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.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.
2.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.
3.A shape is translated by the vector $(- 7 4)$ and then by the vector $(3 - 9)$ . Write down the single column vector that has the same effect as those two translations together.
(a) $(- 4 - 5)$
(b) $(- 10 13)$
(c) $(- 4 - 13)$
(d) $(- 10 - 5)$
4.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?
(a)The length must be written as |AB|, not AB
(b)A different symbol is needed for the length
(c)AB means the segment or its length, shown by context
(d)AB can only mean the segment, never a length
5.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.
(a)0.1 m
(b)2.4 m
(c)7.1 m
(d)0.9 m
6.Two bronze statues are geometrically similar and made from the same solid bronze. Their heights are 30 cm and 45 cm. The smaller statue has a mass of 12 kg. Work out the mass of the larger statue, in kg.
(a)18 kg
(b)27 kg
(c)40.5 kg
(d)54 kg
7.Work out the distance between the point (0, 0) and the point (5, 12).
(a)12
(b)13
(c)17
(d)7
8.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?
(a)4.4
(b)110
(c)11
(d)1.1
9.OABC is a parallelogram, with OA = a and OC = c. X is the point on AC such that AX is a third of XC. Express the vector OX in terms of a and c.
(a)(1/2)a + (1/2)c
(b)(1/4)a + (3/4)c
(c)a + (1/4)c
(d)(3/4)a + (1/4)c
10.A, B, C and D are points on a circle with centre O, in that order around the circle. B lies on the major arc AC, and angle AOC = 152°. In triangle ACD, angle ACD = 30°. Work out the size of angle DAC.
(a)46°
(b)74°
(c)76°
(d)122°
11.A transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.
(a)19
(b)10
(c)20
(d)14
12.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?
(a)No — any two angles enough alone
(b)Yes — third angle may differ
(c)Yes — side must be included
(d)No — third angle is also fixed
13.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.
(a)chord
(b)segment
(c)semicircle
(d)sector
14.A ferris wheel's circular frame has centre O. A support strut runs from O to a point A on the rim, and a second strut runs from O to point B on the rim, with angle AOB = 76°. A cabin is mounted at point C on the major arc AB, and D is a separate point on the minor arc AB. Work out the difference between angle ACB and angle ADB.
(a)104°
(b)38°
(c)180°
(d)142°
15.Two similar model cars have a length scale factor of 2 from the small model to the large model. Priya works out that the area scale factor is 2² = 4, and then says the volume scale factor must also be 4, since that is the number she just calculated. Is Priya correct?
(a)Yes — area and volume always scale by the same factor.
(b)Yes — the volume factor is also 2² = 4, just like area.
(c)No — but the volume factor is 6, from 2 × 3 dimensions.
(d)No — the volume factor is 2³ = 8, not the area factor 4.

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