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Vectors

Secondary 4 practice

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Vectors practice questions

Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Given that a=(n−12)\mathbf{a} = \begin{pmatrix} n \\ -12 \end{pmatrix} and ∣a∣=15|\mathbf{a}| = 15, find the possible values of n.
Show the worked solution
  • ∣a∣=n2+(−12)2=15|\mathbf{a}| = \sqrt{n^2 + (-12)^2} = 15
  • n2+144=225square both sidesn^2 + 144 = 225 \quad \scriptsize\textit{square both sides}
  • n2=225−144n^2 = 225 - 144
  • n2=81n^2 = 81
  • n=±81n = \pm\sqrt{81}
  • n=±9n = \pm 9

Answer: 9,−99,-9

Example 2

Given a=(8−1)\mathbf{a} = \begin{pmatrix} 8 \\ -1 \end{pmatrix}, b=(32)\mathbf{b} = \begin{pmatrix} 3 \\ 2 \end{pmatrix} and c=(10)\mathbf{c} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}, find a+b+c\mathbf{a} + \mathbf{b} + \mathbf{c}.
Show the worked solution
  • a+b+c=(8−1)+(32)+(10)\mathbf{a} + \mathbf{b} + \mathbf{c} = \begin{pmatrix} 8 \\ -1 \end{pmatrix} + \begin{pmatrix} 3 \\ 2 \end{pmatrix} + \begin{pmatrix} 1 \\ 0 \end{pmatrix}
  • =(8+3+1−1+2+0)add corresponding components= \begin{pmatrix} 8 + 3 + 1 \\ -1 + 2 + 0 \end{pmatrix} \quad \scriptsize\textit{add corresponding components}
  • =(121)= \begin{pmatrix} 12 \\ 1 \end{pmatrix}

Answer: 12,112,1

Example 3

Given a=(−43)\mathbf{a} = \begin{pmatrix} -4 \\ 3 \end{pmatrix} and b=(3−3)\mathbf{b} = \begin{pmatrix} 3 \\ -3 \end{pmatrix}, express 2a+3b2\mathbf{a} + 3\mathbf{b} as a column vector.
Show the worked solution
  • 2a=2(−43)=(−86)2\mathbf{a} = 2\begin{pmatrix} -4 \\ 3 \end{pmatrix} = \begin{pmatrix} -8 \\ 6 \end{pmatrix}
  • 3b=3(3−3)=(9−9)3\mathbf{b} = 3\begin{pmatrix} 3 \\ -3 \end{pmatrix} = \begin{pmatrix} 9 \\ -9 \end{pmatrix}
  • 2a+3b=(−86)+(9−9)2\mathbf{a} + 3\mathbf{b} = \begin{pmatrix} -8 \\ 6 \end{pmatrix} + \begin{pmatrix} 9 \\ -9 \end{pmatrix}
  • =(1−3)= \begin{pmatrix} 1 \\ -3 \end{pmatrix}

Answer: 1,−31,-3

Questions parents ask

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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