目次

1. Problem solving and proof:
   1. Mystic rose
   2. The area of a field enclosed by a farmer
2. Algebra indices and surds:
   1. Spiral of Theodorus
3. The quadratic function:
   1. The properties of y = ax^2.
   2. Line of symmetry of a quadratic
   3. The general form of a quadratic
   4. The vertex of a quadratic.
   5. The x and y intercepts of a quadratic.
   6. The properties of a quadratic function
   7. The characteristics of a quadratic function
   8. All characteristics of the quadratic function.
   9. The discriminant
   10. Finding the values of k for real roots of a quadratic.
   11. Solving a quadratic equation by factorisation.
   12. Solving quadratic equations using the formula.
   13. Finding the equation of a quadratic from its graph
   14. Finding the equation of a quadratic from completing the square
   15. Solving a quadratic equation by factorisation
4. Equations and inequalities:
   1. Linear simultaneous equation solver.
   2. Intersection of a quadratic function and a line.
   3. Intersection of a line and circle.
   4. Representing inequalities on a number line
   5. Testing a point for an inequality
   6. Solving a quadratic inequality
5. Coordinate geometry:
   1. The properties of the equation of a straight line.
   2. The gradient between two points
   3. y= mx + c.
   4. Parallel lines
   5. Perpendicular lines.
   6. The equation of a line with known point and gradient.
   7. The midpoint of a line joining two points P and Q
   8. Finding the equation of the perpendicular bisector of two points.
   9. Angle at the centre and circumference
   10. Tangent radius property of a circle
   11. The equation of a circle.
   12. The equation of a circle centre (a, b) and radius r.
   13. Centre of a circle through two points.
   14. Intersection of a line and a circle.
   15. The intersection of a line and a circle.
   16. Intersection of a curve and a circle.
   17. Finding values of k so that the line is a tangent to a circle.
   18. solving simultaneous equations with geometrical meaning
   19. The distance between two points
   20. The equation of a circle passing through 3 points
   21. The equation of an incircle
6. Trigonometry:
   1. Deducing trig ratios for 0 and 90 degrees
   2. Trigonometric graphs in all four quadrants (degrees)
   3. Generating the graph of y=sinx in degrees.
   4. Generating the graph of y=cosx in degrees.
   5. Generating a graph of y=tanx in degrees.
   6. Understanding the unit circle in trigonometry in degrees
   7. Proof of cos(90 - x) = sin x
   8. Proof of sin(90 - x) = cos x
   9. Trigonometrical equation solver using CAST
   10. Equation solver for sin of an angle.
   11. Equation solver for cos of an angle.
   12. Equation solver for tan of an angle.
   13. Pythagoras theorem introduction
   14. Introduction to 3-D trigonometry.
   15. Longest rod in a box
   16. Square based pyramid trigonometry
   17. Finding the radius of a cone.
   18. Graph of y=sin x/x
   19. The unit circle using radian measure
   20. Sine rule with ambiguous case
   21. Sine rule ambiguous case
   22. Unit circle: sin cos and tan in degrees
7. Polynomials:
   1. Sketching a cubic function.
   2. The roots of a polynomial.
   3. Disguised quadratics and the discriminant
   4. Finding the roots of a cubic using the factor theorem
8. Graphs and transformations:
   1. Graphs of functions.
   2. Sketching a cubic function.
   3. Sketching the cubic function by translation and reflection.
   4. Sketching the cubic function by translation and reflection.
   5. The reciprocal function.
   6. Stretches of a cubic function.
   7. Stretches of a reciprocal function.
   8. Vertical translation of a graph
   9. Horizontal translation of a graph.
   10. Stretches parallel to the y-axis.
   11. Stretches parallel to the x-axis.
   12. Reflection in the x-axis.
   13. Reflection in the y-axis.
   14. Single transformations of y=f(x)
   15. Combined transformations of functions.
   16. Combinations of transformations of graphs of functions a stretch and a translation
   17. Transformations of a sine graph
   18. Worksheet for transformations of graphs.
   19. Finding maximum points using translations of functions.
   20. The graph of y=f(x) after a stretch parallel to the y-axis.
   21. The graph of y=f(x) after a stretch parallel to the x-axis.
   22. Stretches of functions parallel to the x-axis.
   23. Graphs showing proportion.
   24. Transformations of 1/x to obtain a bilinear function
   25. Inverse transformations of a function
   26. Combinations of transformations in the wrong order
