Online Advanced Higher Maths tutor

Why Advanced Higher is different

Advanced Higher Maths is closer to first-year university than to Higher. Proof by induction, complex numbers, matrices and differential equations are all new, and the course moves quickly. Classes are often small, and in some schools pupils study it partly on their own or through a shared or online class.

That is where one-to-one teaching helps most. A pupil working largely alone needs someone who can explain why a method works, not only how to apply it, and who can check that a written proof would actually earn its marks.

Tuition is particularly useful if your child:

• is applying for mathematics, physics, engineering or computing at university;
• is studying Advanced Higher with limited teacher time in school;
• finds proof and abstract topics harder than the calculation-heavy ones;
• wants to start first year at university already confident with the methods.

What the Advanced Higher Maths exam looks like

The grade comes from two question papers set and marked by Qualifications Scotland (formerly SQA).

Topics we cover

• Calculus

  • Differentiation: implicit, parametric, related rates
  • Integration by parts and by substitution
  • Partial fractions
  • First- and second-order differential equations

• Algebra

  • Binomial theorem
  • Complex numbers and de Moivre's theorem
  • Sequences and series
  • Maclaurin series
  • Summation and convergence

• Geometry and systems

  • Matrices and determinants
  • Vectors: lines and planes in 3D
  • Systems of equations and Gaussian elimination

• Proof and number

  • Proof by induction
  • Proof by contradiction and counterexample
  • Euclidean algorithm
  • Number bases

Where Advanced Higher pupils usually lose marks

• Proof by induction. Doing the algebra but missing the statements that make it a proof: the base case, the assumption and the conclusion.
• Integration choices. Picking substitution when parts was needed, or the wrong part to differentiate.
• Complex numbers. Errors converting between forms, and missing roots when solving zⁿ = w.
• Differential equations. Forgetting the constant, or applying initial conditions before finding the general solution.

Wondering whether the course is the right choice? Read Is Advanced Higher Maths worth taking?

What lessons look like

Lessons follow your assessment plan and your school's order of topics, so they support class teaching rather than repeat it. Written work between lessons is marked against the official marking instructions, with particular attention to how proofs and explanations are written.

Advanced Higher Maths questions