Geometry and measures worksheet — GCSE Foundation

1.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.

2.A straight line is drawn from the centre of a circle to a point on the circle. Write down the name of this line.

3.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

4.Write down which one of these statements about quadrilaterals is true.

5.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

6.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

7.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

8.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

9.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

10.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

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

12.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.

13.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

14.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

15.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.