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Exam questions · Maths · Vectors, Constructions and Loci

Bearings, Scale Drawings, Plans and Elevations

  • 6 exam questions
  • 18 marks
  • 9 quick checks
  1. 1 Write down [2 marks]

    Write down the three-figure bearing of (a) east, (b) south-west.

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    Model answer

    (a) \(090^\circ\). (b) South is \(180^\circ\) and west is \(270^\circ\), so south-west is halfway: \(225^\circ\).

    Mark scheme

    • (a) \(090^\circ\) — B1
    • (b) \(225^\circ\) — B1
  2. 2 Work out [4 marks]

    The diagram shows three towns \(A\), \(B\) and \(C\). The bearing of \(B\) from \(A\) is \(070^\circ\). The bearing of \(C\) from \(B\) is \(150^\circ\). (a) Work out the bearing of \(A\) from \(B\). (2 marks) (b) Work out the size of angle \(ABC\). (2 marks)

    A diagram of three towns A, B and C with north lines drawn at A and B.
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    Model answer

    (a) \(070 + 180 = 250\), so the bearing is \(250^\circ\). (b) The bearing of \(A\) from \(B\) is \(250^\circ\) and the bearing of \(C\) from \(B\) is \(150^\circ\), so angle \(ABC = 250 - 150 = 100^\circ\).

    Mark scheme

    • (a) \(070 + 180\) or parallel north lines — M1
    • (a) \(250^\circ\) — A1
    • (b) \(250 - 150\) — M1
    • (b) \(100^\circ\) — A1
  3. 3 Work out [2 marks]

    The bearing of \(B\) from \(A\) is \(130^\circ\). Work out the bearing of \(A\) from \(B\).

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    Model answer

    \(130 + 180 = 310\), so the bearing is \(310^\circ\).

    Mark scheme

    • \(130 + 180\) — M1
    • \(310^\circ\) — A1
  4. 4 Work out [3 marks]

    A map has a scale of 1 : 50 000. (a) Two villages are 4 cm apart on the map. Work out the real distance in kilometres. (2 marks) (b) Two other villages are 7.5 km apart. How far apart are they on the map? (1 mark)

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    Model answer

    (a) \(4 \times 50\,000 = 200\,000\) cm \(= 2\) km. (b) \(7.5\) km \(= 750\,000\) cm, and \(750\,000 \div 50\,000 = 15\) cm.

    Mark scheme

    • (a) \(4 \times 50\,000\) — M1
    • (a) 2 km — A1
    • (b) 15 cm — B1
  5. 5 Write down [3 marks]

    A cuboid is 4 cm long, 3 cm wide and 2 cm high. Write down the dimensions of (a) its plan, (b) its front elevation, looking along the 3 cm width, (c) its side elevation, looking along the 4 cm length.

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    Model answer

    (a) The plan is a rectangle 4 cm by 3 cm. (b) The front elevation shows the length and the height, a rectangle 4 cm by 2 cm. (c) The side elevation shows the width and the height, a rectangle 3 cm by 2 cm.

    Mark scheme

    • (a) 4 cm by 3 cm — B1
    • (b) 4 cm by 2 cm — B1
    • (c) 3 cm by 2 cm — B1
  6. 6 Work out [4 marks]

    \(B\) is 5 km from \(A\) on a bearing of \(030^\circ\). \(C\) is 5 km from \(B\) on a bearing of \(150^\circ\). (a) Work out the size of angle \(ABC\). (2 marks) (b) Work out the bearing of \(C\) from \(A\). (2 marks)

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    Model answer

    (a) The bearing of \(A\) from \(B\) is \(030 + 180 = 210^\circ\), and the bearing of \(C\) from \(B\) is \(150^\circ\), so angle \(ABC = 210 - 150 = 60^\circ\). (b) Triangle \(ABC\) is isosceles with a \(60^\circ\) angle, so it is equilateral, and angle \(BAC = 60^\circ\). The bearing of \(C\) from \(A\) is \(030 + 60 = 090^\circ\).

    Mark scheme

    • (a) \(210\) seen — M1
    • (a) \(60^\circ\) — A1
    • (b) Triangle is equilateral, or angle \(BAC = 60^\circ\) — M1
    • (b) \(090^\circ\) — A1

Quick check

  1. 1

    What is the bearing of east?

    1. A\(000^\circ\)
    2. B\(090^\circ\)
    3. C\(180^\circ\)
    4. D\(270^\circ\)
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    B: \(090^\circ\)

    North is 000, east is 090, south is 180 and west is 270.

  2. 2

    What is the bearing of south?

    1. A\(180^\circ\)
    2. B\(090^\circ\)
    3. C\(270^\circ\)
    4. D\(360^\circ\)
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    A: \(180^\circ\)

    South is half a turn from north.

  3. 3

    The bearing of \(B\) from \(A\) is \(130^\circ\). What is the bearing of \(A\) from \(B\)?

    1. A\(050^\circ\)
    2. B\(130^\circ\)
    3. C\(230^\circ\)
    4. D\(310^\circ\)
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    D: \(310^\circ\)

    Add \(180^\circ\): \(130 + 180 = 310\).

  4. 4

    The bearing of \(B\) from \(A\) is \(072^\circ\). What is the bearing of \(A\) from \(B\)?

    1. A\(108^\circ\)
    2. B\(072^\circ\)
    3. C\(252^\circ\)
    4. D\(288^\circ\)
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    C: \(252^\circ\)

    Add \(180^\circ\): \(072 + 180 = 252\).

  5. 5

    The bearing of \(B\) from \(A\) is \(250^\circ\). What is the bearing of \(A\) from \(B\)?

    1. A\(110^\circ\)
    2. B\(070^\circ\)
    3. C\(430^\circ\)
    4. D\(250^\circ\)
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    B: \(070^\circ\)

    Subtract \(180^\circ\): \(250 - 180 = 70\), written as 070.

  6. 6

    From where, and in which direction, is a bearing measured?

    1. AClockwise from the north line
    2. BAnticlockwise from north
    3. CClockwise from east
    4. DAnticlockwise from the path
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    A: Clockwise from the north line

    Bearings are measured clockwise from north.

  7. 7

    A map has a scale of \(1 : 25\,000\). Two towns are 6 cm apart on the map. What is the real distance?

    1. A15 km
    2. B150 km
    3. C150 m
    4. D1.5 km
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    D: 1.5 km

    \(6 \times 25\,000 = 150\,000\) cm \(= 1.5\) km.

  8. 8

    A plan has a scale of \(1 : 1000\). A length of 5 cm on the plan is how long in real life?

    1. A5 m
    2. B500 m
    3. C50 m
    4. D5 km
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    C: 50 m

    \(5 \times 1000 = 5000\) cm \(= 50\) m.

  9. 9

    What is the plan of a solid?

    1. AThe view from the front
    2. BThe view from above
    3. CThe view from the side
    4. DThe view from below
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    B: The view from above

    A plan is a view looking straight down.