Geometry and measures worksheet — GCSE Foundation

1.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.

2.Each of these has an exact value. Write down the one whose value is the greatest.

3.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

4.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

5.A circle has a radius of 3 cm. Work out the diameter of the circle.

6.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?

7.In this question, a curved surface counts as a face. How many faces does a sphere have?

8.A bus journey takes 2.5 hours. Work out how many minutes this is.

9.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

10.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

11.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?

12.e is the column vector with top number 5 and bottom number k. f is the column vector with top number 15 and bottom number 6. Given that f is 3 times e, work out the value of k.

13.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

14.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

15.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?