Index:
Calculations and Mathematics in Society
Calculations, Calculators, Percentages
Standard Form
Fractions
Personal Finance
Distance, Speed & Time
Proportion
Probability, Information Handling & Statistics
Probability
Statistics
Geometry & Trigonometry
Similar Triangles and Similar Shapes
Pythagoras
Trigonometry
SOHCAHTOA
Sine and Cosine Rule
Area of a triangle
Circle
Trigonometric Graphs and Equations
Areas and Volumes
Cylinders & Prisms
Algebra
Positive and Negative Numbers
Removing Brackets, FOIL, Multiplication Tables
Inequalities
Simultaneous Equations
Factors and Factorising
common factors
pairs of brackets
difference of two squares
Sequences
Factors, odd and even numbers
Solving Quadratic Equations
Using and making formulae
Gradient and equation of a straight line
Functions  evaluating
Graphs  parabola, cubic, reciprocal (hyperbola)
The Quadratic Function and its properties
Simplifying algebraic Fractions
Solving algebraic fraction Equations
Indices
Surds
Calculations and Mathematics in Society
Calculations and the Calculator
 Using the calculator
 Standard form
 Fractions
 Percentage Calculations
 Finding a percentage
 Increasing and decreasing using a multiplier
 Reversing the change  working backwards
Personal finance
 Payslips, Wages & Salaries
 Calculating Gross pay, Deductions, Net pay
 Calculating Pension – superannuation
 Using a table to find National Insurance (NI) deduction
 Income Tax calculations  using a table
 Simple interest calculations on savings
 Compound Interest on savings
 VAT  Value Added Tax
 Telephone, Electric and Gas Bills
 Hire Purchase
 Holidays abroad  changing money into different currencies
 Life Insurance
 Calculating premiums
 Appreciation and Depreciation
Distance, speed and time
 DST triangle
 Calculating distance, speed, time
 Changing hours and minutes to decimal fractions of an hour
 Interpreting graphs
Proportion in Practice
 Tutorial on Proportion & Variation
 Direct Proportion
 Writing down a proportionality and then an equation using a constant.
 Direct proportion calculations
 Using squares and square roots
 Inverse Proportion
 Joint variation
 Halving and doubling – including squares.
 Variation with more than one variable changing.
e.g. double one and treble another
Problem Solving
 Mathematical Pictures
 Matching graphs to pictures
Probability, Information Handling and Statistics
Probability
 Calculating simple probability
 Effect of nonreplacement
 Effect of changing probabilty by adding more items
 Combining probabilities – two events
 Mutually Exclusive Events
 Table of outcomes or tree diagram
 Adding probabilities when two events are mutually exclusive.
 P(A or B) = P(A) + P(B)
e.g. Probability of a 3 or a 4 when a dice is rolled = 1/6 + 1/6 = 2/6 = 1/3
 Independent Events
 Table of outcomes or tree diagram
 Multiplying probabilities when two events are independent.
 P(A and B) = P(A) x P(B)
e.g. Probability of a 3 on the first roll and an 4 on the second roll of a dice
= 1/6 x 1/6 = 1/36
 Relative Frequency and Probability
 Experimental Data
 Observation, surveys, Relative frequency Table
 Calculating the probability of an event from the relative frequency
 Expectation = Number of events x P(outcome)
Statistics
 Tutorial on Pie Charts
 Graphs and Charts
 Interpreting  bar graph, line graph, pie chart
 Constructing a pie chart by calculating angles
 Calculating values from a pie chart
 Stem and Leaf Diagrams
 Back to back stem and leaf
 Dotplots – constructing
 describing the distribution
 Five Figure Summary
 Box Plots
 Construct a box plot from a five figure summary
 Comparing distributions
 typical value – Median
 Spread of the marks  Interquartile range or Semi interquartile range
 Calculating quartiles
 Statistical Measures
 Mean, median, mode, range
 Interquartile range, semiinterquartile range
 Standard Deviation
 Calculating mean and standard deviation
 Being able to use both formulae
 Comparing two distributions
 Frequency Tables
 The meaning of a frequency table
 Construction of a frequency table using tally marks
 Calculate mean of a frequency table
 Frequency Tables with class intervals
 Working with midvalue
 Calculate mean
 Cumulative Frequency Tables
 Construction from a frequency table
 Read information from a frequency table.
 Cumulative Frequency Diagrams
(graph)
 Construction from a cumulative frequency table
 Read information from a cumulativefrequency table.
Geometry
Similar Shapes
Pythagoras
 Know Pythagoras' Theorem
 Calculate hypotenuse or a shorter side in a right angled triangle.
 Work with isosceles triangles
 Converse of Pythagoras  Is it a right angle ?
Trigonometry
 SOHCAHTOA – in a right angled triangle.
 Knowing ratios for sine, cosine, tangent.
