Geometry and measures worksheet — GCSE Foundation

1.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.

2.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

3.Which of the following is the correct definition of a regular polygon?

4.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

5.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?

6.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

7.A tank holds 3.2 m³ of water. Work out this volume in litres.

8.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

9.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?

10.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

11.A solid is built from centimetre cubes: a base layer of 2 rows of 3 cubes each (a 3 by 2 rectangle of cubes), with one extra cube placed on top of one corner cube of that base. Looking down from directly above (the plan view), how many squares are visible?

12.A polygon has 9 sides. What is the name of this polygon?

13.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

14.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

15.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.