Geometry and measures worksheet — GCSE Foundation

1.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

2.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

3.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.

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

5.An angle measures 108°. Write down the name given to an angle of this size.

6.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

7.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

8.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?

9.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

10.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

11.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

12.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).

13.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

14.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

15.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.