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Higher Learning Outcomes

Learning Outcomes

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Algebra

Key Skills

  • Manipulating algebraic expressions
  • Identifying and sketching related functions
  • Composite and inverse functions
  • Solving algebraic equations

Learning Outcomes

  • A1 Composite functions
  • A2 Completing the square
  • A3 Sketching after transformations
  • A4 Finding f-1(x)
  • A5 Sketching f′(x) from f(x)
  • A6 Recurrence relations
  • A7 Limits of sequences
  • A8 Quadratic inequalities
  • A9 Discriminant
  • A10 Factorising cubic/quartic expressions
  • A11 Solving cubic/quartic equations
  • A12 Intersections of lines & curves
  • A13 Simplifying log/exp expressions
  • A14 Laws of logs & exponents
  • A15 Solving log/exp equations
  • A16 y = axb and y = abx
  • A17 Straight‑line confirmation
  • A18 Modelling with logs/exponentials
  • A19 Sketching inverses of log/exp functions

Older Learning Outcomes

E&F 1.1 – Algebraic skills with logs & exponentials

E&F 1.3 – Algebraic & trigonometric skills with functions

R&C 1.1 – Solving equations

Apps 1.3 – Sequences

Old Higher Course
Unit 2 LO1 – Factor/remainder theorem
Unit 3 LO3 – Logarithmic & exponential functions

Calculus

Key Skills

  • Differentiating functions
  • Investigating properties of functions
  • Integrating functions
  • Calculating definite integrals
  • Applying differential calculus
  • Applying integral calculus

Learning Outcomes

  • C1 Differentiating algebraic functions
  • C2 Tangents to curves
  • C3 Increasing/decreasing functions
  • C4 Stationary points & sketching
  • C5 Differentiating ksin(x), kcos(x)
  • C6 Chain rule
  • C7 Optimisation
  • C8 Rate of change
  • C9 Integrating algebraic functions
  • C10 ∫(x + q)ⁿ dx
  • C11 ∫ksin(x), ∫kcos(x)
  • C12 ∫(px + q)ⁿ dx
  • C13 ∫psin(qx+r), ∫pcos(qx+r)
  • C14 Solving dy/dx = f(x)
  • C15 Definite integrals
  • C16 Area under curves
  • C17 Area between curves/lines
  • C18 Recovering functions from rate of change

Older Learning Outcomes

Apps 1.4 – Optimisation & area

R&C 1.3 – Differentiation
R&C 1.4 – Integration

Old Higher Course
Unit 1 LO3 – Basic differentiation
Unit 2 LO2 – Basic integration
Unit 3 LO2 – Further calculus

Geometry

Key Skills

  • Rectilinear shapes
  • Circles & graphs
  • Modelling with sequences
  • Vector connections
  • Working with vectors

Learning Outcomes

  • G1 Parallel & perpendicular lines
  • G2 m = tanθ
  • G3 Medians, altitudes, bisectors
  • G4 Perpendicularity
  • G5 Equation of a circle
  • G6 Tangency
  • G7 Line–circle & circle–circle intersections
  • G8 Vector pathways in 3D
  • G9 Collinearity
  • G10 Internal division points
  • G11 Scalar product & angle
  • G12 Using the scalar product
  • G13 Unit vectors i, j, k

Older Learning Outcomes

Apps 1.1 – Rectilinear shapes

Apps 1.2 – Circles
E&F 1.4 – Vectors

Old Higher Course
Unit 1 LO1 – Straight line
Unit 2 LO4 – Circle
Unit 3 LO1 – Vectors in 3D

Trigonometry

Key Skills

  • Solving trigonometric equations
  • Addition & double‑angle formulae
  • Trigonometric identities
  • Manipulating trig expressions

Learning Outcomes

  • T1 Solving trig equations (degrees & radians)
  • T2 Addition & double‑angle formulae
  • T3 Trigonometric identities
  • T4 Converting acosx ± bsinx to kcos(x ± α) or ksin(x ± α)

Older Learning Outcomes

E&F 1.2 – Manipulating trig expressions
E&F 1.3 – Algebraic & trig skills with functions
R&C 1.2 – Solving trig equations

Old Higher Course
Unit 1 LO2 – Functions & graphs
Unit 2 LO3 – Trig formulae
Unit 3 LO4 – Further trig relationships