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Cambridge IGCSE Mathematics practice

exam practice - Use Pythagoras’ theorem and trigonometry to perform calculations and solve problems in three-dimensional space, including finding the angle between a line and a plane. - Pythagoras’ theorem and trigonometry

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Topic

Pythagoras’ theorem and trigonometry

Exam-style question

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Paper 2Core or Extended Mathematics3 marks

A line segment AB is drawn in three-dimensional space. Point A is at the origin (0,0,0) and point B is at (3,4,12).

Description

Coordinates of points A and B

Point A is at (0,0,0) and point B is at (3,4,12).

  1. a

    Calculate the length of the line segment AB.

    Aim for approximately 3 distinct marking points.

    [3]

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Maths method check

  • Topic focus: Pythagoras’ theorem and trigonometry.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Pythagoras’ theorem and trigonometry

Paper 2Core or Extended Mathematics4 marks

Description

Line l and its projection

Line l passes through P(2,1,3). The projection of l onto the horizontal plane makes a 45° angle with the x-axis. The segment PQ has length 10 units and vertical height 6 units.

  1. a

    Calculate the angle between line l and the horizontal plane.

    Aim for approximately 4 distinct marking points.

    [4]