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End-of-unit review

End-of-unit review

1 Draw a line AB 8 cm long. 8 cm
Mark the point X on the line, 3 cm from A. A B
Construct the perpendicular at X, as shown in the diagram. 3 cm X

2 Jake draws a line QR, 8 cm long, at an angle of 40° to a horizontal Q
line through R.
He constructs the perpendicular to QR at Q. It meets the horizontal 8 cm
line at P, as shown in the diagram. 40°
a Draw an accurate copy of the diagram. You may use a protractor to P R
draw the 40° angle, but not for the perpendicular line.
Jake says that angle QPR is 50°.
b Show that he is correct by:
i measuring angle QPR with a protractor
ii calculating angle QPR, using the facts that you know about the sum of the angles in a triangle.
3 Copy the diagram and construct a perpendicular from the point A to the line.

A

4 Draw a circle with a radius of 5 cm.
Using a straight edge and compasses, construct an inscribed square.
5 Draw a circle with a radius of 5 cm.
Using a straight edge and compasses, inside the same circle construct an inscribed equilateral
triangle and an inscribed regular hexagon.
6 Work out the length of the hypotenuse marked in this triangle.
4 mm
8 mm
7 Work out the length of the side marked in this triangle.

0.6 m
0.5 m

8 Work out the length of the diagonal marked in this rectangle.

6 cm

11 cm

9 A rectangle has a length of 12 cm and a diagonal of 13 cm. Draw a diagram to help you solve
Work out the area of the rectangle.
this problem.

8 Constructions and Pythagoras’ theorem 83