a horizontal plane. Vertex E is vertically above C. Triangles BCE and DCE are vertical planes. Triangles ABE and ADE are inclined planes.Diagram 15.1Draw to full scale, the plan of the solid.(b) Another solid cuboid with rectangle base BLKC is joined to … Read more

Question 13 (12 marks): Diagram 13.1 shows three triangles RPQ, UST and RVQ, drawn on a Cartesian plane. Diagram 13.1 (a) Transformation R is a rotation of 90o, clockwise about the centre O. Transformation T is a translation ( 2 3 ) . State the coordinates of the image of point B under each of … Read more

Question 11 (6 marks):Diagram 11 shows the speed-time graph for the movement of a particle for a period of t seconds.Diagram 11(a) State the uniform speed, in ms-1, of the particle.(b) Calculate the rate of change of speed, in ms-2, of the particle in the first 4 seconds.(c) Calculate the value of t, if the distance travelled in the … Read more

Question 9 (6 marks):In Diagram 9, OKLM is a sector of a circle and OAB is a quadrant of a circle with common centre O.Diagram 9It is given that OA = 8 cm, ∠KOM = 90o and OK : OB = 3 : 2.Using  π= 22 7 , calculate(a) the area, in cm2, of the shaded region,(b) the perimeter, in cm, of the … Read more

Question 7 (5 marks):(a) State whether the following statements are true statement or false statement. ( i ) {  }⊂{ S,E,T } ( ii ) { 1 }⊂{ 1,2,3 }={ 1,2,3 } (b) Diagram 7 shows the first three patterns of a sequence of patterns.Diagram 7It is given that the diameter of each circle is 20 cm.(i) Make a general conclusion by induction for the area of the unshaded … Read more

Question 5 (4 marks):Diagram 5 shows a cylindrical tank in a residential area which have 125 houses. Each house received equal volume of water.Diagram 5The diameter of the cylindrical tank is 4 m. It is given that each house has a cuboid tank with a base area of 0.8 m2.Using  π= 22 7 , calculate the … Read more

Question 3 (4 marks):Calculate the value of x and of y that satisfy the following simultaneous linear equations:2x + y = 8–x + 4y = 5Solution: 2x+y=8    …………… ( 1 ) −x+4y=5  …………… ( 2 ) ( 2 )×2:   −2x+8y=10  ……….. ( 3 ) ( 1 )+( 3 ):   y+8y=8+10 9y=18 y= 18 9 y=2 From ( 1 ): 2x+2=8 2x=8−2 2x=6 x= 6 2 x=3 ∴x=3, y=2 … Read more

Question 1 (3 marks):On the graph in the answer space, shade the region which satisfies all three inequalities y ≥ –3x + 6, y > x + 1 and y ≤ 5.Answer:Solution: Question 2 (4 marks):Solve the following quadratic equation: − 2 3x−5 = x 3x−1 Solution: − 2 3x−5 = x 3x−1 −2( 3x−1 )=x( 3x−5 … Read more