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.

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Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.
(a)£100
(b)£65
(c)£35
(d)£50
2.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.
(a)(−18, 23)
(b)(22, −13)
(c)(2, 5)
(d)(12, −4)
3.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.
(a)5 cm
(b)30 cm
(c)7.5 cm
(d)15 cm
4.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?
(a)kite
(b)trapezium
(c)rhombus
(d)parallelogram
5.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.
(a)The angles are not necessarily equal
(b)Similar triangles are never congruent
(c)The scale factor is 2, not 1, so the sides are not equal
(d)Congruent triangles must have a right angle
6.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.
(a)56.5 cm
(b)37.7 cm
(c)9.4 cm
(d)18.8 cm
7.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.
(a)38.47 m²
(b)18.84 m²
(c)3.14 m²
(d)34.54 m²
8.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?
(a)SAS
(b)RHS
(c)ASA
(d)SSS
9.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.
(a)12π cm
(b)6π cm
(c)π cm
(d)2π cm
10.A square has sides of length 7 cm. Work out its area.
(a)49 cm²
(b)21 cm²
(c)28 cm²
(d)14 cm²
11.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.
(a)£3
(b)£15.20
(c)£12
(d)£48
12.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.
(a)1.7 cm
(b)20.0 cm
(c)5.0 cm
(d)6.7 cm
13.A crane's hook starts at the point (3.4, 9.5) on a construction site plan measured in metres. It moves along the vector $(- 4.5 - 1.2)$ to pick up a beam, then along the vector $(- 2.5 0.8)$ to place it. Work out the single column vector that describes the hook's overall movement from its start position to where it places the beam.
(a) $(- 2 - 2)$
(b) $(- 7 - 0.4)$
(c) $(7 - 0.4)$
(d) $(- 7 2)$
14.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?
(a)2.40m
(b)m/2.40
(c)m − 2.40
(d)2.40 + m
15.A footpath is 3750 m long. Work out this distance in kilometres.
(a)3.75 km
(b)0.375 km
(c)37.5 km
(d)375 km

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