Scholar Advanced Higher Maths Past Papers SQA Advanced Higher Maths Check List
The course is based on :
Calculus, Algebra, proof and number theory, Matrices, vectors and complex numbers
An external SQA exam is sat at the end of the course, with calculator and non-calculator papers.
You must have a good grasp of the following :
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
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
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
Applying integration to problems in
context
Using Gaussian elimination to
solve a 3x3 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
Key subskills:
Expand expressions using the binomial theorem.
Key subskills:
Finding the asymptotes of rational functions.
Investigating features of graphs and sketching graphs of functions,
including appropriate analysis of stationary points.
Apps 1.4 Applying algebraic and calculus skills to properties of functions.
Unit 1 LO4Use properties of functions.
Key subskills:
Using Euclid’s algorithm to find the greatest common divisor of two positive integers.
GPS 1.4Applying algebraic skills to number theory.
Unit 3 LO5 Use further number theory and direct methods of proof.
Key subskills:
Expressing proper rational functions as a sum of partial fractions.
MAC 1.1 Applying algebraic skills to partial fractions
Unit 1 LO 1Use algebraic skills.
Key subskills:
Disproving a conjecture by providing a counter-example.
Using direct and indirect proof in straightforward examples.
GPS 1.5Applying algebraic and geometric skills to methods of proof.
Apps 1.3 Applying algebraic skills to summation and mathematical proof .
Unit 2 LO5 Use standard methods to prove results in elementary number theory.
Key subskills :
Finding the general term and summing arithmetic and geometric sequences.
Using the Maclaurin series expansion to find
a stated number of terms of the power series for a simple function.
Power Series
Application of summation formulae
Apps 1.2 Applying algebraic skills to sequences and series.
Apps 1.3 Applying algebraic skills to summation and mathematical proof .
Unit 2 LO4 Understand and use sequences and series.
Unit 3 LO3 Understand and use further aspects of sequences and series.
Key subskills:
Differentiating functions given in the form of a product and in the form of a quotient.
Differentiating exponential and logarithmic functions.
Differentiating inverse trigonometric functions.
Finding the derivative of functions defined implicitly.
Finding the derivative of functions defined parametrically.
First Principles
Differentiation Refresher
Rules
Parametric Differentiation
MAC 1.2
Applying calculus skills through techniques of differentiation.
Unit 1 LO2Use the rules of differentiation on elementary functions.
Unit 2 LO1Use matrix methods to solve systems of linear equations.
Key subskills:
Integrating expressions using standard results.
Integrating by substitution.
Integrating by parts.
MAC 1.3
Applying calculus skills through techniques of integration.
Unit 1 LO3 -Integrate using standard results and the substitution metho .
Unit 2 LO2Use further integration techniques.
Key subskills:
Solving a first order differential equation with variables separable.
Solving a first order linear differential equation using the integrating factor.
Solving second order differential equations.
Applying differentiation to problems, in context where appropriate.
Applying integration to problems, in context where appropriate.
Applications of Calculus
MAC 1.4 Applying calculus skills to solving differential equations.
Apps 1.5 Applying algebraic and calculus skills to problems.
Unit 3 LO4 Solve further ordinary differential equations .
Key subskills:
Performing geometric operations on complex numbers
.
GPS 1.3 Applying geometric skills to complex numbers.
Apps 1.1 Applying algebraic skills to the binomial theorem and to complex numbers.
Unit 2 LO3 Understand and use complex numbers .
Key subskills:
Using Gaussian elimination to solve a 3x3 system of linear equations.
Performing matrix operations of addition, subtraction and multiplication.
Calculating the determinant of a matrix.
Finding the inverse of a matrix.
Matrices - Determinant
Matrices - Inverse
Special Matrices
GPS 1.1 Applying algebraic skills to matrices and systems of equations.
Unit 1 LO5 Use matrix methods to solve systems of linear equations.
Unit 3 LO2Use matrix algebra.
Key subskills:
Calculating a vector product.
Finding the equation of a line in three dimensions.
Finding the equation of a plane.
Vector equations of lines
Vector equation of planes
GPS 1.2 Applying algebraic and geometric skills to vectors.
Unit 3 LO1 Use vectors in three dimensions.
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