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Cambridge IGCSE Mathematics practice

exam practice - 1. Depict vectors using directed line segments. 2. Apply position vectors. 3. Utilize the addition and subtraction of multiple vectors to express specified vectors in relation to two coplanar vectors. 4. Employ vectors for reasoning and resolving geometric problems, such as demonstrating that vectors are parallel, proving that three points are collinear, and tackling vector problems that involve ratios and similarity. - Vector geometry

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Topic

Vector geometry

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Paper 2Core or Extended Mathematics3 marks

Vectors and Geometry

Diagram Description

Triangle with position vectors

Points A and B have position vectors \( \vec{a} \) and \( \vec{b} \) respectively relative to the origin O. Point C lies on the line segment AB such that AC:CB = 2:1.

PointPosition Vector
A\( \vec{a} \)
B\( \vec{b} \)
C?
  1. a

    Calculate Find the position vector of point C in terms of \( \vec{a} \) and \( \vec{b} \).

    Aim for approximately 3 distinct marking points.

    [3]

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Maths method check

  • Topic focus: Vector geometry.
  • 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: Vector geometry

Paper 2Core or Extended Mathematics4 marks

Diagram Description

Points and vectors

Points P, Q, and R have position vectors \( \vec{p} \), \( \vec{q} \), and \( \vec{r} \) respectively. It is given that \( \vec{r} = \vec{p} + 2(\vec{q} - \vec{p}) \).

PointPosition Vector
P\( \vec{p} \)
Q\( \vec{q} \)
R\( \vec{r} \)
  1. a

    Show That points P, Q, and R are collinear.

    Aim for approximately 4 distinct marking points.

    [4]