Geometry and measures worksheet — GCSE Foundation

1.Write down the exact value of cos 45°.

2.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.

3.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

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

5.The perimeter of a square is 20 cm. Work out the area of the square.

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

7.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

8.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

9.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?

10.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).

11.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

12.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.

13.Work out the exact value of (sin 30°)² + (cos 30°)².

14.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

15.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.