Geometry and measures worksheet — GCSE Foundation

1.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

2.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

3.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

4.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

5.Write down the name given to a quadrilateral with exactly one pair of parallel sides.

6.How many edges does a triangular prism have?

7.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?

8.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.

9.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.

10.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

11.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

12.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

13.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

14.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

15.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.