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
(
)
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
(
)
PSLE Mathematics Examination Practice
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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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135
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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
(
)
PSLE Mathematics Examination Practice
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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:
PSLE Mathematics Examination Practice
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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: °
Topic 8 Geometry
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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]
PSLE Mathematics Examination Practice
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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]
147
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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
PSLE Mathematics Examination Practice
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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
PSLE Mathematics Examination Practice
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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]
PSLE Mathematics Examination Practice
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