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Higher Advanced Mathematics SQA
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Higher Advanced Mathematics SQA
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Higher Advanced Mathematics SQA
– Topics
Algebra, Proof and Number Theory
Using Euclid's Algorithm to Find the Greatest Common Divisor of Two Positive Integers
Using Proof by Induction
Using Indirect or Direct Proof in Straightforward Examples
Disproving a Conjecture by Providing a Counterexample
Using the Maclaurin Expansion to FInd Specified Terms of the Power Series for Simple Functions
Applying Summation Formulae
Finding the General Term and Summing Arithmetic and Geometric Progressions
Expanding Expressions Using the Binomial THeorem
Investigating Features of Graphs and Sketching Graphs of Functions
Finding the Asymptotes to the Graphs of Rational Functions
Decomposing a Rational Function into a Sum of Partial Fractions
Calculus
Solving Second-Order Differential Equations
Solving First-Order Linear Differential Equations Using an Integrating Factor
Solving First-Order Differential Equations with Variables Separable
Applying Integration to Problems in Context
Integrating by Parts
Integrating by Substitution
Integrating Expressions Using Standard Results
Applying Differentiation to Problems in Context
Finding the Derivative where Relationships are Defined Parametrically
Finding the Derivative where Relationships are Defined Implicitly
Differentiating Inverse Trigonometric Functions
Differentiating Functions Given in the Form of a Product and in the Form of a Quotient
Differentiating Functions Using the Chain Rule
Differentiating Exponential and Natural Logarithmic Functions
Matrices, Vectors and Complex Numbers
Performing Geometric Operations on Complex Numbers
Performing Algebraic Operations on Complex Numbers
Working with Planes
Working with Lines in 3 Dimensions
Calculating a Vector Product
Using Transformation Matrices
Finding the Inverse of a Matrix
Calculating the Determinant of a Matrix
Understanding and Using Matrix Algebra
Using Gaussian Elimination to Solve a 3x3 System of Linear Equations