SACRED HEARTCANOSSIANCOLLEGE

FINAL EXAMINATION, 2012 –2013

MATHEMATICS

Time allowed: 1 h 30 min Secondary 1 ___ Group ___ No. _____

Total marks: 100 Name: ______

Score: ______

This paper consists of three sections, A, B and C. Answer all questions in each section. The diagrams in this paper are not necessarily drawn to scale.

Section A (20 marks)

Answer all ten questions in this section. For each question choose only one answer. In the following table, put a '' in the box corresponding to the right answer. Each question carries 2 marks.

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
A
B
C
D

1.According to the diagram, find the values of E and F.

A.E = 3, F = 10

B.E = 10, F = 13

C.E = 10, F = 3

D.E = 13, F = 10

2.Jerry has $x. He usesof his money to buy a toy car. His mother then gives him $30 as pocket money so that he has $156. Which of the following equations can be used to find the value of x?

A.x + 30 = 156

B.x –– 30 = 156

C.x –– 30 = 156

D.x –+ 30 = 156

Secondary 1 ___ Group _____ Name ______No. ____

Section A(Continued)

3.In the figure, SR is produced to meet PQ at T. Find the length of TQ.

A.2 units

B.6 units

C.7 units

D.8 units

4.The given figure has both reflectional and rotational symmetry. Find the number of axes of reflectional symmetry and the order of rotational symmetry of the figure.

Number of axes of reflectional symmetry / Order of rotational symmetry
A. / 4 / 2
B. / 4 / 4
C. / 2 / 2
D. / 2 / 4


5.In the figure, AC and BD intersect at E. Find the value of x.

A.28°

B.30°

C.32°

D.41°

6.The figure shows a solid triangular prism. Find its total surface area.

A.330 cm2

B.360 cm2

C.411 cm2

D.420 cm2

Secondary 1 ___ Group _____ Name ______No. ____

Section A(Continued)

7.Which of the following solidsis/ are polyhedron/ polyhedra?

(I) / (II) / (III)

A.(I) only

B.(II) only

C.(I) and (III) only

D.(II) and (III) only

8.Simplify 6a2b÷3ab×2b2.

A.

B.

C. 4ab2

D. 4b2

9.In the figure, PQRTUV, ∠RPQ = y + 6°, ∠TUV = 5y and . Find .

A.112°

B.120°

C.130°

D.136°

10.In the figure, AB//CD. Which of the following must be correct?

A.xy

B.xz

C.xyz

D.xy + z 180

Secondary 1 ___ Group _____ Name ______No. ____

Section B (44marks)

Attempt all nine questions in this section and show your working steps clearly in the space provided.

1.The marked price of a blender is $x. It is sold at a discount of 10% in a shop and the selling price is $1800.

(a)Find the value of x.(2 marks)

(b)If the blender is sold at $x, a profit of 25% is made. Find the cost price of the blender.

(2 marks)

2.The following pie chart shows the favourite sports of the SecondaryOne students in a school. There are 40 Secondary One students whose favourite sport is basketball.

(a)Find the value of x.(2 marks)

(b)Find the total number of Secondary One students in the school. (2 marks)

(c)Find the number of Secondary One students whose favourite sport is table tennis. (2 marks)

Secondary 1 ___ Group _____ Name ______No. ____

Section B(Continued)

3.(a)Solve x– 9 = 2x– 3(x+ 1).(3 marks)

(b)The price of a box of tarts is $1 cheaper than that of a loaf of bread. If 3 times thepriceofaloaf of bread is $58 more than half of the price of a box of tarts, findthe price ofa loaf of bread. (3 marks)

4.In a supermarket, the prices of a can of coke, a carton of chocolate milk and a bottle of orange juice are $6.3, $8.8 and $11.4 respectively. Peter has $60. He wants to buy 3 cans of coke, a carton of chocolate milk and 2 bottles of orange juice.

(a)Estimate the amount that Peter has to pay by rounding up the price of each itemto the nearest integer. (2 marks)

(b)Without working out the exact amount Peter has to pay, show that he has enough money to pay for the items. (2 marks)

Secondary 1 ___ Group _____ Name ______No. ____

Section B(Continued)

5.Figure 1(a) shows a prism with trapezium as its uniform cross-section. , AB = 2, AD = 3, CD = 6, BC = 5 and CG = 4.

