Geometry and measures worksheet — GCSE Foundation

1.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

2.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

3.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.

4.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

5.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.

6.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.

7.Write down the column vector that describes a translation of 5 units to the left and 3 units down.

8.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

9.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.

10.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

11.A regular nonagon has 9 sides. Work out the sum of its interior angles.

12.An angle is measured with a protractor as 47°. What type of angle is this?

13.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.

14.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

15.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.