The course is based on :
Algebra, Calculus, Geometry and Trigonometry

An external SQA exam is sat at the end of the course, with calculator and non-calculator papers.

Scholar
Formulae
Higher Maths Past Papers SQA Higher Maths Check List

National 5 Maths
Advanced Higher Maths

You must have a good grasp of the following :

- Completing the Square.
- Changing the subject of the formula.
- Manipulating Algebraic fractions.
- Factorising.
- Manipulating Surds and Indices.
- Manipulating quadratics.
- Basic Trigonometry.

Key subskills

Factorising a polynomial expression .

Solving polynomial equations.

Using the discriminant.

Solving quadratics

Find the co-ordinates of intersections of curves and straight lines.

Create and use recurrence relations.

Find and use limits of sequences.

Polynomials

Quadratics

Sequences

Key subskills

Simplifying a numerical expression, using the laws of
logarithms and exponents.

Solving logarithmic and exponential equations.

Using the laws of logarithms and exponents.

Exponentials

Logarithms

Graphs

Key subskills

Identifying and sketching related functions.

Determining composite and
inverse functions.

Functions

Graphs

Key subskills

Differentiating functions.

Determining the equation of a tangent to a curve at a
given point by differentiation.

Determining where a function is strictly
increasing/decreasing.

Using nature tables.

Using differentiation to determine the optimal solution for a given problem.

Solve problems using rate of change.

Main Differentiation

Stationary Points and Tangents

Optimisation and Curve Sketching

Key subskills

Integrating functions.

Calculating definite integrals of polynomial functions.

Finding the area between a curve and the x axis.

Finding area under and between curves.

Basic Integration

Area under curves

Key subskills

Determining and using the equation of a circle.

Using properties of tangency.

Determining intersections.

Circles

Key subskills

Find the equation of parallel and perpendicular lines.

Using m = tan θ to calculate a gradient or angle.

Using properties of medians, altitudes and perpendicular bisectors.

General

Straight lines and circles

Key subskills

Working with 2D vectors.

Working with 3D coordinates.

Using vector components

Basic Vectors

Other Vectors

Key subskills

Application of the addition or double angle formulae.

Application of trigonometric identities.

Converting acos x± bsin x to k cos(x ±α) or k sin(x ±α, k > 0.

Deriving formulae

Radians and Exact Values

Wave Theory

Manipulating algebraic expressions

Identifying and sketching related functions

Determining composite and inverse functions

Solving algebraic equations

- A1 Determining a composite function
- A2 Completing the square in a quadratic expression
- A3 Identifying or sketching a function after a transformation
- A4 Determining f
^{-1}(x) of functions - A5 Sketch f'(x) given the graph of y = f(x)
- A6 Determining and using a recurrence relation
- A7 Finding and interpreting the limit of a sequence, where it exists
- A8 Solve quadratic inequalities
- A9 Use the discriminant
- A10 Factorising a cubic or quartic polynomial expression
- A11 Solving a cubic or quartic polynomial equation
- A12 Finding the coordinates of the point(s) of the intersection of a straight line and a curve or of two curves
- A13 Simplifying a numerical expression using the laws of logarithms and exponents
- A14 Using the laws of logarithms and exponents
- A15 Solving logarithmic and exponential equations
- A16 Solve equations involving y = ax
^{b}and y = ab^{x} - A17 Use a straight line graph to confirm relationships of the form
y = ax
^{b}and y = ab^{x} - A18 Model mathematically situations involving the logarithmic or exponential function
- A19 Sketching the inverse of a logarithmic or an exponential function

E&F 1.1 Applying algebraic skills to logarithms and exponentials.

E&F 1.3
Applying algebraic and trigonometric skills to functions.

R&C 1.1
Applying algebraic skills to solve equations.

Apps 1.3 Applying algebraic skills to sequences.

Old Higher Course

Unit 2 LO1 Use the factor/remainder theorem
and apply quadratic theory.

Unit 3 LO3
Logarithmic and exponential functions.

Differentiating functions

Using differentiation to investigate the nature and properties of functions

Integrating functions

Using integration to calculate definite integrals

Applying differential calculus

Applying integral calculus

- C1 Differentiating an algebraic function
- C2 Use differentiation to find the equation of a tangent to a curve at a given point
- C3 Determining where a function is strictly increasing/decreasing
- C4 Use stationary points to sketch graphs
- C5 Differentiate ksin(x) and kcos(x)
- C6 Differentiating a composite function using the chain rule
- C7 Determining the optimal solution for a given problem
- C8 Solving problems using rate of change
- C9 Integrating an algebraic function
- C10 Integrating functions of form f(x)=(x + q)
^{n}n ≠-1 - C11 Integrating ksin(x) and kcos(x)
- C12 Integrating functions of form f(x)=(px + q)
^{n}n ≠-1 - C13 Integrate psin(qx+r) and pcos(qx+r)
- C14 Solve differential eqns of form dy/dx=f(x)
- C15 Calculating definite integrals of functions
- C16 Finding the area between a curve and the x-axis
- C17 Finding the area between a straight line and a curve or two curves
- C18 Determine and use a function from a given rate of change and initial conditions

Apps 1.4
Applying calculus skills to optimisation and area.

R&C 1.3
Applying calculus skills of differentiation.

R&C 1.4
Applying calculus skills of integration.

Old Higher Course

Unit 1 LO3 Use basic differentiation .

Unit 2 LO2 Use basic integration.

Unit 3 LO2 Use further differentiation and integration .

Applying algebraic skills to rectilinear shapes

Applying algebraic skills to circles and graphs

Modelling situations using sequences

Determining vector connections

Working with vectors

- G1 Finding equations of parallel and perpendicular ines
- G2 Use m = tanθ
- G3 Use properties of medians, altitudes and perpendicular bisectors
- G4 Determine whether or not two lines are perpendicular
- G5 Determining and using the equation of a circle
- G6 Using properties of tangency
- G7 Determining the intersection of circles or a line and a circle
- G8 Determining the resultant of vector pathways in three dimensions
- G9 Working with collinearity
- G10 Determining the coordinates of an internal division point of a line
- G11 Evaluate a scalar product and determine the angle between two vectors
- G12 Use the scalar product
- G13 Use unit vectors
**i, j, k**

Apps 1.1 Applying algebraic skills to rectilinear shapes.

Apps 1.2 Applying algebraic skills to circles.

E&F 1.4 Applying geometric skills to vectors

Old Higher Course

Unit 1 - LO1-Use the properties of the Straight Line

Unit 2 LO4 Use the equation of the circle.

Unit 3 LO1 Use vectors in three dimensions

Solving trigonometric equations

Application of the addition or double angle formulae

Application of trigonometric identities

Manipulating trigonometric expressions

- T1 Solving trigonometric equations in degrees or radians
- T2 Application of the addition or double angle formulae
- T3 Application of trigonometric identities
- T4 Converting acos x± bsin x to k cos(x ±α) or k sin(x ±α, k > 0

E&F 1.2 Applying trigonometric skills to manipulating expressions.

E&F 1.3 Applying algebraic and trigonometric skills to functions.

R&C 1.2 Applying trigonometric skills to solve equations.

Old Higher Course

>Unit 1 LO2 Associate
functions and graphs and solve related equations.
Unit 2 LO3 Apply trigonometric formulae.

Unit 3 LO4 Apply further trigonometric relationships .