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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) south, (b) north-west. [2 marks]

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    Model answer

    (a) \(180^\circ\). (b) North is \(000^\circ\) (or \(360^\circ\)) and west is \(270^\circ\), so north-west is \(315^\circ\).

    Mark scheme

    • (a) \(180^\circ\) — B1
    • (b) \(315^\circ\) — B1
  2. 2 Work out [4 marks]

    The diagram shows three towns \(A\), \(B\) and \(C\). The bearing of \(B\) from \(A\) is \(125^\circ\). The bearing of \(C\) from \(B\) is \(215^\circ\). (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) \(125 + 180 = 305\), so the bearing is \(305^\circ\). (b) The bearing of \(A\) from \(B\) is \(305^\circ\) and the bearing of \(C\) from \(B\) is \(215^\circ\), so angle \(ABC = 305 - 215 = 90^\circ\).

    Mark scheme

    • (a) \(125 + 180\) — M1
    • (a) \(305^\circ\) — A1
    • (b) \(305 - 215\) — M1
    • (b) \(90^\circ\) — A1
  3. 3 Work out [2 marks]

    The bearing of \(Q\) from \(P\) is \(072^\circ\). Work out the bearing of \(P\) from \(Q\). [2 marks]

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    Model answer

    \(072 + 180 = 252\), so the bearing is \(252^\circ\).

    Mark scheme

    • \(072 + 180\) — M1
    • \(252^\circ\) — A1
  4. 4 Work out [3 marks]

    A scale drawing has a scale of 1 : 25 000. [3 marks] (a) Two points are 6 cm apart on the drawing. Work out the real distance in kilometres. [2 marks] (b) A real distance is 3 km. How long is it on the drawing? [1 mark]

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    Model answer

    (a) \(6 \times 25\,000 = 150\,000\) cm \(= 1.5\) km. (b) \(3\) km \(= 300\,000\) cm, and \(300\,000 \div 25\,000 = 12\) cm.

    Mark scheme

    • (a) \(6 \times 25\,000\) — M1
    • (a) 1.5 km — A1
    • (b) 12 cm — B1
  5. 5 Write down [3 marks]

    A cuboid is 5 cm long, 2 cm wide and 3 cm high. Write down the dimensions of (a) its plan, (b) its front elevation, looking along the 2 cm width, (c) its side elevation, looking along the 5 cm length. [3 marks]

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    Model answer

    (a) The plan is 5 cm by 2 cm. (b) The front elevation is 5 cm by 3 cm. (c) The side elevation is 2 cm by 3 cm.

    Mark scheme

    • (a) 5 cm by 2 cm — B1
    • (b) 5 cm by 3 cm — B1
    • (c) 2 cm by 3 cm — B1
  6. 6 Work out [4 marks]

    A ship sails 10 km from \(P\) to \(Q\) on a bearing of \(060^\circ\). It then sails 10 km from \(Q\) to \(R\) on a bearing of \(180^\circ\). (a) Work out the size of angle \(PQR\). [2 marks] (b) Work out the bearing of \(P\) from \(R\), given that triangle \(PQR\) is isosceles. [2 marks]

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    Model answer

    (a) The bearing of \(P\) from \(Q\) is \(060 + 180 = 240^\circ\), and the bearing of \(R\) from \(Q\) is \(180^\circ\), so angle \(PQR = 240 - 180 = 60^\circ\). (b) With \(QP = QR\) and a \(60^\circ\) angle, the triangle is equilateral, so angle \(QRP = 60^\circ\). From \(R\), \(Q\) is due north (\(000^\circ\)) and \(P\) is \(60^\circ\) to the west of north, so the bearing of \(P\) from \(R\) is \(360 - 60 = 300^\circ\).

    Mark scheme

    • (a) \(240\) seen — M1
    • (a) \(60^\circ\) — A1
    • (b) Equilateral, so angle \(QRP = 60^\circ\) — M1
    • (b) \(300^\circ\) — 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.