Geometry and measures worksheet — GCSE Foundation

1.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

2.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

3.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

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

5.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?

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

7.A polygon has 12 straight sides. What is the mathematical name for this polygon?

8.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

9.A roof has two triangular sections, P and Q. Section P has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them. Section Q has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them, arranged the same way round. A roofer wants to cut identical triangular felt panels for both sections without measuring Section Q separately. Which condition confirms that the two sections are congruent?

10.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

11.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

12.Write down the exact value of sin 60°.

13.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

14.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

15.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?