Geometry and measures worksheet — GCSE Foundation

1.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

2.A cylindrical tin has a curved surface, a flat circular base and a flat circular lid. A label is stuck around the curved surface only. How many of the tin's faces are NOT covered by the label?

3.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?

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

5.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

6.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?

7.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

8.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.

9.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?

10.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?

11.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?

12.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

13.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

14.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

15.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.