Unit 1
Chapter 1  The straight line
 Distance formula
 Midpoint formula
 Gradient formula
 Gradient  angle formula
 Gradients of horizontal and vertical linesParallel and perpendicular lines
 Product of perpendicular gradients = 1
Forms of the equation of a line:
y = mx + c gradient m and yintercept c
ax + by + c = 0 linear form  usually with integer coefficients
Finding the equation of a straight line
y  b = m(x  a) line has equation m and passes through point (a, b)
Lines in triangles
Median
of a triangle the line from a vertex to the midpoint of the opposite side.
Altitude
of a triangle  the line from a vertex perpendicular to the opposite side.
Perpendicular bisector
of a line  passes through the midpoint of the line at right angles to it.
Intersection
of two lines  solve the equations of the two lines simultaneously.
Chapter 2.1  Composite and inverse functions
 Domain and range
 Composite Functions f(g(x))
 Working with fractions
 Functions with inverses
 Reflection in the line y = x
Chapter 2.2  Algebraic functions and graphs
 Completing the square
 Maximum and minimum values
 Working with fractions
 Sketching the graph of a quadratic equation
 Graphs of related functions
 y = f(x) Reflect in x axis
 y = f(x) Reflect in y axis
 y = f(x + a) Move graph a units to the LEFT
 y = f(x  a) Move graph a units to the RIGHT
 y = f(x) + a Move graph a units UP
 y = f(x)  a Move graph a units DOWN
 y = kf(x) Scale graph in ydirection
 y = f(kx) Scale graph in x direction
Remember to show the images of any given points on the graph.
 Graphs of exponential functions  sketching them and recognising them
 Graphs of logarithmic functions  sketching them and recognising them
Special Logarithms
 Make use of the two special logs
and the relationship between
the exponential and logarithmic functions
Chapter 2.3  Trigonometric functions and radians
 Degrees and radians
 Changing between degrees and radians
 Angles larger than 90°
 Angles of all sizes 0 to 360° and radian equivalent
 Using ASTC (All Sinners Take Care) for angles in all 4 quadrants.
 Exact Values
 Knowing exact values for sin, cos, tan of 30°, 45°, 60° and radian equivalent
 Trigonometric Graphs
 Sketching and recognising trigonometric graphs in the form y = a sin bx + c
 Equations
 Solving basic trigonometric equations with solutions in 0 to 360° or radians
Chapter 3.1  Differentiation
 Differentiation gives the gradient function
 The gradient function lets you calculate the gradient at any point on the graph.
 IMPORTANT  you can only differentiate powers of x at this point.
 Rules for differentiation
 Must be in straight line form  change any surds to index form
 Multiply by the index and then decrease the index by 1
 The derivative of x is 1
 The derivative of a constant is 0
 Carry through any multipliers  integer or fractional.
 You should be confident at differentiating:
 Positive and negative indices
 Fractional indices
 Dealing with integer or fractional multipliers
 You should be able to split fractions into separate powers of x
 You should be able to multiply out brackets using FOIL.
 Using Leibniz notation for differentiation
 Find the equation of a tangent to a curve at a given point.
 Finding the point on a curve when you are given the value of the gradient.
 Sketch the graph of a derived function
 Also sketch the graph of a possible function given the derived function graph.
Chapter 3.2  Using Differentiation
 Finding stationary points
 Maximum and minimum points
 Nature of stationary points  Table of Signs
 Maximum and minimum values on closed intervals
 Problem Solving
 Making a formula
 Forming a constraint
 Finding the maximum or minimun value.
 The derivative as a rate of change
 Velocity and acceleration
 x is displacement, t is time
 velocity = dx/dt
 acceleration = dv/dt .
 maximum height occurs when velocity = 0
 The common linkage between displacement, velocity and acceleration is t the time of the event.
Chapter 4  Sequences
 nth term formulae  finding and generating terms.
 Recurrence relation formulae  finding formula and generating terms
 Using a recurrence relation to describe a problem
 Using a geometric sequence
 growth and decay
 interest calculations
 appreciation and depreciation
 Finite and infinite sequences
 Finding the limit of an infinite sequence as n tends to infinity
 Solving problems with the linear recurrence relation
 Condition for limit of a linear recurrence relation
 Finding the limit of a recurrence relation
 Working with recurrence relations algebraically
 Sequences with the same limits
 Using simultaneous equations
 Finding constants
