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

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    Model answer

    (a) \(270^\circ\). (b) North-east is halfway between north and east, \(045^\circ\).

    Mark scheme

    • (a) \(270^\circ\) — B1
    • (b) \(045^\circ\) — B1
  2. 2 Calculate [4 marks]

    The diagram shows two points \(A\) and \(B\). On a map, \(AB\) is 4 cm and the scale is 1 : 50 000. The bearing of \(B\) from \(A\) is \(240^\circ\). (a) Calculate the bearing of \(A\) from \(B\). [2 marks] (b) Calculate the real distance \(AB\) in kilometres. [2 marks]

    A diagram of two points A and B with north lines at both points.
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    Model answer

    (a) The bearing is more than \(180^\circ\), so subtract: \(240 - 180 = 60\), written \(060^\circ\). (b) \(4 \times 50\,000 = 200\,000\) cm \(= 2\) km.

    Mark scheme

    • (a) \(240 - 180\) — M1
    • (a) \(060^\circ\) — A1
    • (b) \(4 \times 50\,000\) — M1
    • (b) 2 km — A1
  3. 3 Calculate [2 marks]

    The bearing of \(B\) from \(A\) is \(250^\circ\). Calculate the bearing of \(A\) from \(B\). [2 marks]

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    Model answer

    \(250 - 180 = 70\), so the bearing is \(070^\circ\).

    Mark scheme

    • \(250 - 180\) — M1
    • \(070^\circ\) — A1
  4. 4 Calculate [3 marks]

    A plan is drawn with a scale of 1 : 200. [3 marks] (a) A wall is 6 cm long on the plan. Calculate its real length in metres. [2 marks] (b) A room is 8 m long. Calculate its length on the plan. [1 mark]

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    Model answer

    (a) \(6 \times 200 = 1200\) cm \(= 12\) m. (b) \(8\) m \(= 800\) cm, and \(800 \div 200 = 4\) cm.

    Mark scheme

    • (a) \(6 \times 200\) — M1
    • (a) 12 m — A1
    • (b) 4 cm — B1
  5. 5 Write down [3 marks]

    A triangular prism has a base of 6 cm and a height of 4 cm in its triangular face, and the prism is 10 cm long. It lies on a rectangular face. Write down the dimensions of (a) its plan, (b) its elevation from the end, (c) its elevation from the side. [3 marks]

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    Model answer

    (a) The plan is a rectangle 6 cm by 10 cm. (b) The elevation from the end is the triangle, with base 6 cm and height 4 cm. (c) The elevation from the side is a rectangle 10 cm by 4 cm.

    Mark scheme

    • (a) A rectangle 6 cm by 10 cm — B1
    • (b) A triangle with base 6 cm and height 4 cm — B1
    • (c) A rectangle 10 cm by 4 cm — B1
  6. 6 Calculate [4 marks]

    \(B\) is on a bearing of \(090^\circ\) from \(A\), and \(AB = 8\) km. \(C\) is on a bearing of \(180^\circ\) from \(B\), and \(BC = 6\) km. (a) Calculate the length \(AC\). [2 marks] (b) Write down the bearing of \(A\) from \(B\). [1 mark] (c) Write down the angle \(ABC\). [1 mark]

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    Model answer

    (a) Angle \(ABC = 90^\circ\), so \(AC^2 = 8^2 + 6^2 = 100\) and \(AC = 10\) km. (b) \(090 + 180 = 270^\circ\). (c) The bearing of \(A\) from \(B\) is \(270^\circ\) and the bearing of \(C\) from \(B\) is \(180^\circ\), so angle \(ABC = 270 - 180 = 90^\circ\).

    Mark scheme

    • (a) \(8^2 + 6^2\) — M1
    • (a) 10 km — A1
    • (b) \(270^\circ\) — B1
    • (c) \(90^\circ\) — B1

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.