Geometry and measures worksheet — GCSE Foundation

1.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

2.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

3.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

4.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

5.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?

6.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

7.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

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

9.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.

10.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

11.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?

12.Write down the term for the distance all the way around the edge of a circle.

13.A sector of a circle has radius 9 cm and angle 60°. Using π = 3.14, work out the area of the sector, to 1 decimal place.

14.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.

15.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.