Mathematics: Advanced Higher
Recommended Entry Requirements:
- Ideally, Higher Maths A/B pass
Course Content:
Calculus
Differentiating exponential and natural logarithmic functions
Differentiating functions using the chain rule
Differentiating functions given in the form of a product and in the form of a quotient
Differentiating inverse trigonometric functions
Finding the derivative where relationships are defined implicitly
Finding the derivative where relationships are defined parametrically
Applying differentiation to problems in context
Integrating expressions using standard results
Integrating by substitution
Integrating by parts
Applying integration to problems in context
Solving first-order differential equations with variables separable
Solving first-order linear differential equations using an integrating factor
Solving second-order differential equations
Algebra, proof and number theory
Decomposing a rational function into a sum of partial fractions (denominator of degree at most three)
Finding the asymptotes to the graphs of rational functions
Investigating features of graphs and sketching graphs of functions
Expanding expressions using the binomial theorem
Finding the general term and summing arithmetic and geometric progressions
Applying summation formulae
Using the Maclaurin expansion to find specified terms of the power series for simple functions
Disproving a conjecture by providing a counterexample
Using indirect or direct proof in straightforward examples
Using proof by induction
Using Euclid’s algorithm to find the greatest common divisor of two positive integers
Matrices, vectors and complex numbers
Using Gaussian elimination to solve a 3 3 system of linear equations
Understanding and using matrix algebra
Calculating the determinant of a matrix
Finding the inverse of a matrix
Using transformation matrices
Calculating a vector product
Working with lines in three dimensions
Working with planes
Performing algebraic operations on complex numbers
Performing geometric operations on complex numbers
Assessment:
- The Advanced Higher course is 100% externally assessed by formal exam.
Candidates must complete two external examinations set by the SQA.
Paper 1 – Non calculator
Paper 2 – Calculator
