A-level Pure Maths 1

Coming soon... 

We review the A-level pure maths as an introduction to university-level mathematics. We are NOT interested in the A-level exams. We are interested in refining our understanding of the maths!

  • Lecture 1: Algebra (Part 1)
    1. Background algebra
    2. Linear equations
    3. Changing the subject of a formula
    4. Quadratic equations
    5. Solving quadratic equations
  • Lecture 2: Algebra (Part 2)
    1. Equations that cannot be factorized
    2. The graphs of quadratic functions
    3. The quadratic formula
    4. Simultaneous equations
    5. Inequalities
  • Lecture 3: Coordinate geometry (Part 1)
    1. Coordinates
    2. Plotting, sketching and drawing
    3. The gradient of a line
    4. The distance between two points
    5. The mid-point of a line joining two points
  • Lecture 4: Coordinate geometry (Part 2)
    1. The equation of a straight line
    2. Finding the equation of a line
    3. The intersection of two lines
    4. Drawing curves
    5. The intersection of a line and a curve
  • Lecture 5: Sequences and series
    1. Definitions and notations
    2. Arithmetic progressions
    3. Geometric progressions
    4. Binomial expansions
  • Lecture 6: Functions
    1. The language of functions
    2. Composite functions
    3. Inverse functions
  • Lecture 7: Differentiation (Part 1)
    1. The gradient of a curve
    2. Finding the gradient of a curve
    3. Finding the gradient from first principles
    4. Differentiating by using standard results
    5. Using differentiation
    6. Tangents and normals
  • Lecture 8: Differentiation (Part 2)
    1. Maximum and minimum points
    2. Increasing and decreasing functions
    3. Points of inflection
    4. The second derivative
    5. Applications
    6. The chain rule
  • Lecture 9: Integration (Part 1)
    1. Reversing differentiation
    2. Finding the area under a curve
    3. Area as the limit of a sum
    4. Areas below the x-axis
    5. The area between two curves
  • Lecture 10: Integration (Part 2)
    1. The area between a curve and the y-axis
    2. The reverse chain rule
    3. Improper integrals
    4. Finding volumes by integration
  • Lecture 11: Trigonometry (Part 1)
    1. Trigonometry background
    2. Trigonometric functions
    3. Trigonometric functions for angles of any size
    4. The sine and cosine graphs
    5. The tangent graph
  • Lecture 12: Trigonometry (Part 2)
    1. Solving equations using graphs of trigonometric functions
    2. Circular measure
    3. The length of an arc of a circle
    4. The area of a sector of a circle
    5. Other trigonometric functions
  • Lecture 13: Vectors
    1. Vectors in two dimensions
    2. Vectors in three dimensions
    3. Vector calculations
    4. The angle between two vectors

Reference

  • Sophie Goldie (2012), Pure Mathematics 1, Hodder Education.
  • Jean Linsky, James Nicholson, Brian Western (2018), Complete Pure Mathematics 1, Oxford University Press.

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