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 tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.
(a)A tangent always passes through the centre of the circle
(b)A tangent is always parallel to the radius it touches
(c)The angle in a semicircle is 90°
(d)The angle between a tangent and a radius is 90°
2.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.
(a)105°
(b)55°
(c)108°
(d)210°
3.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?
(a)(2, −8)
(b)(6, 2)
(c)(6, 8)
(d)(−2, 8)
4.e is the column vector with top number 5 and bottom number k. f is the column vector with top number 15 and bottom number 6. Given that f is 3 times e, work out the value of k.
(a)18
(b)9
(c)3
(d)2
5.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
6.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
7.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.
(a)96 cm²
(b)24 cm²
(c)16 cm²
(d)64 cm³
8.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.
(a)36 cm
(b)12 cm
(c)7 cm
(d)4 cm
9.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.
(a)180°
(b)60°
(c)90°
(d)45°
10.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) $(11 - 5.2)$
11.A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.
(a)12.6 cm
(b)169 cm
(c)19 cm
(d)13 cm
12.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.
(a)3 cm
(b)6 cm
(c)8 cm
(d)30 cm
13.Triangle J is mapped onto triangle K by a single transformation with centre O. Triangle K is half the size of triangle J and is inverted (turned through 180°). Which of these transformations maps J onto K?
(a)An enlargement, centre O, scale factor −2.
(b)An enlargement, centre O, scale factor −1/2.
(c)A rotation of 180° about O, with no change in size.
(d)An enlargement, centre O, scale factor 1/2.
14.PT is a tangent to a circle with centre O, touching the circle at T. C is a point on the circle such that C lies inside angle OTP (the right angle between the radius OT and the tangent PT), and OC is a radius. Angle TOC = 130°. Work out the size of angle PTC, the angle between the tangent PT and the chord TC.
(a)65°
(b)50°
(c)25°
(d)115°
15.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).
(a)(−3, 3)
(b)(3, −3)
(c)(3, 3)
(d)(7, 5)

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