Mathematics
Higher
Mathematics
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View topicsHigher Mathematics is the qualification Scottish universities look for in almost every quantitative degree, and it is a significant step up from National 5. The course is examined in two papers (one non-calculator, one calculator) plus content assessed across Expressions and Functions, Relationships and Calculus, and Applications.
Calculus is the centre of the course: differentiation and integration, rates of change, stationary points, and areas under curves. Alongside it sit the straight line and circle in coordinate geometry, vectors in three dimensions, trigonometric identities and equations, logarithms and exponentials, and recurrence relations.
Higher rewards fluent technique above all: pupils who can differentiate, integrate and manipulate trigonometric expressions without hesitation have time left to think about the harder questions. That fluency is exactly what regular 1-on-1 practice builds.
Important Topics
- DifferentiationRules of differentiation, rates of change, stationary points, curve sketching and optimisation.
- IntegrationIndefinite and definite integrals, areas between curves and differential equations.
- The Straight Line & CircleGradient, perpendicular lines, medians, altitudes, and the equation of a circle with tangents.
- Functions & GraphsComposite and inverse functions, graph transformations, exponentials and logarithms.
- TrigonometryRadians, identities, the wave function, addition formulae and solving trig equations.
- VectorsThree-dimensional vectors, the scalar product, collinearity and the angle between vectors.
- Polynomials & QuadraticsThe remainder and factor theorems, the discriminant and solving polynomial equations.
- SequencesRecurrence relations, limits and modelling with sequences.
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