Geometry and measures worksheet — GCSE Foundation

1.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?

2.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

3.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?

4.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

5.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

6.Work out the exact value of sin 45° × cos 45°.

7.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

8.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

9.A circle is drawn on a page. Write down how many radii can be drawn in the circle.

10.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

11.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

12.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

13.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

14.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

15.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?