Geometry and measures worksheet — GCSE Foundation

1.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

2.A circle is drawn on a page. Write down how many radii can be drawn in the circle.

3.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?

4.Work out the distance between the points (−3, 4) and (5, −2).

5.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.

6.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

7.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

8.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

9.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

10.A cube has all of its edges the same length. How many planes of symmetry does it have?

11.A submarine travels due south. What is the three-figure bearing for this direction?

12.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

13.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

14.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

15.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.