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 · 15 questions

MathsUKwww.geekhero.co.uk

1.Point P is translated by the vector (5, −2), and the image is then rotated 90° clockwise about the origin to give the point (3, 9). Work out the coordinates of P.
(a)(−11, −2)
(b)(4, −1)
(c)(−4, 1)
(d)(−14, 5)
2.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.
(a)1000 kg
(b)0.254 kg
(c)0.0625 kg
(d)1 kg
3.A student says the reverse of the translation vector $(- 9 4)$ is $(9 4)$ . Write down the correct reverse translation vector.
(a) $(- 9 - 4)$
(b) $(- 9 4)$
(c) $(9 - 4)$
(d) $(9 4)$
4.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.
(a)4912 cm²
(b)2400 cm²
(c)3028 cm²
(d)3656 cm²
5.Two vertical masts stand on level ground, 40 m apart. One mast is 30 m tall and the other is 50 m tall. Work out the straight-line distance between the tops of the two masts. Give your answer to 1 decimal place.
(a)44.7 m
(b)34.6 m
(c)50.0 m
(d)60.0 m
6.Shape S has an area of 5 cm². Shape S is enlarged by a scale factor of −3 to give shape T. Work out the area of shape T.
(a)−15 cm²
(b)45 cm²
(c)9 cm²
(d)15 cm²
7.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?
(a)Angle D = angle A
(b)BC = 8 cm
(c)EF = 8 cm
(d)DE = 8 cm
8.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.
(a)10√3 m
(b)5/√3 m
(c)5√3 m
(d)5√3/2 m
9.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.
(a)−32
(b)48
(c)32
(d)37
10.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
11.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?
(a)17 cm
(b)0.17 cm
(c)1700 cm
(d)170 cm
12.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?
(a)Square-based pyramid
(b)Cube
(c)Cuboid
(d)Triangular prism
13.A drone starts at the point (3.5, −2) on a grid measured in metres. It flies by the vector $(4.5 - 6.2)$ to check a first sensor. The drone then needs to fly in a straight line to reach the point (−1.7, 9) to check a second sensor. Work out the column vector of this second flight.
(a) $(6.5 1)$
(b) $(- 6.5 - 1)$
(c) $(6.5 - 4.4)$
(d) $(11 - 5.2)$
14.In triangle ABC, AB = 15.6 cm, AC = 8.9 cm and angle BAC = 112°, the angle between them. Work out the area of triangle ABC. Give your answer to 1 decimal place.
(a)128.7 cm²
(b)26.0 cm²
(c)64.4 cm²
(d)112.8 cm²
15.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?
(a)Rhombus
(b)Square
(c)Rectangle
(d)Kite

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