Online Higher Maths tutor

Why Higher Maths catches people out

Plenty of pupils who found National 5 comfortable get their first poor mark in Higher. The content moves faster, but the bigger change is in the questions. A National 5 question usually points to its method. A Higher question might combine a circle, a tangent and a quadratic in one problem, and the first job is working out where to begin.

Tuition helps most when:

• the jump from National 5 has knocked your child's confidence;
• a university course or apprenticeship needs a particular Higher grade;
• calculus or the wave function hasn't clicked in class;
• the prelim showed which topics need rebuilding before May.

What the Higher Maths exam looks like

There is no coursework. The grade comes from two question papers set and marked by Qualifications Scotland (formerly SQA).

That's 120 marks in total, at a little over a minute per mark. Speed and accuracy in algebra matter as much as understanding the topics.

Topics we cover

• Algebra and functions

  • Composite and inverse functions
  • Graph transformations
  • Polynomials and synthetic division
  • Quadratic inequalities and the discriminant
  • Recurrence relations
  • Logarithms and exponentials

• Geometry

  • The straight line: perpendicular bisectors, medians, altitudes
  • Equation of a circle and tangents
  • Vectors in 3D, scalar product, collinearity

• Trigonometry

  • Radians and exact values
  • Addition and double-angle formulae
  • Trigonometric equations
  • The wave function

• Calculus

  • Differentiation and the chain rule
  • Stationary points and curve sketching
  • Optimisation problems
  • Integration and areas between curves
  • Rates of change

Where Higher pupils usually lose marks

• Algebra slips in Paper 1. Negative signs, fractional indices and expanding brackets, with no calculator to catch the error.
• Not knowing where to start. Multi-part questions on circles, lines and functions that need a plan before any calculation.
• Missing the "nature" step. Finding stationary points but not justifying whether each is a maximum or minimum, which is a separate mark.
• Radians and degrees. Answering in the wrong one, or leaving the calculator in the wrong mode.
• The wave function. Getting the quadrant of the angle wrong when finding k cos(x − a).

Saba's guides on the jump from National 5 to Higher and optimisation problems include fully worked examples.

What lessons look like

Each one-hour lesson works through the topics in your assessment plan, mixing explanation with exam-style questions. Between lessons there is a short piece of work, marked against the official marking instructions so you can see where each mark comes from. Parents receive a short note after each lesson.

From the prelim onwards, lessons shift towards timed papers and towards recognising which method a question needs, which is the skill that most separates a C from an A at Higher.

Higher Maths questions