MATH NOTES

MATH NOTES v1.0.0

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PURE MATH

BINOMIAL EXPANSION

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Includes

• Introduction to Pascal's triangle
• Expanding binomials
• Examples of types of questions

1. Finding the coefficient of a specific term
2. Finding the term independent of x
3. Expanding the binomial
4. Finding the coefficient of a specific x where r is not given
5. Finding an extra unknown in the binomial
6. Two bracket questions
7. Binomial estimation / approximation
8. Finding an unknown n using the expansion of ncr

COORDINATE GEOMETRY
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QUADRATIC FUNCTIONS
Includes

• General from
• Turning point form
• X-intercept form
• Completing the square

CIRCLES, TANGENTS, TRIANGLES

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Includes

• Gradient formula
• tanx=m
• Distance formula
• Midpoint formula
• Perpendicular lines
• Parallel lines
• Straight line formulas
• Circle formulas
• Diameter subtends 90 degrees
• Pythagorus
• Consecucircles
• Secant
• Tangent
• Center radius form
• Perpendicular bisectors of chords

FUNCTIONS
EXPONENTIAL AND LOG FUNCTIONS

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Includes:

• Exponential functions introduction, transformations and reflections
• Log functions as inverse of exponential functions
• How to graph exponential and log functions
• Laws of exponents
• Log laws

INTEGRATION AND DIFFERENTIATION

INTEGRATION AND DIFFERENTIATION 1

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OPEN CHAIN RULE EXAMPLES

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Includes:
Introduction to:

1. Power rule to differentiate
2. Reverse power rule to integrate
3. Chain rule to differentiate
4. Reverse chain to rule integrate

INTEGRATION AND DIFFERENTIATION 2

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Includes:

• Power rule
• Chain rule
• Tangents and normal to the curve
• Stationary points and first derivative (Max/min/point of inflection)
• Second derivative (concavity/nature of stationary points/ point of inflection)
• Sketch of the relationship between the curve, first and second derivative
• Sketching cubic graphs
• Optimisation / modelling
• Definite integrals (area / volume)

SEQUENCES AND SERIES

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Includes:

• Arithmetic sequences and series
• Geometric sequences and series
• Sigma notation
• Quadratic sequences
• Examples of the following:

1. Finding the position
2. Finding the value
3. Finding a formula for the nth term
4. Examples of sigma notation
5. Examples of the use of simultaneous equations
6. Finding certain terms in a sequence
7. Sum to n questions
8. Sum to infinity questions
9. Problem solving questions
10. Problems with extra unknowns in the sequence or series
11. Recurring decimals proof using sum to infinity

NATURE OF ROOTS

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• Includes notes and examples using the discriminant to comment on the nature of the roots of quadratic functions

POLYNOMIALS

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Includes:

1. Factoring cubic functions
2. Factor and remainder theorem

TRIGONOMETRY

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Includes:

• Trig graphs
• Unit circle
• Pythagorus
• Special triangles
• Area rule
• Cos rule
• Sin rule
• Reduction formulae
• Co-ratios
• Cartesian plane quadrants in degrees and radians
• Converting to degrees or radians
• Quotient identity
• Pythagorean identity
• Double angle formulae
• Compound angle formulae
• General solution

STATISTICS

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