Geometry and measures worksheet — GCSE Foundation

1.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

2.Write down the exact value of tan 45°.

3.p is the column vector with top number 5 and bottom number 2. q is the column vector with top number 1 and bottom number 6. Work out p + q, giving your answer as a column vector in the form (top, bottom).

4.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

5.Write down the exact value of cos 60°.

6.A vertical line passes through the point (5, 2). Write down the equation of this line.

7.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

8.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?

9.Write down the name given to a quadrilateral with exactly one pair of parallel sides.

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

11.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

13.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

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

15.How many vertices does a square-based pyramid have?