Grade 9 vector problems are challenging questions on a higher GCSE exam paper. They often require students to understand ratios, set up and solve a pair of simultaneous equations and have excellent algebraic notation skills. For these reasons, I ensure 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 after-school revision class.

You can view this question in the grades 8 and 9 revision lessons.

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 paths using a highlighter before writing any algebra. This way, they would have a picture to refer back to when algebra became complicated.
Most of the class chose to work out the vector OQ rather than QM. Either way, it was essential to identify the vector as a proportion of the straight-line OQM. I encouraged students to label the proportion as â€˜xâ€™, which was more familiar than Î».

## Setting up Simultaneous Equations

Most of the students could work out both vectors from OQ in terms of a and b. However, some students needed help setting up the two simultaneous equations by equating the a and b terms. Setting up the equations 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. Again, 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.

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