Geometry and measures worksheet — GCSE Foundation

1.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

2.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.

3.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

4.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

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

6.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.

7.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

8.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

9.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.

10.Each of these has an exact value. Write down the one whose value is the greatest.

11.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

12.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.

13.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?

14.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

15.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.