 Finding a short side
 Finding the hypotenuse
 Finding an angle
 Applications of trigonometry to isosceles triangles
 The Sine Rule
 Finding a side, Finding an angle, Finding the altitude of a triangle
 The Cosine rule – with cyclic permutation
 Finding a side SAS, Finding an angle SSS
 Area of a triangle
 Area = (SAS)
 Selecting a strategy
 If a right angled triangle  use SOHCAHTOA
 If not:
 SAS, SSS use cosine rule
 All other cases use sine rule
 Applications
Symmetry in the Circle
 Angles in circles
 Isosceles triangles
 calculating base angles and centre angle
 Angles in a semicircle
 Tangents to a circle
 are at right angles to the radius at the point of contact
 Symmetry about a diameter
 Chords
 Isosceles triangles
 Applications
 Using Pythagoras
 Milk and oil tanker
 Bridges
 Tunnels
 Shelters
 Widths and heights
 Using Trigonometry – SOHCAHTOA
 Fractions of a circle
 Lengths of Arcs
 Areas of Sectors
Trigonometry – Calculations, Graphs and Equations
Areas and Volumes
 Rectangle, Triangle and Circle
 Areas, Perimeters, Using on the calculator
 Composite shapes
 Area calculations
 Perimeter calculations
 Areas of quadrilaterals
 Rhombus and kite
 Parallelogram
 Trapezium
 Using Pythagoras
 Using Trigonometry  SOHCAHTOA
 Prisms
 Identifying a prism – uniform crosssection
 Volume = Area of cross section x height
 Cylinders
 volume
 Working with cubic centimetres and litres
 Calculating the height or radius
 Area  curved surface area:
 Open and closed cylinders  Area of lid or base =
Algebra
Positive and negative numbers
 Add and subtract positive and negative numbers
 Multiply and divide positive and negative numbers
 Simplifying expressions
 Solving simple equations
Brackets and Equations
 Examples
 Solutions
 Removing a single bracket
 Solving equations with single brackets
 Using FOIL  to multiply a pair of brackets
 Using a multiplication table
 Breaking brackets when squared e.g.
Inequalities
 Solving simple inequalities – with and without brackets
 Know that multiplication or division by a negative number changes direction of inequality
Simultaneous Equations
 Tutorial
 Forming simultaneous equations to describe a problem
 Solving simultaneous equations
 using graphs
 by substitution
 by elimination
 Applications to problem solving
Factors
Quadratic Equations
 Tutorial
 Solving quadratic equations
 Using graphs
 Factorising
 Using common factor to obtain solutions
 Difference of two squares
 Putting a trinomial into two brackets
 Solving using the formula
 Quadratic equations as mathematical models  Problem solving
Formulae
 Substituting numbers into formulae
 Making up your own formulae when reading a question
 Changing the subject of the formula
 Being able to reason the result if variables are halved or doubled
Gradient and Equation of a Straight Line
 Tutorial
 Calculating a gradient:
 Equation of a straight line
 y = mx + c m = gradient c = yintercept
 Write down gradient and yintercept from the basic equation
 Sketching a line from the equation
 A point lying on a line satisfies the equation of the line
 Finding equation of a line with gradient and a point
 Finding equation of a line through two points
 Rearranging an equation to find the gradient and yintercept.
 Straight Lines as mathematical models
 Writing down the equation from the graph
 Problem solving applications
 Bestfitting straight line
 Plotting experimental data, including the mean
 Finding the best fitting straight line
 Find the equation of the line
 Use the equation to predict a value
Functions and Graphs
 Tutorial
 Evaluating a function
 e.g. If f(x) =3x  7, evaluate when x = 1
 Work back to the input
 e.g. If f(x) = 7x+3, find a, if f(a) = 10
 Graphs of functions
 Recognise: Linear, Quadratic, Cubic, Reciprocal functions
 Knowing and understanding properties of the quadratic function
 The parabola is a quadratic function
 Minimum value
 Axis of symmetry
 goes through the minimum and is the line x = 0
 Graphs of parabolas
 Identify orientation
 (which way up it is) u or n
 Identify maximum or minimum
 value of x for which max or min occurs
 identify axis of symmetry
 x = ........ (value of x on which the turning point lies)
 Identify roots of the equation
 where f(x) = 0 ie. where graph cuts the xaxis
Fractions and Equations
 Tutorial
 Simplifying fractions
 cancelling down
 spotting and using common factors
 spotting and using difference of two squares
 Multiplication and division
 Multiply  multiply tops, multiply denominators
 Divide  invert (flip) second fraction and change to multiply
 Addition and subtraction
 Solving equations with fractions
 Remove fractions first
 Remove brackets
Indices and Surds
 Tutorial on Indices
 Rules of indices
 Zero and negative indices
 Dealing with multipliers
 ,
 Fractional indices
 Surds
 Applications
 Simplifying
 by forming a product with the largest perfect square factor
 Adding and subtracting surds
 Simplifying expressions by combining them
 Rationalising the denominator
 multiply top and bottom by appropriate surd
e.g. since

