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			Standard Grade Credit Level


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		Quiz 1 - PowerPoint Download Answer Key Course material - grouped by topic click on links for more detail
		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 non-replacement 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, semi-interquartile 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 mid-value 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 Scale Factors and scale models Calculations with similar shapes Linear, area and volume scale factors Similar triangles 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 SOH-CAH-TOA – 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 semi-circle are right angles 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 – SOH-CAH-TOA Fractions of a circle Lengths of Arcs Areas of Sectors Trigonometry – Calculations, Graphs and Equations Exact values of sin, cos, tan 30°, 45°, 60 3D Calculations visualising right angles in 3D drawings of cuboids Calculation of face and space diagonals Sine, cos, tan of angles of all sizes Using ASTC Tutorial on Trigonometric Graphs Trigonometric functions and their graphs Graph of the sine and cosine function Graph of the tangent function Sketching Trigonometric Graphs Solving Trigonometric Equations Two useful formulae 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 - SOH-CAH-TOA Prisms Identifying a prism – uniform cross-section 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 Factorising using common factors The difference of two squares Solutions to examples Factorising a trinomial - into two brackets Factors and sequences Using expressions for odd and even numbers Simplification of expressions Using nth term formula. 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 = y-intercept Write down gradient and y-intercept 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 y-intercept. Straight Lines as mathematical models Writing down the equation from the graph Problem solving applications Best-fitting 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 of f is 0, when x = 0 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 x-axis 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 common denominator Solving equations with fractions Remove fractions first Remove brackets Indices and Surds Tutorial on Indices Rules of indices Simplifying expressions Zero and negative indices Dealing with multipliers , Fractional indices Surds Tutorial on Surds Rules for 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
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