   27. Max/min point on the reciprocal of a quadratic function
   28. Properties of reciprocal functions
   29. Properties of a cubic function
   30. Transformations of a reciprocal graph
9. Binomial theorem and counting principles:
   1. The binomial theorem for any rational index.
10. Differentiation:
    1. Gradient between two points.
    2. Introduction to the gradient of a curve.
    3. Open top box from a piece of paper.
    4. Differentiation by first principles
    5. To find the coordinates of where the gradient is 8
    6. Where the gradient of a function is the same as a line
    7. Where the gradient of a function is the same as a line
    8. The tangent and normal to a curve y = f(x)
    9. Tangent normal extended response.
    10. Finding the equation of a normal from a curve and line
    11. Increasing and decreasing function
    12. Showing a function always is decreasing.
    13. Proving a cubic function is decreasing.
    14. Turning points introduction.
    15. Using the 2nd derivative to classify stationary points.
    16. Using the 2nd derivative test cases of failure.
    17. Using the 2nd derivative to classify stationary points with a point of inflection.
    18. Maximum and minimum points
    19. A case where the 2nd derivative test does not work
    20. Concavity
    21. Maximum volume of a cylinder cut from a sphere
    22. The area of a rectangle enclosed in a quadratic
    23. The maximum volume of a cylinder inside a cone
11. Integration:
    1. The general solution and particular solution
    2. Definite integral investigation
    3. The area under a curve and the x-axis.
    4. Finding equal area using integration
    5. Finding the area enclosed by a cubic and x-axis
    6. Finding the equation of a normal from a curve and line
12. Vectors:
    1. The addition of vectors.
    2. The subtraction of vectors.
    3. The multiplication of a vector by a scalar.
    4. A vector in component and magnitude-direction forms
    5. Position vectors in component form in 2D.
    6. Position vectors and scalar multiples of vectors.
    7. The magnitude or length of a vector in 2D and 3D
    8. Finding the vector joining the point P and Q and its magnitude.
    9. The scalar product proof
    10. Scalar product 3d
13. Exponentials and logarithms:
    1. The properties of the exponential and logarithic functions.
    2. Properties of an exponential function.
    3. The exponential function introduction.
    4. Finding the number e
    5. The derivative of f(x)=lnx
    6. Conversation to linear form.
    7. Conversion to linear form using natural logs
    8. Conversion to linear form: Chemical reaction
14. Proof
15. Trigonometry and circular measure
    1. Generating the graph of f(x) = sinx
    2. Generating the graph of f(x) = cosx
    3. Generating the graph of f(x) = tanx
    4. Understanding the unit circle in radians
    5. Small angles from the unit circle.
    6. Small angles measured in radians.
    7. Small angles measured in radians approximations using graphs.
    8. Modelling tides in a harbour
    9. Combinations of transformations for a sine graph
    10. The amplitude and period of sin or cos graphs
    11. How to change the period of a sine graph
    12. How to change the period of a cosine graph
    13. Trigonometric graphs in all four quadrants (radians)
    14. Unit circle: sin cos and tan in radians
16. Sequences and series:
    1. Arithmetic Sequences and series
    2. Geometric sequences and series
17. Functions
    1. The vertical line test for a function.
    2. Finding maximum points using translations of functions.
    3. Horizontal translation of a graph.
    4. Horizontal translation of a graph.
    5. Reflection in the x-axis.
    6. Reflection in the y-axis.
    7. The graph of y=f(x) after a stretch parallel to the y-axis.
    8. The graph of y=f(x) after a stretch parallel to the x-axis.
    9. Combined transformations of functions.
    10. Combinations of transformations of graphs of functions a stretch and a translation
    11. Worksheet for transformations of graphs.
    12. The composite of two functions.
    13. The inverse of a function.
    14. The inverse of a quadratic function.
    15. The modulus function.
    16. The graphs of y = |f(x)| and y = f(|x|).
    17. Finding the gradient of the inverse function from a function.
    18. Domain and range of a function
    19. Finding the gradient of the inverse function from a function
    20. An odd function
    21. An even function
    22. Drawing transformations of a piecewise function
