Geometry and measures worksheet — GCSE Foundation

1.A hiker walks due west. What is the three-figure bearing for this direction?

2.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

3.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

4.A straight line is drawn from the centre of a circle to a point on the circle. Write down the name of this line.

5.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.

6.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.

7.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

8.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

9.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

10.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.

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.Work out the exact value of tan 30° + tan 30°.

13.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

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

15.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.