(a)CD is drawn on the isometric grid paper. Complete the 2-D representation of the prism. (2 marks)

(b)The prism in Figure 1(a) is placed horizontally as shown in Figure 1(b). Draw the

cross-section of the prism when it is cut by a plane along the dotted line FC vertically.

(2 marks)

Secondary 1 ___ Group _____ Name ______No. ____

Section B(Continued)

6.In the figure, AFE is a straight line. The area of CDEF is 30 cm2.

(a)Find the length of FE.(3 marks)

(b)Find the area of BCD.(2 marks)

7.In the figure, ADBC and BD = CD.

(a)Prove that △ABD△ACD.(3 marks)

(b)If AB = x + 3 and AC = 5 –x, find the value of x.(2 marks)

Secondary 1 ___ Group _____ Name ______No. ____

Section B(Continued)

8.In the figure, BAE and CAD are straight lines and BC // DE.

(a)Prove that △ABC ~ △AED.(3 marks)

(b)If AB = 10cm, AE = 5cm and BC = 12 cm, find ED.

(3 marks)

  1. In the figure, AB = 4.5, BC = 7.5, AC = 6, PQ = 3, QR = 5and PR = 4.

Prove that ABCPQR.(4 marks)

Secondary 1 ___ Group _____ Name: ______( )

Section C (36 marks)

Attempt all three questions in this section and show your working steps clearly in the space provided.

1.(a)Figure 1(a) shows a solid prism.

(i)Find the volume of the prism.(3 marks)

(ii)Find the total surface area of the prism.(3 marks)

Secondary 1 ___ Group _____ Name: ______( )

Section C (Continued)

1.(b)Figure 1(b) shows an open water tank in the form of a prism with trapezium as its uniform cross-section. Suppose the tank has negligible thickness. , , and . PQ = 20 cm, PS = 30 cm, WV = 60 cm, QR = 50 cm and SW = 40 cm.

(i)Find the outer surface area of the open tank.(2 marks)

(ii) If the tank contains18000 cm3 of water, find the depth of water in the tank.

(2 marks)

(iii)The solid prism in Figure 1(a) is put into the water tank in Figure 1(b). It is completely immersed in water and no water overflows. Find the rise in water level.

(2 marks)

Secondary 1 ___ Group _____ Name: ______( )

Section C (Continued)

2. (a)The figure showsthree points, P, Q and R on a polar coordinate plane.

(i)Write down the polar coordinates of Q.(1 mark)

(ii)Find the length of PQ.(1 mark)

(iii)Find∠QOR.(1 mark)

(b)The figure shows shape P and a line AB. Reflect shape Pabout the line AB. Draw and label theimage Q . (2 marks)

(c) In the figure, A(3, 0),B(6, 5)and C (c, 0)are the vertices of ABC. The area of ABCis 30 square units. Find the coordinates of C. (2 marks)

Secondary 1 ___ Group _____ Name: ______( )

Section C (Continued)

2.(d)The figure shows a vertical line l and a parallelogram ABCD. The coordinates of A, B, C and D are(2, 4), (5, 4), (4,2) and (1, 2) respectively.

(i)If ABCD is reflected about the line l to, draw in the figure and

find the coordinates ofA1. (2 marks)

A1= ______

(ii)If ABCD is rotated anticlockwise about O (0,0) through 270°to, draw

in the figure and find the coordinates of.(2 marks)

A2= ______

(iii)If D (1, 2) is rotated clockwise about O (0, 0)through and then reflected about the x-axis to obtain pointP,write down the coordinates of P. (1 mark)

P = ______

Secondary 1 ___ Group _____ Name: ______( )

Section C (Continued)

3.(a)In the figure, AB // DC and Prove that .(3 marks)

(b)In the figure, EDC and DFG arestraight lines,BA // EC // MNand FM // IG.

(i)Find the marked angles, p and q.(Give reasons.)(5 marks)

(ii)Prove that BC // DG.(2 marks)

(iii)Prove that EC // HG.(2 marks)

END OF PAPER

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