    23. Combinations of transformations for graphs
    24. The graphs of y = |f(x)| and y = f(|x|)
    25. Composite functions with restrictive domains and inverse
18. Differentiation shape of curve, chain, product and quotient rules:
    1. The shape of a curve
    2. Non-stationary points of inflection and concavity.
    3. The rate of change of a shadow
19. Trigonometric functions:
    1. y=1/sinx=cosecx
    2. y = 1/cosx = secx
    3. y = 1/tanx = cotx
    4. The inverse of y = sinx
    5. The inverse of y = cosx
    6. The inverse of y=tanx
    7. Understanding the unit circle in trigonometry in degrees.
    8. Describing transformations of a sine graph
20. Further algebra:
21. Trigonometric identities:
    1. Sine and cosine properties
    2. Horizontal translation of a sine graph
    3. Horizontal translation of a cosine graph
    4. acosx - bsinx = Rcos(x + alpha).
    5. Transformation of y=acosx-bsinx to Rcos(x+alpha)
    6. Writing acosx+bsinx in the form Rcos(x-a)
    7. Properties of tan(-θ)
    8. Harmonic motion of a particle with damping
22. Further differentiation:
    1. Derivative of y=a^x
    2. The number e
    3. The derivative of f(x) = lnx
    4. Derivative of sinx in radians
    5. Derivative of cosx in radians
    6. Derivative of tanx
    7. The derivative of sinx from first principles.
    8. The equations of tangent and normal for a parametric curve
    9. The parametric equation of a circle with chord and tangent
    10. Projectile motion of a rocket using parametric equations.
    11. Tangents on an ellipse.
    12. Curve sketching a natural log function showing concavity
    13. Stationary points on a circle
23. Integration:
    1. Finding the number e
    2. Small angles measured in radians.
    3. Gradient function of trig functions.
    4. Definite integral investigation
    5. The area under a curve and the x-axis.
    6. The area bounded between two curves.
    7. The trapezium rule.
24. Parametric equations:
    1. Parametric equations introduction
    2. Parametric equations introduction
    3. Parametric equations using theta 01
    4. Paramentric equations using theta 02
    5. The parametric equation of a hyperbola.
    6. The parametric equation of a circle.
    7. The equations of tangent and normal for a parametric curve
    8. The parametric equation of a circle with chord and tangent
    9. Projectile motion of a rocket using parametric equations.
    10. Tangents on an ellipse.
    11. Opposite directions on a parametric curve
    12. Parametric integration
    13. Parametric equations using trigonometry
    14. The motion of a particle parametrically
25. Vectors in three dimensions
    1. The addition of vectors.
    2. The subtraction of vectors.
    3. The multiplication of a vector by a scalar.
    4. 2D vectors in magnitude-direction and component forms.
    5. Position vectors in component form in 3D.
    6. The magnitude or length of a vector in 2D and 3D
    7. Finding the vector joining the point P and Q and its magnitude.
    8. A trapezium and parallel vectors.
    9. The scalar product proof
    10. Scalar product 3d
    11. Finding the area of a triangle in 3-Dimensions.
    12. Finding a vector in 3d space.
    13. A parallelogram in 3d space.
26. Using integration to solve differential equations:
    1. The limiting value of a differential equation 01.
    2. The limiting value of a differential equation 02.
    3. Solving a differential equation for an electrical circuit.
    4. Solution of a 1st order differential equation with slope field.
    5. Differential equation solution of a mass being projected upwards
    6. 1st order differential equation by separating the variables
    7. 1st order trig differential equation by separating the variables
    8. Solution of a 1st order differential equation by separating the variables (Harder)
    9. Solution of a differential equation by separating the vars
27. Numerical methods:
    1. Fixed point iteration 01
    2. Fixed point iteration staircase diagram.
    3. Fixed point iteration 02.
    4. Fixed point iteration cobweb diagram.
    5. Fixed point iteration of a trig function.
    6. Fixed point iteration staircase diagrams
    7. The Newton-Raphson method.
    8. Newton-Raphson method for finding roots.
    9. Introduction to the trapezium rule
    10. Trapezium rule.
    11. Trapezium rule for concave downwards,
    12. Using the trapezium rule with radians
    13. Using rectangles to find bounds for the area under a curve.
    14. Using rectangles to find bounds for the area under a curve.
    15. Area under the curve x^x