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21 questions at your level
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Level 2
Level 3
Level 4
Level 5
Ruler-and-compass constructions
10 questions
Lesson
Not started
Mark as done
The diagram shows an angle
P
Q
R
PQR
P
QR
.
R
Q
P
Using ruler and compasses only, construct the bisector of angle
P
Q
R
PQR
P
QR
. You must show all your construction arcs.
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Level 3
3 marks
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The diagram shows a straight line
l
l
l
, a point
P
P
P
which is not on the line, and a point
Q
Q
Q
which is on the line.
P
Q
l
(a)
Using ruler and compasses only, construct the perpendicular from
P
P
P
to the line
l
l
l
. You must show all your construction arcs.
(b)
Using ruler and compasses only, construct the perpendicular to
l
l
l
at the point
Q
Q
Q
.
(c)
Aisha says "the perpendicular I drew in part (a) is the shortest path from
P
P
P
to the line". Explain why Aisha is right.
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Level 3
6 marks
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(a)
Draw a straight line and mark a point
P
P
P
on it. Using ruler and compasses only, construct an angle of
90
°
90°
90°
at
P
P
P
.
(b)
By adding one further construction, obtain an angle of
45
°
45°
45°
at
P
P
P
. Show all your construction arcs.
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Level 3
4 marks
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(a)
Draw a line segment
M
N
MN
M
N
of length
7.6
7.6
7.6
cm. Using ruler and compasses only, construct the perpendicular bisector of
M
N
MN
M
N
.
(b)
Your bisector crosses
M
N
MN
M
N
at the point
X
X
X
. Write down the length of
M
X
MX
M
X
.
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Level 3
3 marks
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Loci & regions
11 questions
Lesson
Not started
Mark as done
The diagram shows a plan of a rectangular shed measuring
30
30
30
m by
15
15
15
m, drawn to a scale of
1
1
1
cm to
5
5
5
m.
30 m
15 m
shed
A security light lights up all the ground within
20
20
20
m of the outside walls of the shed.
On the plan, draw accurately the locus of the points that are exactly
20
20
20
m from the outside of the shed.
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Level 3
4 marks
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A treasure map is drawn to a scale of
1
1
1
cm to
4
4
4
m.
On the map, the treasure is buried at the point that is equidistant from a rock
R
R
R
and a well
W
W
W
, and also equidistant from two straight paths that meet at a point
T
T
T
(measured within the acute angle between the paths).
(a)
Name the construction needed for each of the two conditions.
(b)
A student measures the distance from
R
R
R
to the treasure on the map as
5.5
5.5
5.5
cm. Work out the real distance from the rock to the treasure.
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Level 3
4 marks
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Two statues,
A
A
A
and
B
B
B
, stand
12
12
12
m apart in a park. A fountain is to be built so that it is exactly the same distance from
A
A
A
as from
B
B
B
.
(a)
Describe fully the locus of possible positions for the fountain.
A plan of the park is drawn to a scale of
1
1
1
cm to
2
2
2
m.
(b)
Work out the length of
A
B
AB
A
B
on the plan.
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Level 3
3 marks
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A
B
C
D
ABCD
A
B
C
D
is a rectangular room, with the corner
A
A
A
where walls
A
B
AB
A
B
and
A
D
AD
A
D
meet.
A sensor must be placed so that it is
closer to wall
A
B
AB
A
B
than to wall
A
D
AD
A
D
.
(a)
Describe the boundary of the region where the sensor can go, and how you would construct it.
The room measures
8
8
8
m by
6
6
6
m. A plan is drawn to a scale of
1
1
1
cm to
2
2
2
m.
(b)
Work out the dimensions of the room on the plan.
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Level 3
4 marks
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Mark as done
The point
D
D
D
is shown on a centimetre grid.
A point
Q
Q
Q
is no more than
3
3
3
cm from the point
D
D
D
.
Kofi is asked to shade the region where the point
Q
Q
Q
could be.
His answer is shown on the grid.
10
12
14
16
18
20
22
11
12
13
14
15
16
17
18
19
20
21
D
Explain the mistake Kofi has made.
(1 mark)
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Level 3
1 mark
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