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Iportant Maths Topics
Key Topics: Probability Area and Perimeter Triganometry Volume D/T and V/T Graphs Graph Transformation Graphs of Sine and Cosine Quadratic Equations Simaltaneous Equations and Graphs Trial and IMprovement Quadratic Formula Completeing the Square Factorising Quadratics Algebraic Fractions and D.O.T.S Speed, Distance and Time Formula Triangles Variation Direct InverseProportioin Compound Growth and Decay Percentage Problems Calculation Bounds Standard Index Forms
Histograms
When to Use a Histogram When the data are numerical. When you want to see the shape of the data’s distribution, especially when determining whether the output of a process is distributed approximately normally. When analyzing whether a process can meet the customer’s requirements. When analyzing what the output from a supplier’s process looks like. When seeing whether a process change has occurred from one time period to another. When determining whether the outputs of two or more processes are different. When you wish to communicate the distribution of data quickly and easily to others. Histogram Construction: Collect at least 50 consecutive data points from a process. Use the histogram worksheet to set up the histogram. It will help you determine the number of bars, the range of numbers that go into each bar and the labels for the bar edges. After calculating W in step 2 of the worksheet, use your judgment to adjust it to a convenient number. For example, you might decide to round 0.9 to an even 1.0. The value for W must not have more decimal places than the numbers you will be graphing. Draw x- and y-axes on graph paper. Mark and label the y-axis for counting data values. Mark and label the x-axis with the L values from the worksheet. The spaces between these numbers will be the bars of the histogram. Do not allow for spaces between bars. For each data point, mark off one count above the appropriate bar with an X or by shading that portion of the bar. Histogram Analysis: Before drawing any conclusions from your histogram, satisfy yourself that the process was operating normally during the time period being studied. If any unusual events affected the process during the time period of the histogram, your analysis of the histogram shape probably cannot be generalized to all time periods. Analyze the meaning of your histogram’s shape.
Pythagoras
http://www.bbc.co.uk/bitesize/ks3/maths/shape_space/pythagoras_theorem/revision/2/ Use this URL to find out more information on pythagoras and to have a go at practise questions. 2D Pythagoras 3DPythagoras
Cumulative Frequency
Table example: Shoe size Frequency Cumulative Frequency 3-5 3 3 6-8 12 15 9-11 9 24 12-15 4 28 Range - Largest number minus the lowest = 28 Median - Middle = 14 Upper Quatrile = 75% of data Lower Quartile = 25% of data Interquartile Range (IQR) = Upper - Lower Quartile A cumlative Freqency Graph always forms an S shape.
Circle Theorems Rules
First circle theorem - angles at the centre and at the circumference. Second circle theorem - angle in a semicircle. Third circle theorem - angles in the same segment. Fourth circle theorem - angles in a cyclic quadlateral. Fifth circle theorem - length of tangents. Sixth circle theorem - angle between circle tangent and radius. Seventh circle theorem - alternate segment theorem.
Trigonometry
The three formulae: sin, cos, tan The sides of the right-angled triangles are given special names - the hypotenuse, the opposite and the adjacent. The hypotenuse is the longest side and is always opposite the right angle. The opposite and adjacent sides relate to the angle under consideration. sin = opposite / hypotenuse cos = adjacent / hypotenuse tan = opposite / adjacent Which formula you use will depend on the information given in the question. There are a couple of ways to help you remember which formula to use. Remember SOHCAHTOA (it sounds like 'Sockatoa') or Some Old Hag Cracked All Her Teeth On Apples.
Transformations
Enlargement- Scale Factor, Point of enlargement Translation -Vector Rotation - Angle of rotation, direction of rotation, point of rotation Reflection -Mirror Line
Types of Graphs
Cumulative Freqency Histograms Line Graghs Pie Chart Bar Graph Line Graph Quadratic graphs
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