PSLE Mathematics

Topi c

08

Geometry

Section A: 1-mark Multiple Choice Questions (Paper 1, Booklet A) Time allocated: 6 minutes 1. AB and CD are straight lines. Find the value of x in the figure below.

D 135°

A

x

B

4x

C

(1) 27°

(2) 45°

(3) 108°

(4) 135°

135° ÷ 5 = 27°

(

1

)

2. The figure below, not drawn to scale, shows an isosceles triangle. Find ∠a. a 34°

(1) 34°

(2) 68°

(3) 112°

(4) 158°

Topic 8 Geometry

08 Geometry.indd 133

(

)

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3. In the diagram below, Andy is standing at point O facing the market. Which place will he be facing if he turns 270° anti-clockwise? stadium

church

market

Park

swimming pool

park RIVERMALL

shopping centre

school cinema

(1) shopping centre

(2) school

(3) swimming pool

(4) church

(

)

4. The figure below is made up of a parallelogram, ABDE, and an equilateral triangle, BCD. Find the value of ∠BAE. A

B

E

(1) 120°

(2) 135°

(3) 150°

(4) 160°

134

08 Geometry.indd 134

D

C

(

)

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5. In the figure below, not drawn to scale, find the value of ∠b. b 68°

138°

(1) 42°

(2) 60°

(3) 70°

(4) 80°

(

)

(

)

6. ABC is a straight line. Find ∠c.

A

18°

c B

68° C

(1) 86°

(2) 94°

(3) 108°

(4) 112°

Topic 8 Geometry

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Section B: 2-mark Multiple Choice Questions (Paper 1, Booklet A) Time allocated: 10 minutes 1. In the figure, not drawn to scale, FGH is an equilateral triangle, GHI is an isosceles triangle. FGI = 29º. Find ∠IHJ. F

I

29°

G

J

H

(1) 58°

(2) 62°

(3) 89°

(4) 91°

60° – 29° = 31° 31° x 2 = 62° (

2

)

2. In the figure, not drawn to scale, KLMN is a square and KNO is an equilateral triangle.

Find ∠LOK.

O

K

N

L

M

(1) 10°

(2) 15°

(3) 20°

(4) 30°

136

08 Geometry.indd 136

Hint: Is Triangle LOK isosceles?

(

)

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3. The figure below is made up of 3 triangles. PQ, RS and TU are straight lines. Find the sum of angles p, q, r, s, t and u.

P p

R r

t

T

S

(1) 180°

(2) 270°

(3) 360°

(4) 450°

s

q

u

U

Q

(

)

4. The figure below is not drawn to scale. ABCD is a parallelogram. DEF is a straight line. Find ∠CDE. D

A

E

62°

(1) 28°

(2) 31°

(3) 45°

(4) 62°

Topic 8 Geometry

08 Geometry.indd 137

C

B

F

(

)

137

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5. In the figure below which is not drawn to scale, ABCD is a rhombus. Find ∠CAE.

A

Hint: What is ∠CAD? B

118°

38° D E

C

(1) 19°

(2) 24°

(3) 31°

(4) 38°

(

)

6. In the figure (not drawn to scale), FGH is a right-angled triangle, FIJ is an isosceles triangle. HFJ and GFI are straight lines. Find ∠d.

H 52°

Hint: What is ∠IFJ? I d

J

(1) 76°

(2) 104°

(3) 128°

(4) 142°

138

08 Geometry.indd 138

F

G

(

)

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Section C: 1-mark Short-answer Questions (Paper 1, Booklet B) Time allocated: 6 minutes 1. The diagram below shows a trapezium, ABCD, not drawn to scale. Find ∠ABC. B

A

180° – 55° = 125°

105°

55°

D

Answer:

125

°

2. Find ∠e. e

39°

Answer:

°

Answer:

°

3. Find ∠f.

101°

f

37°

Topic 8 Geometry

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4. Find the sum of ∠g and ∠h. g 57°

h

61°

Answer:

°

Answer:

°

5. In the figure below, find ∠i.

82° i

31°

6. You are facing F now. If you turn 135° in the clockwise direction, which direction will you be facing?

A B

H

C

G

D

F

140

08 Geometry.indd 140

E

Answer:

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Section D: 2-mark Short-answer Questions (Paper 1, Booklet B) Time allocated: 10 minutes 1. In the figure below, not drawn to scale, ABC is an equilateral triangle, DE, FG and HJ are straight lines. What is the sum of ∠j, ∠k and ∠l?

F

D

A

180° – 60° = 120°

k

120° x 3 = 360° J

i C

I

E

B

H

G

Answer:

360

°

2. In the figure below, not drawn to scale, KL and MN are straight lines. Find ∠m.

K

N

Common Mistake:

m

∠m = 43° + 39°

M

39°

43°

L

Topic 8 Geometry

08 Geometry.indd 141

Answer:

°

141

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3. In the figure below, PQRS is a square and PST is an isosceles triangle. ∠BPT= 153°.

Find the value of ∠PTS. T

Common Mistake: ∠PTS = 153° – 90° P

153°

Q

S

R

Answer:

°

4. WXYZ consists of two isosceles triangles, WXY and WYZ. ∠XWY = 62° and the ratio of ∠WXY : ∠WZY is 2 : 3. Find ∠n.

W n X

Z

Y

Answer: °

142

08 Geometry.indd 142

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5. The figure below is not drawn to scale. ∠a is thrice the size of ∠b. Find ∠b. a

Hint:

b

What is the sum of ∠a and ∠b?

