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 drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.
(a)(−35, 55)
(b)(35, −55)
(c)(−35, −55)
(d)(35, 55)
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 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
4.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.
(a)6 cm
(b)21 cm
(c)12 cm
(d)7.5 cm
5.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.
(a)8100 minutes
(b)25 minutes
(c)2.5 minutes
(d)25 000 minutes
6.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.
(a)£50.24
(b)£25.12
(c)£200.96
(d)£100.48
7.A drone starts at the point (2, −3) on a coordinate grid. It flies by the vector $(4 6)$ and then by the vector $(- 9 - 1)$ . Write down the column vector that would take the drone straight back to its starting point.
(a) $(- 5 - 5)$
(b) $(5 - 5)$
(c) $(- 5 5)$
(d) $(- 13 - 7)$
8.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
(a)30°
(b)150°
(c)15°
(d)36°
9.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
(a)sin 30°
(b)tan 0°
(c)cos 45°
(d)sin 90°
10.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
11.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.
(a)56°
(b)146°
(c)34°
(d)124°
12.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.
(a)62°
(b)59°
(c)90°
(d)118°
13.Point P has coordinates (4, 2). P is rotated 90° clockwise about the point (1, 1), and the image is then reflected in the line x = 1. Work out the coordinates of the final image of P.
(a)(−2, 2)
(b)(2, −2)
(c)(2, 4)
(d)(0, −2)
14.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)
15.A trapezium has vertices (0, 2), (4, 2), (3, 5) and (1, 5). It is rotated 180° about the point (2, 2), and the image is then translated by the vector (1, −5). Work out the coordinates of the image of (0, 2).
(a)(1, −7)
(b)(5, −3)
(c)(3, 7)
(d)(4, 2)

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