Browse Constructions & loci

21 questions at your level

DifficultyAll Level 2 Level 3 Level 4 Level 5

Ruler-and-compass constructions

10 questions

LessonNot started

(a) Using ruler and compasses, construct triangle

ABC

AB = 7

BC = 6

AC = 5

cm.

(b) Construct the perpendicular bisector of

BC

and the bisector of angle

BAC

. Extend both constructed lines far enough for them to cross, and mark the crossing point

X

. (You may find that

X

lies outside the triangle.)

(c) Ravi says "

X

is the same distance from

B

C

, and it is also the same distance from

AB

AC

." Explain why Ravi is right.

●●●●●Level 56 marksStart

Using ruler and compasses only, construct an angle of

75°

. You must show all your construction arcs.

Hint: $75 = 60 + 15$ .

●●●●●Level 54 marksStart

Loci & regions

11 questions

LessonNot started

PQRS

is a rectangular garden measuring

16

10

m. The plan below is drawn to a scale of

1

2

m.A pond is to be built in the garden so that it is:

* more than

12

P

, and * less than

6

m from the side

QR

, and * nearer to the side

PQ

than to the side

SR

.

On the plan, show by shading the region where the pond can be built. You must show all your construction lines.

●●●●●Level 55 marksStart

A goat is tied by a

10

m rope to the corner

G

of a shed which measures

8

6

m. The shed stands in a large open field, and the goat cannot go inside the shed.Diagram NOT accurately drawn

Work out the total area of the field the goat can graze. Give your answer correct to 3 significant figures.

●●●●●Level 54 marksStart