Sacred Heart Canossian College Mathematics Common Test 4 (2012-2013)

Time allowed: 60 minutes Secondary 1 ___ Group ___ No. _____

Total marks: 80 Name: ___________________________

Score: _____________

This paper consists of three sections, A , B and C. Answer all questions in each section.

Section A: Multiple Choice Questions (18 marks)Answer all SIX questions in this section. For each question choose only one answer and put a ' ✓ ' in the box corresponding to the right answer in the following table. Each question carries 3 marks.

1 2 3 4 5 6

A

B

C

D

1. In the figure, the container in the shape of a triangular prism contains 2 100 cm3 of water. Find the depth of water. A. 5

B. 7C. 10D. 14

2. In ABC and XYZ, which of the following is/are true?

(I) If AB = XY, BC = YZ, CA = ZX, then ABC XYZ.(II) If A = X, B = Y, C = Z, then ABC XYZ.(III) If area of ABC = area of XYZ, then ABC XYZ.A. (I) onlyB. (I) and (II) onlyC. (II) and (III) onlyD. (I), (II) and (III)

20 cm15 cm

25 cm

Let d cm be the depth of water

Secondary 1 ___ Group _____ Name _____________________________ No. ____

3. Which of the following cannot be folded into the prism on the right?

A. B.

C. D.

4.

In the above figure, Fig. B is the image after Fig. A is rotated about the point O. Which of the following transformations about Fig. A is correct?

A. Fig. A is rotated anticlockwise about the point O through 90. B. Fig. A is rotated clockwise about the point O through 90. C. Fig. A is rotated clockwise about the point O through 180. D. Fig. A is rotated clockwise about the point O through 270.

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Secondary 1 ___ Group _____ Name _____________________________ No. ____

5. In the figure, find the volume of the right prism.

A.B. 28 cm3

C. 22 cm3

D. 18 cm3

6. In the figure, AOB and COD are straight lines. Find

AOD.A. 55B. 75C. 105D. 125

Section B: (34 marks)Answer all EIGHT questions in this section and show your working steps in the space provided.

1. (a) It is given that , AB = 6 cm, BC = 8 cm and CA = 10 cm.Find the lengths of XY and ZX . (2 marks)

(given)XY = 6cm (corr. sides of )ZX = 10cm (corr. sides of )

(b) It is given that . Find the values of a, b and c. (3 marks)

b =

c =

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x + 20 352x

A

BC

D

O

4

110

R

P

D

E F

30

a

Q

The volume = [5(4) – 3(2)]2= 28 cm3

x + 20 = (vert. opp. s)x = 55

55+ 20 + AOD = 180AOD = 105

Secondary 1 ___ Group _____ Name _____________________________ No. ____

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Secondary 1 ___ Group _____ Name _____________________________ No. ____2. In the figure, if AB = AD and CB = CD, prove that ABC ADC. (3 marks)

AB = AD (given)CB = CD (given)AC = AC (common)

(SSS)(SSS)

3. Referring to the figure, find(a) the value of y. (Give reasons.) (2 marks)

(s at a pt.)

y =

(b) reflex ∠AOD. (1 mark)reflex∠AOD = 2( ) + + 3( )

= 4. In the figure, ABC and DBFG are straight lines, EAD = 90 and AC // FH.

(a) Find p, q and r. (Give reasons.) (5 marks)

∠AOD = (vert.opp.s) p =

(∠ sum of ) q =

(∠ sum of ) r =

(b) Prove that EA // DC . (2 marks)

∠ADC=∠EAD= q+r =

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p

q

HF

r

G

A

B

C

D

Secondary 1 ___ Group _____ Name _____________________________ No. ____5. (a) Plot the following points on the polar coordinate plane on the right. (2 marks)

A(4, 300o) B(3, 30o) C(2, 120o)

(b) Find ∠AOB (1 mark)

∠AOB = 90。

(c) Find the area of △ABC. (2 marks)Area of △ABC

=

= 9 sq. units

6. The figure shows a prism. Find the total surface area of the prism. (3 marks)

The total surface area

cm3

7. Solve the following equations. (a) (2 marks)

y = 2

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5.5 cm

7 cm

10 cm

4 cm

5m

8 cm

4.5 cm

A (4,300 。)

C (2,120 。) B (3,30 。)

Secondary 1 ___ Group _____ Name _____________________________ No. ____

(b) (3 marks)

8. The following figure shows a prism. AB is drawn on the isometric grid paper. Complete the 2-D representation of the prism. (3 marks)

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C

D

E

F

Secondary 1 ___ Group _____ Name _____________________________ No. ____Section C : (28 marks)Attempt BOTH questions in this section and show the working steps clearly in the space provided.

1. (a) In the figure, AB // CD // FE and CB // DE.(i) Find the values of x and y. (Give reasons.) (5 marks)

∠CDE + 75° = 180° (int. ∠s, AB // DE)

y + 105° = 180° (int. ∠s, AB // DE)

(ii) Prove that DP // EQ. (3 marks)

(s at a pt.)

= =

supp.)

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y

2x+25

75

116

221

A

B

P

Q

E

C

F

D

Secondary 1 ___ Group _____ Name _____________________________ No. ____(b) In the figure, BA // DE // HG and CD // EF. Find the values of p, q and r. (Give reasons.)

(8 marks)Draw a line IC such that BA//IC//DE.

Draw a line FJ such that DE//FJ//HG.

(s at a pt.)

2. (a) In the figure, O is the origin. A(0, 6), B(4, 0), C(5,0) and D(0,9) are vertices of a quadrilateral.

(i) Find the area of △OAB. (1 mark)

Area of △OAB

(ii) Find the area of quadrilateral ABCD. (2 marks)

Area of quadrilateral ABCD

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AB

C

D E

F

H G

q

r

p

256

42

78

(0,9)

(0,6)

(4,0) (5,0)

Secondary 1 ___ Group _____ Name _____________________________ No. ____

(b) The figure shows a trapezium ABCD. AB and DC are horizontal lines and AE⊥DC.

(i) If AB = 16 units, find the coordinates of point B. (1 mark)

B = (4,10)

(ii) Given that the area of trapezium ABCD is 288 sq. units, find the length of DC. (2 marks)

(iii) Write down the coordinates of point C. (1 mark)

C = (6,-6)

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(-14,-6) D E

(-12,10) A

Secondary 1 ___ Group _____ Name _____________________________ No. ____

(c) The figure shows a △ABC and a horizontal line L . The coordinates of A, B and C are (2, -2), (3,-5) and (1,-6) respectively.

(i) If △ABC is reflected about L to △A’B’C’, draw the image △A’B’C’ and write down the coordinates of A’. (2 marks)

A’ = (2,4)

(ii) If △ABC is rotated clockwise about the origin O(0 , 0) through 270∘to △A’’B’’C’’, draw the image △A’’B’’C’’ and write down the coordinates of B’’. (3 marks)

B’’ = (5,3)

END OF PAPER

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O 1O

2 3 4 5 6 7 8

1O

2

3

4

5

6

7

8

-1O

-2-3-4-5-6-7-8-1O-2

-3

-4

-5

-6

-7

-8

x

L

A

B

C

B’

A’

C’

A’’

B’’

C’’