igureMaths
Log in
Start free
←
Constructions & loci
Get dealt questions instead
→
Browse Constructions & loci
21 questions at your level
Difficulty
All
Level 2
Level 3
Level 4
Level 5
Ruler-and-compass constructions
10 questions
Lesson
Not started
Mark as done
(a)
Draw a straight line and mark a point
X
X
X
on it.
Using ruler and compasses only, construct an angle of
60
°
60°
60°
at
X
X
X
. You must show all your construction arcs.
(b)
Hence construct an angle of
30
°
30°
30°
.
(c)
Explain why the construction in part (a) gives exactly
60
°
60°
60°
.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
Elin bisects the angle at
Q
Q
Q
using the standard construction: an arc centred at
Q
Q
Q
cuts the two arms at points
S
S
S
and
T
T
T
, then equal arcs centred at
S
S
S
and at
T
T
T
cross at the point
U
U
U
, and she draws the line
Q
U
QU
Q
U
.
Explain
why
this construction bisects the angle. You should refer to the triangles
Q
S
U
QSU
QS
U
and
Q
T
U
QTU
QT
U
.
●●●●
●
Level 4
3 marks
Start
→
Loci & regions
11 questions
Lesson
Not started
Mark as done
The diagram shows a plan of a field with a straight fence and two trees,
A
A
A
and
B
B
B
. The plan is drawn to a scale of
1
1
1
cm to
10
10
10
m.
A
B
fence
A bird table is to be placed so that it is:
* less than
45
45
45
m from tree
A
A
A
,
and
* nearer to tree
A
A
A
than to tree
B
B
B
,
and
* more than
20
20
20
m from the fence.
On the plan, show by shading the region where the bird table can be placed. You must show all your construction lines.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
A guard dog is attached by a
5
5
5
m chain to a ring that slides freely along a straight rail of length
20
20
20
m, fixed to the ground in a large open yard.
20 m
Diagram NOT accurately drawn
(a)
Describe the region of the yard the dog can reach.
(b)
Work out the area of this region. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
5 marks
Start
→