|
|
Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | IGCSE Extended |
(a) If A is the point (3,5) write down the position vector of A.
(b) If B is the point (6,9) find \(\mid\overrightarrow{AB} \mid\) the magnitude of \( \overrightarrow{AB}\).
The following diagram is not to scale.
\(O\) is the origin, \(\overrightarrow{OP}=p\) and = \(\overrightarrow{OQ}=q\).
\(OP\) is extended to \(R\) so that \(OP=PR\).
\(OQ\) is extended to \(S\) so that \(OQ=QS\).
(c) Write down \(\overrightarrow{RQ}\) in terms of \(p\) and \(q\).
(d) \(PS\) and \(RQ\) intersect at \(M\) and \(RM=2 MQ\).
Use vectors to find the ratio \(PM:PS\), showing all your working.
2. | IB Standard |
Two points \(A\) and \(B\) have coordinates (1 , 3 , 6) and (8 , 7 , 10) respectively.
(a) Find \( \overrightarrow{AB} \) in terms of the unit vectors \(i, j\) and \(k\).
(b) Find \(\mid\overrightarrow{AB} \mid\)
Let \( \overrightarrow{AC} = 5i + 2j - k\)
(c) Find the angle between \(AB\) and \(AC\).
(d) Find the area of triangle \(ABC\).
(e) Hence or otherwise find the shortest distance from \(C\) to the line through \(A\) and \(B\).
3. | IB Analysis and Approaches |
Consider the vectors \(\mathbf{a}\) and \(\mathbf{b}\) such that \(\mathbf{a} = \begin{pmatrix} 16 \\ -12 \end{pmatrix} \) and \( |\mathbf{b}| = 11\).
(a) Find the possible range of values for \(|\mathbf{a+b}|\).
Consider the vector \(\mathbf{p}\) such that \(\mathbf{p=a+b}\).
(b) Given that \(|\mathbf{a+b}|\) is a minimum, find \(\mathbf{p}\).
Consider the vector q such that \(\mathbf{q} = \begin{pmatrix}x \\ y \end{pmatrix} \) , where \(x,y \in \mathbb{R} \).
(c) Find \(\mathbf{q}\) such that \(\mathbf{|q| = |b|}\) and \(\mathbf{q}\) is perpendicular to \(\mathbf{a}\).
If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
The solutions to the questions on this website are only available to those who have a Transum Subscription.
Exam-Style Questions Main Page
To search the entire Transum website use the search box in the grey area below.
Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
