Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher 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 Higher

Maths · GCSE Higher · Geometry and measures · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.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
2.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)
3.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.
(a)0.2 hours
(b)25 hours
(c)5 hours
(d)125 hours
4.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.
(a)105°
(b)55°
(c)108°
(d)210°
5.A jug holds 750 ml of water. Work out what fraction of a litre this is.
(a)3/4
(b)1/4
(c)4/3
(d)3/10
6.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
(a)11
(b)13
(c)22
(d)15
7.Which of these statements about the area formula Area = 1/2ab sin C is correct?
(a)AB, BC and angle ABC: Area = 1/2 × AB × BC × sin(BAC)
(b)Three sides, no angle: Area still = 1/2 AB×AC×sin(BAC)
(c)AB, AC and angle BAC: Area = 1/2 × AB × AC × sin(BAC)
(d)AB, AC and angle ABC: Area = 1/2 × AB × AC × sin(ABC)
8.A point is translated twice by the vector $(5 - 3)$ . Write down the single column vector that describes the overall translation.
(a) $(5 - 3)$
(b) $(10 - 6)$
(c) $(5 - 6)$
(d) $(15 - 9)$
9.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.
(a)27 cm
(b)45 cm
(c)15 cm
(d)11 cm
10.A vertical line passes through the point (5, 2). Write down the equation of this line.
(a)x = 2
(b)x = 5
(c)y = 2
(d)y = 5
11.Point A(1, 2) is enlarged to give image point A′(7, −4). The centre of enlargement lies on the x-axis. Work out the scale factor of the enlargement.
(a)−2
(b)3
(c)2
(d)−1/2
12.A, B and C are points on a circle with centre O. B is on the major arc AC. Angle AOC = (4x + 20)°. Work out the size of angle ABC in terms of x, in its simplest form.
(a)(4x + 20)°
(b)(2x + 10)°
(c)(8x + 40)°
(d)(4x + 10)°
13.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.
(a)16 cm³
(b)96 cm³
(c)144 cm³
(d)288 cm³
14.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.
(a)65°
(b)115°
(c)25°
(d)295°
15.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
(a)17
(b)24
(c)15
(d)7.5

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