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 triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.
(a)120 units²
(b)60 units²
(c)30 units²
(d)65 units²
2.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.
(a)33
(b)11
(c)36
(d)35
3.Which of these statements about solving a triangle is correct?
(a)Two sides + a non-included angle: cosine rule gives the angle directly.
(b)Two sides + angle between them: use the sine rule.
(c)All three sides: use the sine rule for any angle.
(d)Two angles and a side: sine rule finds other sides.
4.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.
(a)10.4 cm
(b)4.0625 cm
(c)9.5 cm
(d)13 cm
5.Points A, B, C and D lie on a circle with centre O, in that order around the circle, and AC is a diameter. Which of the following circle facts does NOT apply to this diagram?
(a)Angle at the centre = twice angle at circumference.
(b)Opposite angles of a cyclic quadrilateral sum to 180°.
(c)Tangent-chord angle = angle in the alternate segment.
(d)Angle in a semicircle = 90°.
6.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.
(a)35 cm
(b)7 cm
(c)2.33 cm
(d)21 cm
7.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?
(a)ABC ≅ ZXY
(b)ABC ≅ ZYX
(c)ABC ≅ XYZ
(d)ABC ≅ YXZ
8.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.
(a)12 cm
(b)486 cm
(c)6 cm
(d)45 cm
9.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
10.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.
(a)1 : 3000
(b)1 : 30
(c)1 : 300
(d)1 : 3
11.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.
(a)SSS
(b)SAS
(c)RHS
(d)AAS
12.A cube has all of its edges the same length. How many planes of symmetry does it have?
(a)9
(b)6
(c)12
(d)3
13.To prove that the angle at the centre is twice the angle at the circumference, a student draws radii OA and OC, where A and C are points on the circle and O is the centre. The student's first step is: 'Since OA = OC, both being radii of the circle, triangle OAC is isosceles, so angle OAC = angle OCA.' Is this first step correct?
(a)No — radii are equal only to the very same point.
(b)Yes — OA = OC (radii), so the base angles are equal.
(c)No — it needs AC equal too, making it equilateral.
(d)Yes — angle AOC = 90°, so it is automatically isosceles.
14.Which of these statements about the area formula Area = 1/2ab sin C is correct?
(a)AB, BC and angle ABC: Area = 1/2 × AB × BC × sin(BAC)
(b)Three sides, no angle: Area still = 1/2 AB×AC×sin(BAC)
(c)AB, AC and angle BAC: Area = 1/2 × AB × AC × sin(BAC)
(d)AB, AC and angle ABC: Area = 1/2 × AB × AC × sin(ABC)
15.A circle with centre O has radius 17 cm. A chord AB is drawn so that the perpendicular distance from O to AB is 8 cm. Work out the length of the chord AB.
(a)15 cm
(b)30 cm
(c)25 cm
(d)9 cm

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