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.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.
(a)1600
(b)500
(c)8
(d)16
2.A support strut for a shed roof is in the shape of a right-angled triangle. The two shorter sides of the strut are 5 m and 9 m. Work out the length of the sloping strut (the hypotenuse). Give your answer correct to 1 decimal place.
(a)106 m
(b)10.2 m
(c)14 m
(d)10.3 m
3.A, B and C are points on a circle with centre O. B is on the minor arc AC. Angle ABC = 100°. Work out the size of the non-reflex angle AOC.
(a)200°
(b)160°
(c)50°
(d)80°
4.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.
(a)8,000,000 cm³
(b)8,000 cm³
(c)8 cm³
(d)80,000 cm³
5.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
(a)3
(b)7
(c)14
(d)5
6.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.
y = x
(a)(−7, −3)
(b)(7, 3)
(c)(−3, 7)
(d)(3, −7)
7.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?
(a)080°
(b)100°
(c)180°
(d)440°
8.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.
(a)16 cm³
(b)96 cm³
(c)144 cm³
(d)288 cm³
9.A student is asked to rearrange the cosine rule a² = b² + c² − 2bc cos A to make cos A the subject. They write: cos A = (a² − b² − c²) / (2bc). Is the student's rearrangement correct?
(a)Yes — the sign does not matter for cos A.
(b)No — should divide by −2bc, not +2bc; sign is wrong.
(c)No — the denominator should be bc, not 2bc.
(d)Yes — the rearrangement is correct as written.
10.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.
(a)£2.50
(b)£5.00
(c)£325.00
(d)£3.25
11.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?
(a)A reflection in the y-axis
(b)A reflection in the x-axis
(c)A rotation of 180° about the origin
(d)No transformation — the shape is unchanged
12.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.
(a)20
(b)22
(c)18
(d)16
13.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.
(a)17
(b)7
(c)144
(d)13
14.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.
(a)60 g
(b)430 g
(c)460 g
(d)403 g
15.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°

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