Geometry and measures worksheet — GCSE Foundation

1.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

2.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

3.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.

4.Which of the following is the correct definition of a regular polygon?

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

6.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.

7.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.

8.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?

9.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

10.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

11.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

12.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?

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

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

15.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?