Geometry and measures worksheet — GCSE Foundation

1.How many vertices does a cuboid have?

2.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.

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

4.Write down the exact value of cos 30°.

5.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

6.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

7.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

8.A regular nonagon has 9 sides. Work out the sum of its interior angles.

9.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

10.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

11.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

12.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

13.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

14.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?

15.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.