Maths AA DP1-2 (SL & HL)

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Formulae (SL & HL)

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204 Terms

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Arithmetic Sequence

Increases or decreases by the addition of a numerical factor.

<p>Increases or decreases by the addition of a numerical factor.</p>
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Arithmetic Sum

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Geometric Sequence

Increases or decreases by the multiplication of a numerical factor.

<p>Increases or decreases by the multiplication of a numerical factor.</p>
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Geometric Sum

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Convergent Series

Keeps decreasing until it converges at one value e.g. geometric sequences.

<p>Keeps decreasing until it converges at one value e.g. geometric sequences.</p>
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Divergent Series

Keeps increasing till infinity e.g. arithmetic sequences.

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Combinatorics

The number of way you choose r objects from n choices.

<p>The number of way you choose <strong><em>r</em></strong> objects from <strong><em>n</em></strong> choices.</p>
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Permutations

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Binomial Expansion

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Binomial Expansion for Fractional Powers

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Binomial Expansion for Negative Powers

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Proof by Mathematical Induction

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Zero and One Power Rules (Indices)

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Product and Greater Exponent Rules (Indices)

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Quotient and Negative Exponent Rules (Indices)

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Fractional and Same Exponent Rules (Indices)

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Inverse Function Rule (Logarithms)

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Basic Logarithms

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Addition Rule (Logarithms)

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Subtraction Rule (Logarithms)

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Power Rule (Logarithms)

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Log of Base and 1 (Logarithms)

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Quotient Rule (Logarithms)

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Negative and Fractional Rules (Logarithms)

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Natural Logs and Greater Exponent Rules (Logarithms)

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Concept of ‘i’

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Imaginary/Complex Numbers

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Absolute Value (Complex Numbers)

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Addition Rule (Complex Numbers)

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Multiplication by a Scalar (Complex Numbers)

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Complementary Imaginary Numbers

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Magnitude of Complex Numbers

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Polar Form (Complex Numbers)

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Angle of a Complex Number

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Angles in each Quadrant (Complex Numbers)

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Euler’s Form (Complex Numbers)

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Representation of Complex Numbers

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Symmetry of Complex Numbers

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Product Rule (Complex Numbers)

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Quotient Rule (Complex Numbers)

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De Moivre’s Theorem

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Roots of Complex Numbers

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Vertex Form of a Function

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Inverse Form of a Function

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Graph of 1/x

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Graph of x2

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Graph of x3

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Graph of ax

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Graph of a-x

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Graph of x1/2 (Square Root of x)

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Quadratic Formula

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Translations of Functions

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Dilations of Functions

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Exponential Growth (Functions)

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Rational Functions

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Partial Fractions

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Absolute Value (Functions)

The absolute value of any number a is the ‘real’ value of a, i.e. it is always greater than zero.

<p><span>The absolute value of any number <strong><em>a</em></strong> is the ‘real’ value of <strong><em>a</em></strong>, i.e. it is always greater than zero.</span></p>
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Graph of Absolute Value Functions

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Absolute Value of Negative Numbers

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Absolute Value of Zero

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Product Rule (Absolute Value)

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Quotient Rule (Absolute Value)

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Addition Rule (Absolute Value)

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Subtraction Rule (Absolute Value)

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Comparison of Absolute Numbers

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Distance Formula (2D)

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Coordinates of Midpoints (2D)

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Parallel and Perpendicular Lines

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Surface Area and Volumes of Common Solids

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Distance Formula (3D)

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Coordinates of Midpoints (3D)

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Radians

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Common Angles in Radians

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Sine and Cosine in the Unit Circle

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Unit Circle

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Arc Length

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Area of a Sector

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Sine Rule

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Cosine Rule

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Area of any Triangle

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tan (θ)

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cosec (θ)

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sec (θ)

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cot (θ)

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Pythagorean Identity (Trigonometry)

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sin(2θ) - Double Angles

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cos(2θ) - Double Angles

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tan(2θ) - Double Angles

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sec2(θ)

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cosec2(θ)

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sin (A±B) - Compound Angles

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cos (A±B) - Compound Angles

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tan (A±B) - Compound Angles

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Transformations (Trigonometry)

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Graphs of sin(x), cos(x) and tan(x)

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Periodicity of Angles in Radians

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Directed Line Segment

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Vectors

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Properties of Vectors

  • Collinearity - Two points are colinear if they lie on the same line.

  • Coplanarity - Two points or lines are coplanar if they lie in the same plane.

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Parallelogram Rule (Vectors)

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