Build the vector by following a route
Any required vector is a sum of journeys: , where . Express everything in the given base vectors and , then collect terms.
Use the section/midpoint formula
If divides with then . The midpoint is the special case .
Parallel ⇔ scalar multiple
means is parallel to and times its length; if they also share a point, the points are collinear. This is how vector "proofs" are argued.
Drawn from real examiner reports.
Sloppy notation — equating vectors to scalars
Writing a vector equal to a number, or dividing one vector by another, loses the communication marks on a top-grade question.
Reported on Nov 2024 Paper 1H (Q24): "a complete mixture of inaccurate notation, with vectors put equal to scalars and vectors divided by vectors … essential that students … use correct notation for vectors."
Sign errors and missing brackets
Dropping a bracket when expanding something like flips a sign and ruins the simplification.
Reported on Nov 2024 Paper 1H (Q24): "many errors were seen, especially with signs and missing brackets."
Assuming a false relationship between vectors
Guessing e.g. instead of finding two genuinely independent expressions for the same vector and equating them.
Reported on June 2024 Paper 2H (Q24): "Some students made incorrect assumptions, such as OQ = 2OP … Those that could write OQ in two different ways often resulted in a correct outcome."
Wrong order for AB (it is b − a)
Going from A to B through O gives . Writing instead gives , the reverse vector — every later sign then comes out wrong.
AO = −OA: keep the sign
When a route passes through the origin, . Dropping the minus sign on this reversal is a very common slip that changes the whole simplified answer.
Section ratio m:n gives m/(m+n)
For , — the fraction is , not . Using is the most common ratio error on these parts.
Find the same vector two ways, then equate
For "find the ratio / value" parts, write the target vector along two different routes (using a parameter where needed) and equate the coefficients of and .
Keep brackets when expanding
When you expand something like , keep the bracket so the multiplies both terms. Dropping it turns into and wrecks the simplification.
Collect the a-terms and b-terms
After following the route, gather all the coefficients together and all the coefficients together. Writing the answer as a number times plus a number times gives the simplest form.
Every vector between labelled points is a chain of journeys you already know: Write each piece in the base vectors and , keep brackets, then collect like terms.
Why can writing "AB = 5" lose a mark?
In triangle , and . is the midpoint of . Find in terms of and , giving your answer in its simplest form.
