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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Geometry and measures worksheet — GCSE Higher

Maths · GCSE Higher · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.A triangular plot of land has sides AB = 13 m and AC = 10 m, with angle BAC = 72° between them. Work out the perimeter of the plot. Give your answer to 1 decimal place.
(a)39.7 m
(b)26.7 m
(c)36.7 m
(d)41.7 m
2.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.
(a)242
(b)62
(c)118
(d)28
3.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.
(a)45 m
(b)4500 m
(c)450 m
(d)0.45 m
4.A solid is built from centimetre cubes: a base layer of 2 rows of 3 cubes each (a 3 by 2 rectangle of cubes), with one extra cube placed on top of one corner cube of that base. Looking down from directly above (the plan view), how many squares are visible?
(a)3
(b)5
(c)7
(d)6
5.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
(a)vertically opposite angles are equal
(b)corresponding angles are equal
(c)base angles of an isosceles triangle are equal
(d)angles in a triangle add up to 180°
6.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?
(a)0
(b)2
(c)4
(d)1
7.From an external point P, two tangents PA and PB touch a circle with centre O at the points A and B. Angle APB = 50°. Work out the size of angle OAB.
(a)25°
(b)65°
(c)50°
(d)70°
8.Triangle A has vertices (2, 1), (5, 1) and (2, 4). It is translated by the vector (−3, 2) and the image is then reflected in the x-axis. Work out the coordinates of the image of (5, 1).
(a)(2, 1)
(b)(2, 3)
(c)(2, −3)
(d)(5, −1)
9.Triangle T has a vertex A at (3, 1). It is enlarged by a scale factor of −2, centre (1, 1). Work out the coordinates of the image of point A.
(a)(−6, −2)
(b)(5, 1)
(c)(−3, 1)
(d)(2, 1)
10.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector $(- 9 6)$ to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
(a) $(- 2 8)$
(b) $(- 7 - 2)$
(c) $(7 2)$
(d) $(- 7 4)$
11.Point P has coordinates (2, 1). Transformation A reflects a point in the x-axis. Transformation B translates a point by the vector (0, 4). Work out the coordinates of the image of P when A is applied first, followed by B.
(a)(2, −5)
(b)(2, 3)
(c)(2, 5)
(d)(2, −1)
12.A shape is translated by the vector (5, −3), and the image is then translated by the vector (−5, 3). Which single transformation has the same overall effect as this combination, for every point?
(a)A reflection in the x-axis
(b)A translation by the vector (10, −6)
(c)A rotation of 180° about the origin
(d)No transformation — every point stays exactly where it was
13.A, B and C are points on a circle with centre O. B is on the minor arc AC. Angle ABC = 100°. Work out the size of the non-reflex angle AOC.
(a)200°
(b)160°
(c)50°
(d)80°
14.In geometry, which of the following best describes a 'plane'?
(a)A flat surface extending infinitely in two directions
(b)A straight line extending in one direction
(c)A single, fixed position with no size
(d)A flat, bounded face on a 3D shape
15.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
(a)1
(b)5
(c)0
(d)6

Build your own mix at the worksheet builder.