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 parallelogram-shaped tile has two sides of 6 cm and 9 cm, with an angle of 60° between them. Work out the area of the tile. Give your answer to 1 decimal place.
(a)27.0 cm²
(b)46.8 cm²
(c)13.0 cm²
(d)23.4 cm²
2.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.
(a)17.5 cm
(b)24 cm
(c)12 cm
(d)6 cm
3.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.
(a)40 cm²
(b)120 cm²
(c)24 cm²
(d)15 cm²
4.Triangle S has vertices (2, 2), (5, 2) and (2, 5). It is mapped onto triangle S′ with vertices (2, 5), (5, 5) and (2, 2). Which single composition of two transformations maps S onto S′?
(a)Reflect in the x-axis, then translate by (0, 7).
(b)Reflect in the x-axis, then translate by (7, 0).
(c)Reflect in the y-axis, then translate by (0, 7).
(d)Rotate 180° about the origin, then translate by (0, 7).
5.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
(a)2
(b)−2
(c)8
(d)0.5
6.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.
(a)(3, −4)
(b)(3, −1)
(c)(3, −5)
(d)(−3, 5)
7.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
(a)(5, 7)
(b)(2, 2)
(c)(4, 8)
(d)(6, 10)
8.A tent has the cross-section of a right-angled triangle. The sloping side of the cross-section is 10 m long, and it makes an angle of 60° with the horizontal ground. Using the exact value of cos 60°, work out the horizontal distance covered by the sloping side.
(a)8.7 m
(b)20 m
(c)5 m
(d)10 m
9.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.
(a)Major arc
(b)Minor segment
(c)Chord
(d)Minor arc
10.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
(a)Angles in a triangle sum to 180°
(b)Angles on a straight line sum to 180°
(c)Vertically opposite angles are equal
(d)Base angles of an isosceles triangle are equal
11.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.
(a)9
(b)4.5
(c)18
(d)90
12.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.
(a)44
(b)22
(c)10
(d)5.5
13.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.
(a)7 cm³
(b)70 cm³
(c)35 cm³
(d)140 cm³
14.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?
(a)No — the angle is not between the two sides
(b)Yes — SSS, since three measurements are given
(c)Yes — SAS, since two sides and an angle match
(d)No — because only two sides were measured
15.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1

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