Mathematics GCSE Revision Key points to remember Mr Collins Maths Mr Collins Maths Data Handling & Probability

Scatter Graphs Correlation: ‘positive’, ‘negative’, or ‘no’ Always draw a line of best fit on the scatter graph – especially when asked to ‘estimate’ a value off the graph Example: Estimate the distance (Km) for an engine size of 1.5 litres Draw a line from 1.5 litres on the engine axis (horizontal) and then when it hits your line of best fit, go along to the Distance axis (vertical). Read off the value – this is your answer Describe the relationship type questions: ‘Negative correlation’ or ‘as the engine size increases the distance (Km) decreases’

Stem & Leaf Diagrams The ‘leaf’ part of the diagram must be in order (the numbers should go from smallest to highest from left to right) You’ll lose a mark if you don’t do this! Stems (usually the 1st digit of your numbers; the 1st two digits if you have 3-digit numbers) Leafs – the last digit in each of your numbers You MUST include a ‘Key’. You’ll lose a mark if you don’t do this! 2 3 4 5 9 1 3 5 6 9 2 3 3 4 6 8 9 2 4 5 Key: 2|9 = 29mph Check you have the correct number of numbers in your ‘leaf’ section – this should equal that in the question (16) If you miss one out, or add an additional number in you’ll lose a mark

Plot the frequencies at the midpoints of each group! Frequency Polygons Plot the frequencies at the midpoints of each group! Midpoints 25 35 45 55 65 Join the points up with a straight line between each pair Don’t forget to join the first and last points to complete the polygon (many sided shape)

Check all the rows/columns add up Two Way Tables How did you get to school today? Fill in the bits of information that you know (that you’re given in the question) Walked Bicycle Car TOTAL Girls Boys 19 20 10 49 Now, using this information, fill in the blanks – simple addition/subtraction! 16 21 14 51 Check all the rows/columns add up 35 41 24 100 Answer the question!!

Questionnaires Possible Reasons: ‘Overlapping Boundaries’ – the £30 appears in two option boxes, which one do you tick? No option for less than £10 spent (non-exhaustive option boxes) No time frame stated – is it per month, week, year?? (b) Design a better question for Paula’s questionnaire to find out how much money people spend buying CDs. You need to give: A question, re-worded as above, but with a time period. i.e. ‘How much money do you spend, per week, buying CDs?’ [1 mark] Option boxes (at least 3) that do not overlap and include all possible outcomes [1 mark] i.e. £0 - £10 £11 - £20 £21 - £30 £31 or more

Estimating the Mean from a Grouped Frequency Table First, find the midpoints of the groups so we can take our best estimate. Midpoints 5 15 25 35 45 Mid x freq (fx) 5x3 = 15 15x8 = 120 25x11 = 275 35x9 = 315 45x9 = 405 3+8+11+9+9 = 40 15+120+275+315+405 = 1130 Multiply the midpoints by the frequencies to create a new column (fx) It’s an estimate because we don’t know the exact times Bob’s friends took to get to work; we just know that 3 of his friends took somewhere between 0 and 10 minutes to get to work...etc...! Add up this column Divide the total of your created column by the total of the frequency column 1130/40 = 28.25 minutes (your estimated mean & answer!) Add up the frequency column (might be stated in the question)

Box Plots (HT Only) Note: the numbers are in order from smallest to biggest! Complete the box by joining around the centre 3 marks (the quartiles and the median), then draw lines to the lower and upper values. Like this... You need 5 things to draw a box plot: Lowest value, lower quartile, median, upper quartile, highest value The middle value of all the numbers to the left of the median The middle value The middle value of all the numbers to the right of the median

Cumulative Frequency Curves (HT Only) a ‘running total’ of the frequencies You can then find the median, LQ and UQ... Add these up as you go down to fill in the cumulative frequency table Join with a smooth curve! 11 34 65 92 100 UQ UQ = (100/4)x3 = 75 median Median = 100/2 = 50 The last row should equal the value given in the question (100 in this case) LQ LQ = (100/4) = 25 Now plot these cumulative frequencies at the END POINTS of each group

Stratified Random Sampling (HT Only) A stratified sample is when you take a representative portion of each group within your sampled population 80 In this case, look at the total column in the table (567), otherwise just add up each group until you get the total! 94 = 13.2627866... 567 Round...13

The area of each bar represents the frequency Histograms (HT Only) 5 4 3 2 1 A histogram plots frequency density, not frequency Frequency Density = Frequency/Class Width Frequency density Scale your axes appropriately Frequency density 15/5 = 3 25/5 = 5 36/10 = 3.6 24/20 = 1.2 Now draw the bars to make your histogram (no gaps in between them) The area of each bar represents the frequency

5 red marbles + 3 green marbles = 8 marbles in total Probability (Tree Diagrams) (HT Only) 5 red marbles + 3 green marbles = 8 marbles in total After the 1st pick you have 1 marble less for the 2nd pick (so in total we have 7) Depending on what has been picked out in the 1st pick the probabilities for the 2nd pick change 5 red marbles/8 marbles in total Adds to 1 Each ‘branch’ of the tree diagram should add to 1 as all probabilities for a singles event occurring add to 1 Adds to 1 Adds to 1 3 green marbles/8 marbles in total

Probability (Tree Diagrams) (HT Only) AND = multiply OR = add Probability (Tree Diagrams) (HT Only) This means he could take: a red AND then a green (different colours) OR a green AND then a red (different colours) So, if he could get different colours by doing red AND green OR by doing green AND red...we add these together to get the final probability of getting different colours red AND then green green AND then red