Forms of Vectors ● Vectors have both direction and magnitude ● May be written in bold, underlined or with an arrow above them to show their direction ● Magnitude-direction form: ○ Written in brackets ○ (magnitude, direction as angle) ○ Direction angle measured...

# Pure

## Trigonometry

Functions for Angles Between 0° and 90° Common Values of Sin, Cos and Tan Functions for Angles of Any Size ● Imagine triangle with hypotenuse h ● Opposite side = h sin θ ● Adjacent side = h cos θ The Angles of Trigonometric Functions ● Imagine a triangle inside a...

## Surds and Indices

Rational and Irrational ● Some numbers are irrational - cannot be expressed as fractions as decimals go on forever without pattern ● Square root of number that isn’t perfect square is also irrational ● However this is partly rational as you can write it as the square...

## Quadratic Functions

Graphs ● Factorising quadratic expression gives information about the graph of the function ● X-intercepts found from numbers in each bracket ● Y-intercept is product of numbers in brackets ● If there is a single negative x in the factorised expression, the graph is...

## Polynomials

Graphs Sketching Polynomials ● Factorise the expression as much as possible to give the x-intercepts ● Set x equal to 0 and find the y-intercept ● Consider what happens as x tends towards ±∞ ● Make sure the graph is the right way up Finding the Equation of a...

## Graphs and Transformations

Reciprocal Graphs Points of Intersection ● Coordinates of POI satisfy the equations of both curves/lines ● Solve equations simultaneously to get coordinates of POI ● Mark on graph when sketching Proportional Relationships ● If y is directly proportional to x then the...

## Inequalities

Symbols ● < → less than ● > → greater than ● ≤ → less than or equal to ● ≥ → greater than or equal to ● Number line inequalities - filled-in circle means ‘or equal to’ ● Graphical inequalities - solid line means ‘or equal to’ Linear Inequalities ● Involves only...

## Exponentials and Logarithms

Exponential Functions ● In the form y = ax ● Often used to model growths → exponential growths take the form y = cakx ● Can also have exponential decays (take the form y = ca-kx ) Logarithms ● Logarithms (logs) are the inverse of exponentials ● logab = x ⇔ ax = b ●...

## Binomial Expansion

Pascal’s Triangle You can expand an expression in the form (a + b)n using Pascal’s triangle ● Find the n th row of the triangle ● The coefficient of each term is multiplied by the corresponding number on the row of the triangle (ie the second term’s coefficient is...