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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.
(a)2.1 m
(b)0.3 m
(c)2.25 m
(d)1.5 m
2.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.
(a)the lens-shaped region where the two circles overlap
(b)the whole smaller circle, since it fits inside the larger one
(c)no overlap — 30 km and 20 km don't add to 40 km
(d)a straight strip, exactly halfway between the two
3.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?
(a)(3, 9)
(b)(6, 2)
(c)(2, 3)
(d)(−2, 6)
4.Write down the exact value of sin 0°.
(a)1/2
(b)0
(c)1
(d)undefined
5.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?
(a)AAA applies, because both triangles have a right angle
(b)The triangles cannot be proved congruent from this information
(c)RHS applies: the right angle, hypotenuse and one matching side are all equal
(d)SSS applies, because all three sides must be equal in any right-angled triangle
6.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?
(a)Right
(b)Acute
(c)Reflex
(d)Obtuse
7.Work out the distance between the point (0, 0) and the point (5, 12).
(a)12
(b)13
(c)17
(d)7
8.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?
(a)AB = CD
(b)AB ∥ CD
(c)AB ⊥ CD
(d)AB ≅ CD
9.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?
(a)8
(b)9
(c)3
(d)6
10.Triangle ABC has AB = 8 cm, BC = 10 cm and CA = 6 cm. Triangle LMN has LM = 10 cm, MN = 6 cm and NL = 8 cm. The two triangles are congruent by SSS. Which of the following correctly matches the corresponding vertices?
(a)A↔L, B↔M, C↔N (ABC≅LMN)
(b)A↔N, B↔M, C↔L (ABC≅NML)
(c)A↔N, B↔L, C↔M (ABC≅NLM)
(d)A↔M, B↔N, C↔L (ABC≅MNL)
11.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?
(a)Not enough information
(b)Cuboid — not necessarily a cube
(c)Triangular prism
(d)Cube — only a cube fits this
12.Write down the term for the distance all the way around the edge of a circle.
(a)diameter
(b)circumference
(c)area
(d)radius
13.Write down which one of these statements about quadrilaterals is true.
(a)Every square is a rectangle
(b)Every rectangle is a rhombus
(c)Every rectangle is a square
(d)Every rhombus is a rectangle
14.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.
(a)π cm
(b)4π cm
(c)10π cm
(d)2π cm
15.A submarine travels due south. What is the three-figure bearing for this direction?
(a)270
(b)090
(c)018
(d)180

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