Grade 9 vector problems tend to be one of the most challenging questions on a higher GCSE exam paper. They often require students to have a good understanding of ratio, to set up and solve a pair of simultaneous equations and excellent algebraic notation skills. For these reasons I make sure students have lots of exposure to vector problems as part of their exam revision.
I posed this question to my most able Year 11 students last half term as part of an afterschool revision class.
You can view this question in the grades 8 and 9 revision lesson.
We began sketching the diagram and noting the given facts. Next, we discussed possible routes that would take us from O to Q or Q to M. I encouraged students to mark the routes using a highlighter before they wrote any algebra. This way they would have a picture to refer back to when the algebra became complicated.
The majority of the class chose to work out the vector OQ rather than QM. Either way, it was important to identify the vector as a proportion of the straight line OQM. I encouraged students to label the proportion as ‘x’ as this was more familiar to them than λ.
Most of the students were able to work out both vectors from OQ in terms of a and b. As expected, a little help was needed to set up the two simultaneous equations by equating the a and b terms. However, this was quickly addressed and everyone chose to use the substitution method rather than elimination to work out the two proportions.
Overall, this question took about 30 minutes to work through from start to finish. I encouraged students to work together throughout the problem with me providing 1-2-1 support.
My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.
Mathematics curriculum intent, implementation and impact for Heads of Maths and Maths Teachers
Solving quadratic inequalities by factorisation and sketched graphs.
How to work out a GCSE grade 9 vectors problem with ratio.