Geometry and measures worksheet — GCSE Foundation

1.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

2.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

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.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

5.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

6.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.

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

8.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

9.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?

10.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

11.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.

12.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

13.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

14.An angle is measured with a protractor as 47°. What type of angle is this?

15.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.