WhizzNotes

Mathematics Advanced

Functions, trigonometry, exponentials and logarithms, calculus, sequences, financial maths and statistics for Year 11 and 12. Every topic starts from Year 9 and 10, so it also works as a Year 10 exam refresher.

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Pick your year on any chapter.

Unit 1 Functions

  1. 1The Algebra ToolkitExpanding, factorising, index laws, surds and solving equations. The skills every later chapter uses.
  2. 2Straight Lines and Coordinate GeometryGradient, y = mx + c, distance, midpoint, parallel and perpendicular lines, and linear models.
  3. 3Quadratics and ParabolasSolving quadratics three ways, sketching parabolas, the vertex, and the discriminant.
  4. 4Working with FunctionsFunction machines, function notation, domain and range, the vertical line test, composite, odd and even functions.
  5. 5A Library of GraphsRecognise and sketch cubics, hyperbolas, exponentials, circles, absolute value and polynomial graphs.
  6. 6Graph TransformationsMoving, flipping and stretching graphs. Translations, reflections and dilations of any function.
  7. 7Modelling with FunctionsDirect and inverse variation, solving equations with graphs, and choosing a function to model real data.

Unit 2 Trigonometric Functions

  1. 8Right-Angled TrigonometryPythagoras, sine, cosine and tangent, angles of elevation, bearings and exact values.
  2. 9The Sine Rule, Cosine Rule and Triangle AreaSolving triangles without a right angle. Sine rule, cosine rule, area formula and the ambiguous case.
  3. 10Radians and the Unit CircleArcs and sectors, measuring angles in radians, and trig ratios for any angle using the unit circle.
  4. 11Graphs of Trigonometric FunctionsThe waves of sin, cos and tan. Amplitude, period, phase shift and modelling things that repeat.
  5. 12Trigonometric Identities and EquationsKey identities, reciprocal ratios, proving identities and solving trig equations over a domain.

Unit 3 Exponential and Logarithmic Functions

  1. 13Exponential Functions and the Number eGrowth and decay, graphs of exponentials, Euler's number e and the derivative of e to the x.
  2. 14LogarithmsWhat a log is, the log laws, natural logs, log graphs and solving exponential equations.

Unit 4 Calculus: Differentiation

  1. 15Rates of Change and the DerivativeFrom average speed to the gradient of a curve. Limits, first principles and what differentiable means.
  2. 16The Rules of DifferentiationPower rule, sums, product, quotient and chain rules, and the derivatives of eˣ, ln x, sin x, cos x and tan x.
  3. 17Tangents, Stationary Points and Curve SketchingEquations of tangents and normals, increasing and decreasing, stationary points, concavity and sketching curves.
  4. 18Applications of DifferentiationRates of change, motion in a straight line, and optimisation problems that find the best possible answer.

Unit 5 Calculus: Integration

  1. 19Anti-DifferentiationWorking backwards from a gradient. Primitives, the constant C, and the standard integrals.
  2. 20The Definite Integral and Area Under a CurveArea from rectangles and trapeziums, the trapezoidal rule, the fundamental theorem of calculus and signed area.
  3. 21Areas Between Curves and Applications of IntegrationArea between two curves, total change from a rate, and motion problems solved by integrating.

Unit 6 Sequences and Series

  1. 22Arithmetic Sequences and SeriesNumber patterns that add the same amount each step. The nth term, the sum of n terms and sigma notation.
  2. 23Geometric Sequences and SeriesPatterns that multiply by the same number each step. The nth term, sums, and the limiting sum of an infinite series.

Unit 7 Financial Mathematics

  1. 24Simple Interest, Compound Interest and DepreciationHow money grows and how assets lose value. Simple and compound interest, compounding periods and depreciation.
  2. 25Annuities and LoansRegular deposits and regular repayments. Future value, present value, interest factor tables and reducing balance loans.

Unit 8 Statistical Analysis

  1. 26Probability, Sets, Venn Diagrams and Two-Way TablesSample spaces, complements, Venn diagrams and two-way tables, set notation, the addition rule and conditional probability.
  2. 27Multi-Stage Experiments and Tree DiagramsTwo-step experiments, grids and tree diagrams, with and without replacement, and the "at least one" trick.
  3. 28Data, Summary Statistics and Bivariate DataMean, median, quartiles, box plots, standard deviation, distribution shape, correlation and lines of best fit.
  4. 29Discrete Random VariablesProbability distributions, expected value, fair games, variance and standard deviation of a random variable.
  5. 30Continuous Random VariablesMeasured data, histograms as areas, probability density functions, cumulative distribution, median, mean and variance.
  6. 31The Normal DistributionThe bell curve, z-scores, the 68-95-99.7 rule, standard normal tables and finding probabilities.

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