Watch out
Choosing a method from a remembered keyword instead of reading the whole question.
Back to National 5 Mathematics
SQA National 5 Mathematics
Scalar multiples
Multiplying vectors by constants and interpreting direction.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Read the command word and identify what is being asked.
- Write down the relevant formula, rule or algebraic structure before substituting values.
- Keep working set out line by line so method marks are clear.
Explanation
Scalar multiples is part of Vectors in SQA National 5 Mathematics. The key skill is choosing a method and communicating the working clearly.
For scalar multiples, underline the values or algebraic terms you are given, choose the matching rule, then simplify one line at a time.
National 5 answers should show enough working for a marker to follow the method. Exact answers are expected where the question asks for exact form; otherwise round only at the end.
Key formulae and rules
- Calculator and non-calculator methods may both be useful.
- Vector path rule: AB = b − a when OA = a and OB = b
Check
Check direction and length separately. A correct vector needs both components in the right order.
Exam tip
Method marks come from clear setup and correct mathematical notation, not just a final answer.
Calculator tip
Use brackets for fractions, powers and square roots, then round only at the final line.
Worked examples
Worked example 1
Find a vector from coordinates
A(2, 1) and B(7, 5). Find AB.
- Subtract start from destination.
- AB = (7 − 2, 5 − 1)
Answer: AB = (5, 4)
Worked example 2
Reverse direction
If AB = (5, 4), find BA.
- Reverse the signs of both components.
So: BA = (-5, −4)
Worked example 3
Use position vectors
If OA = a and OB = b, write AB.
- Move from A to O: −a.
- Move from O to B: b.
Answer: AB = b − a
Watch out
- Choosing a method from a remembered keyword instead of reading the whole question.
- Dropping negative signs, powers or brackets during the working.
- Giving a rounded decimal when an exact answer or algebraic form is needed.