Geometry and measures worksheet — GCSE Foundation

1.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

2.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

3.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

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

5.Two similar triangles have lengths in the ratio 3 : 4. The perimeter of the smaller triangle is 24 cm. Work out the perimeter of the larger triangle.

6.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

7.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

8.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?

9.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

10.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

11.Work out the exact value of tan 30° + tan 30°.

12.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

13.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².

14.A jug holds 750 ml of water. Work out what fraction of a litre this is.

15.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?