Geometry and measures worksheet — GCSE Foundation

1.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

2.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

3.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

4.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

5.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

6.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

7.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

8.In this question, a curved surface counts as a face. How many faces does a cone have?

9.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?

10.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.

11.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

12.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.

13.Write down the column vector, from the options given, that would move a point to the right and downwards.

14.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.

15.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?