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 · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².
(a)384 cm²
(b)38 cm²
(c)3070 cm²
(d)1535 cm²
2.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.
(a)615.44 cm²
(b)1436.03 cm³
(c)153.86 cm²
(d)87.92 cm²
3.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector $(- 9 6)$ to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
(a) $(- 2 8)$
(b) $(- 7 - 2)$
(c) $(7 2)$
(d) $(- 7 4)$
4.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?
(a)SAS
(b)RHS
(c)ASA
(d)SSS
5.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.
(a)37.68 cm²
(b)1808.64 cm²
(c)150.72 cm²
(d)452.16 cm²
6.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?
(a)320
(b)180
(c)295
(d)310
7.A triangular field ABC is to be fenced all the way round. AB = 45 m, AC = 38 m and angle BAC = 110°. Fencing costs £6.50 per metre. Work out the total cost of the fencing. Give your answer to the nearest penny.
(a)£851.18
(b)£151.11
(c)£442.70
(d)£982.20
8.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?
(a)335°
(b)025°
(c)155°
(d)065°
9.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?
(a)Yes, it folds into a cube
(b)No, it needs one more square
(c)No, it has one square too many
(d)Yes, but only if two squares overlap
10.In triangle PQR, PQ = 8 cm and QR = 11 cm. Angle QPR = 50°. A student calculates the area of the triangle as Area = 1/2 × 8 × 11 × sin 50°. Is the student's method correct?
(a)Yes — any angle works with any two sides.
(b)Yes — PQ and QR are the arms of angle QPR.
(c)No — 50° is angle P, not between PQ and QR.
(d)No — the formula needs all three sides.
11.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.
(a)£30.00
(b)£26.25
(c)£25.00
(d)£52.50
12.Shape S is enlarged by a scale factor of −3 about a fixed centre. Which statement correctly describes the image compared to the original shape?
(a)3 times the size, opposite side, rotated 180°
(b)3 times the size, same side as the original
(c)3 times the size, same orientation, just further away
(d)1/3 the size, opposite side of the centre
13.A footpath is 3750 m long. Work out this distance in kilometres.
(a)3.75 km
(b)0.375 km
(c)37.5 km
(d)375 km
14.In triangle ABC, angle BAC = 42°, angle ABC = 63° and BC = 8.4 cm. Work out the length of AC. Give your answer to 1 decimal place.
(a)6.3 cm
(b)12.6 cm
(c)11.2 cm
(d)12.1 cm
15.Point P has coordinates (2, 1). Transformation A reflects a point in the x-axis. Transformation B translates a point by the vector (0, 4). Work out the coordinates of the image of P when A is applied first, followed by B.
(a)(2, −5)
(b)(2, 3)
(c)(2, 5)
(d)(2, −1)

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