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 · 15 questions

MathsUKwww.geekhero.co.uk

1.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
(a) $(- 5 - 3)$
(b) $(- 3 5)$
(c) $(3 - 5)$
(d) $(- 3 - 5)$
2.Vector A is $(- 5 2)$ and vector B is $(5 - 2)$ . Write down how vector B compares to vector A.
(a)B is the same as A
(b)B is unrelated to A in direction
(c)B is twice A
(d)B is the reverse of A
3.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?
(a)A parallelogram
(b)A rectangle
(c)An L-shape
(d)A T-shape
4.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?
(a)035°
(b)325°
(c)350°
(d)215°
5.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.
(a)a line parallel to both, 3 cm from each
(b)the perpendicular bisector of the gap
(c)a line parallel to both, 6 cm from each
(d)a circle of radius 3 cm, centred midway
6.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
(a)(3, 3)
(b)(4, 0)
(c)(4, 3)
(d)(3.5, 3)
7.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.
(a)No, because the triangles may be different sizes
(b)Yes, by the SSS condition
(c)No, because no side lengths are given
(d)Yes, by the AA condition
8.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.
(a)7 cm
(b)17 cm
(c)13 cm
(d)60 cm
9.A square has sides of length 7 cm. Work out its area.
(a)49 cm²
(b)21 cm²
(c)28 cm²
(d)14 cm²
10.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.
(a)5√2 cm
(b)5√3 cm
(c)10√2 cm
(d)5 cm
11.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?
(a)arc
(b)tangent
(c)chord
(d)radius
12.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.
(a)1 : 3000
(b)1 : 30
(c)1 : 300
(d)1 : 3
13.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)
14.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
(a)£24.00
(b)£2.94
(c)£29.40
(d)£2940.00
15.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).
(a)(9, −5)
(b)(1, 7)
(c)(12, −1)
(d)(7, −2)

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