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Advanced Higher Learning Outcomes

Learning Outcomes

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Algebra, Proof & Number Theory

Learning Outcomes

  • 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

Older Learning Outcomes

Apps 1.1 Applying algebraic skills to the binomial theorem and to complex numbers.

Apps 1.2 Applying algebraic skills to sequences and series.

Apps 1.3 Applying algebraic skills to summation and mathematical proof .

Apps 1.3 Applying algebraic skills to summation and mathematical proof .

Apps 1.4 Applying algebraic and calculus skills to properties of functions.

GPS 1.4 Applying algebraic skills to number theory.

GPS 1.5 Applying algebraic and geometric skills to methods of proof.

MAC 1.1 Applying algebraic skills to partial fractions



Old Advanced Higher Course

Unit 1 LO1 Use algebraic skills

Unit 1 LO4 Use properties of functions.

Unit 2 LO4 Understand and use sequences and series.

Unit 2 LO5 Use standard methods to prove results in elementary number theory.

Unit 3 LO3 Understand and use further aspects of sequences and series.

Unit 3 LO5 Use further number theory and direct methods of proof.

Calculus

Learning Outcomes

  • 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 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

Older Learning Outcomes

MAC 1.2 Applying calculus skills through techniques of differentiation.

MAC 1.3 Applying calculus skills through techniques of integration.

MAC 1.4 Applying calculus skills to solving differential equations.



Unit 1 LO3 Integrate using standard results and the substitution method.

Unit 2 LO2 Use further integration techniques.

Unit 3 LO4 Solve further ordinary differential equations.

Matrices, Vectors & Complex Numbers

Learning Outcomes

  • 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

Older Learning Outcomes

GPS 1.1 Applying algebraic skills to matrices and systems of equations.

GPS 1.2 Applying algebraic and geometric skills to vectors.

GPS 1.3 Applying geometric skills to complex numbers.

Apps 1.1 Applying algebraic skills to the binomial theorem and to complex numbers.



Old Higher Course

Unit 1 LO5 Use matrix methods to solve systems of linear equations.

Unit 2 LO3 Understand and use complex numbers .

Unit 3 LO1 Use vectors in three dimensions.

Unit 3 LO2 Use matrix algebra.