Printable · GCSE Foundation · ages 14-16
Geometry and measures worksheet — GCSE Foundation
Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Geometry and measures worksheet — GCSE Foundation
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- 1.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.
- 2.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.
- 3.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.
- 4.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.
- 5.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.
- 6.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?
- 7.A scale drawing uses a scale of 1 : 60. A path on the drawing is measured as 9.8 cm long. What is the real length of the path, in metres, to 1 decimal place?
- 8.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?
- 9.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.
- 10.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?
- 11.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?
- 12.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?
- 13.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.
- 14.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.
- 15.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.
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