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 rotation of 180° about the point (3, 2) can be written as a reflection in the line x = 3, followed by a reflection in a second line, for every point in the plane. Which line is the second line?
(a)x = 2
(b)y = 3
(c)y = x
(d)y = 2
2.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.
(a)12 cm²
(b)20 cm²
(c)24 cm²
(d)18 cm²
3.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.
(a)441 cm
(b)21 cm
(c)35 cm
(d)9 cm
4.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?
(a)AB, CD and EF are all parallel
(b)None of the lines are parallel
(c)AB ∥ CD only; EF not confirmed
(d)EF is parallel to AB
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.Shape T has a vertex at (5, 3). T is enlarged by scale factor −1, centre (2, 1). Work out the coordinates of the image of the vertex (5, 3).
(a)(5, 3)
(b)(−1, −1)
(c)(−5, −3)
(d)(9, 5)
7.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.
(a)0.14 cm
(b)1008 cm
(c)3.5 cm
(d)7 cm
8.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
9.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.
(a)4
(b)45
(c)8
(d)315
10.Quadrilateral ABCD has vertices A(1, 1), B(5, 1), C(5, 4) and D(1, 4). The quadrilateral is translated by the vector $(3 - 2)$ . Which of these points is NOT a vertex of the image?
(a)(−1, 1)
(b)(3, 4)
(c)(−1, 4)
(d)(3, 7)
11.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?
(a)Triangle
(b)Trapezium
(c)Square
(d)Pentagon
12.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.
(a)The same as the cylinder's volume
(b)Two thirds of the cylinder's volume
(c)One third of the cylinder's volume
(d)Half the cylinder's volume
13.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.
(a)3.2 cm
(b)16 cm
(c)17 cm
(d)20 cm
14.Two similar bottles have heights in the ratio 1 : 2. Write down the ratio of their volumes.
(a)1 : 8
(b)1 : 4
(c)1 : 6
(d)1 : 2
15.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.
(a)Major segment
(b)Minor segment
(c)Semicircle
(d)Minor arc

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