Geometry and measures worksheet — GCSE Foundation

1.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.

2.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.

3.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.

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

5.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).

6.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.

7.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

8.Work out the exact value of sin 45° × cos 45°.

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

10.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

11.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

12.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.

13.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.

14.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

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?