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Pure Mathematics 1

Uncategorized

What Will You Learn?

  • Quadratics
  • Coordinate Geometry
  • Circular Geometry
  • Circular Measure
  • Trigonometry
  • Series
  • Differentiation
  • Integration
  • Functions

Course Content

Quadratics
(Disguised) Quadratic expressions/equations, completing the square, quadratic formula, middle-term factorization, sketching, and discriminants.

  • Quadratics 1
    40:54
  • Quadratics 2
    40:58
  • Quadratics 3
    39:16
  • Quadratics 4
    55:06
  • Quadratics 5
    41:37
  • Quadratics 6
    36:53
  • Quadratics 7
    50:36
  • Quadratics 8
    00:00
  • Quadratics 2017
    25:37
  • Quadratics 2018
    41:35
  • Quadratics 2018 Left
    12:00
  • Quadratics 2019
    26:11
  • Quadratics 2019 Left
    00:00
  • Quadratics 2020
    27:05
  • Quadratics 2021
    46:05
  • Quadratics 2022
    00:00
  • Quadratics 2022 Left
    00:00
  • Quadratics 2022 Mistakes
    00:00
  • Quadratics 2023
    00:00
  • Quadratics 2023 Left
    00:00
  • Quadratics 2023 Mistakes
    00:00
  • Quadratics 2024
    00:00
  • Quadratics 2024 Left
    00:00
  • Quadratics 2025
    43:11
  • Quadratics Lecture Notes

Coordinate Geometry
Lines, gradient / slope, slope-intercept form, perpendicular & parallel lines, ratios, 2D shapes and their properties, areas, and intersection of two functions.

Circular Geometry
Equation of a circle (radius and center), points inside / outside a circle, circle properties & theorems, angle properties, and relationship between 2 circles.

Circular Measure
Triangles, sine rule, cosine rule, circle, sector, segment, arc length, angle of a sector, perimeters, and areas.

Trigonometry
Trigonometric identities, trigonometric graphs, solving trigonometric equations (through ASTC and graphically), triangles, and finding different trigonometric functions.

Series
APGP: Arithmetic progression, difference, sum of finitely many terms, geometric progression, ratio, sum of finitely many terms, and sum to infinity. Binomial: Binomial expansion, ascending and descending order, coefficient / general term formula, and factorial.

Differentiation
Derivative / gradient / slope, power rule for differentiation, chain rule / internal differentiation, gradients of the tangent and normal lines, finding tangent and normal lines, stationary points, stationary values, nature of stationary points, mensuration formulae, maximizing / minimizing volume, area, etc., finding rates of changes, angle of a line, angle between two lines, angle between two parallel lines, and the definition of the derivative.

Integration
Power rule, chain rule, equation of a curve, area under the curve, area between two functions, improper integrals, and volume of revolution.

Functions

Solved yearly past-papers from 2017 – 2025 inclusive, variants 2 and 3, with mark schemes