Answer:

°

6. AC and DE are straight lines. ∠CBD is twice the size of ∠EBF. Find ∠ABD. E

A

Hint: F B

D

What is the sum of ∠CBD and ∠EBF?

63°

C

Answer: °

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Section E: 2-mark Short-answer Questions (Paper 2) Time allocated: 10 minutes 1. In the figure below, find the sum of ∠p and ∠q.

50° p q

150°

180° – 150° = 30° 180° – 50° = 130° 180° – 30° - 130° = 20° (Method — 1 m)

20° x 2 = 40° (Method — 1 m, Answer — 1 m)

Answer:

40°

[3 m]

2. In the figure below, find the ratio of ∠s and ∠t. t 39°

s

155°

144

08 Geometry.indd 144

Answer:

[3 m]

PSLE Mathematics Examination Practice

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3. In the figure below, find w

138° x

(a ∠w

(b) ∠x.

Answer: (a)

[1 m]

(b)

[2 m]

4. In the figure below, find the difference between ∠y and ∠z.

69°

z

y

31°

Topic 8 Geometry

08 Geometry.indd 145

Answer:

[3 m]

145

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5. The figure below is made up of 1 equilateral triangle and 1 isosceles triangle. What fraction of ∠a is ∠b? a

b

[3 m]

Answer:

6. In the figure below, find ∠c.

100° 42°

c

146

08 Geometry.indd 146

Answer:

[ 3 m]

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Section F: 3-mark Long-answer Questions (Paper 2) Time allocated: 18 minutes 1. In the figure below, find (a) ∠d

(b) ∠e.

66°

d

98°

37°

(a) 66° - 37° = 29°

d = 90° - 29°

= 61° (Method — 1 m, Answer — 1 m)

(b) (180° - 98°) ÷ 2 = 41° 90° - 41° = 49°

e = 180° - 49° x 2 = 82° (Method — 1 m, Answer — 1 m)

61°

Answer: (a) [2 m]

Topic 8 Geometry

08 Geometry.indd 147

(b)

82°

[2 m]

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2. In the figure below, ∠a is thrice of ∠b, find (a) ∠a

Hint:

(b) ∠c.

What is the sum of ∠a and ∠b?

28°

c

b

a

Answer: (a)

[3 m]

(b)

[3 m]

Answer: (a)

[3 m]

(b)

[1 m]

3. In the figure below, find

(a ∠d

(b) ∠e.

131°

61°

e

49°

d

148

08 Geometry.indd 148

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4. The figure below shows a parallelogram. Find (a) ∠f

(b) ∠g

(c) ∠h. g 39° 71°

74°

h

f

Answer: (a)

[1 m]

(b)

[2 m]

(c)

[1 m]

Answer: (a)

[2 m]

(b)

[2 m]

5. In the figure below, find (a) ∠i

(b) ∠j.

112°

Topic 8 Geometry

08 Geometry.indd 149

69° i

j

149

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6. In the figure below, ABCD is a parallelogram. Find (a) ∠g

(b) the difference between ∠h and ∠I. A

Hint: What is ∠BAE?

D h

B

64°

g E

i

C

Answer: (a)

[2 m]

(b)

[2 m]

150

08 Geometry.indd 150

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Section G: 4-mark Long-answer Questions (Paper 2) Time allocated: 24 minutes 1. In the figure below, ABCD is a parallelogram and BFEC is a rhombus. DBF is a straight line. Find (a) ∠CFE

(b) ∠ABD.

226°

D

A

C

54°

E

B

F

(a) 360° – 54° – 226° = 80°

∠CFE = 80° ÷ 2

= 40° (Method — 1 m, Answer — 1 m)

(b) 180° - 80°= 100° 180° - 100° = 80° (Method — 1 m)

∠ABD = 180° - 54° - 80° = 46° (Method — 1 m, Answer — 1 m)

Answer: (a)

40°

[2 m]

(b)

46°

[3 m]

Topic 8 Geometry

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151

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2. In the figure below, ABCD is a parallelogram and CDE is a triangle. EG is a straight line and HG is parallel to DC. ∠DGH = 99° and ∠ADG = 128°.

(a) Find ∠ABC.

(b) Find ∠BEF.

Hint:

What is ∠CDG?

E

F

A

128° 99°

H

B

C

D

G

Answer: (a)

[2 m]

(b)

[3 m]

3. In the figure below, ABCD is a parallelogram and BEFC is a rhombus. DBE is a straight line. Find (a) ∠BEC

Hint:

(b) ∠ABD.

What is ∠BCF? 238° C

D

A

52°

F

B

E

Answer: (a)

[2 m]

(b)

[3 m]

152

08 Geometry.indd 152

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4. The trapezium below is made up of 3 triangles. Find (a) ∠m

(b) ∠n.

49°

n

m

76°

Answer: (a)

[3 m]

(b)

[2 m]

5. The figure below is made up of a rhombus, HKML, 2 isosceles triangles, LMJ and KMJ, and 1 more triangle. Find (a) ∠LMJ

Hint:

(b) ∠GHK. G 61°

What is ∠GJH?

K

M

H

J

L

Answer: (a) [3 m]

Topic 8 Geometry

08 Geometry.indd 153

(b)

[2 m]

153

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6. In the figure below, QV is parallel to TU. Find (a) ∠QPT

(b) sum of ∠RVU and ∠SUV.

What is ∠QRT?

U

V

151° R

Q

Hint:

S

34° T

P

154

08 Geometry.indd 154

Answer: (a)

[3 m]

(b)

[2 m]

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