Welcome to the Revision Conference

1. Welcome to the Revision Conference

2. Four Learning Sessions: • Data • Algebra • Shape • Number • Assessment after each session • Time with your teachers to go through assessments • Exam Technique – the tricks of the exam • Breaks & Lunches Program of the Conference

3. Sampling & Questionnaires Stem-and-leaf Scatter Graphs Session 1 - Data Frequency Polygons

4. Sampling You want to find out how much exercise people in your town do. - You go to the local sports centre to carry out a survey • Comment on this sampling technique

5. Sampling You want to work out what proportion of a magazine is pictures. - You count the number of pictures on the first 3 pages • Comment on this sampling technique

6. Questionnaires Normally 2 parts to an exam question: • Critique a questionnaire – say what is wrong • Improve a questionnaire • Questionnaire involves: • A question • Response boxes

7. Questionnaires Questions: • Must state a time period • e.g. per day, per week, per month etc Response Boxes: • Must NOT overlap • Is there a zero or more than option? • Options must mean the same thing to everyone • (a lot, excellent, not much are NOT GOOD numerical options are normally better)

8. Questionnaires Critique & Improve: “How much money do you spend on magazines?” • State TWO criticisms: • Improve this questionnaire:

9. Questionnaires Critique & Improve: “How many pizzas have you eaten?” • State TWO criticisms: • Improve this questionnaire:

10. Questionnaires Critique & Improve: “How many DVDs do you watch?” • State TWO criticisms: • Improve this questionnaire:

11. Stem and Diagram Stem (tens) Leaf (units) 0 1 2 3 4 The data below represents test results for 16 students in year 11. 7384122208524 15132345 17111730

12. Key Stem (tens) Leaf (units) 0 5 7 8 1 1 3 5 7 7 2 0 2 3 4 3 0 8 4 1 5 Constructing 7384122208524 15132345 17111730 1 | 3 = 13 • Work out: • Mode • Median • Range

13. Stem (tens) Leaf (units) What is the probability of selecting a student at random who scored at least 30 in the test? How many students scored at least 30 in the test? Mode 0 5 7 8 1 1 3 5 7 7 2 0 2 3 4 Median 3 0 8 The median is halfway between 17 and 20 4 1 5 Range ___ – ___ = ___ Interpreting 17 The mode is ___ 18.5 This is ____ 45 5 40 4 4 16 4 16

14. Key Stem (tens) Leaf (units) 1 0 5 5 7 2 1 4 6 7 8 3 1 2 2 2 5 7 8 4 3 7 5 1 4 8 Interpreting 1735 243227 37 153826 51314358 4710153221 542832 2 | 3 = 23 • Mode • Median • Range

15. Key Stem (tens) Leaf (units) Mode 1 0 5 5 7 2 1 4 6 7 8 3 1 2 2 2 5 7 8 Median 4 3 7 The median is halfway __ 5 1 4 8 Range ___ – ___ = ___ Interpreting 1735 243227 37 153826 51314358 4710153221 542832 2 | 3 = 23 32 The mode is ___ 32 58 10 48

16. Scatter graphs • What can you expect…….. • Plot (extra) coordinates • Describe the correlation • Draw a line of best fit • Use your line of best fit to estimate values BE CAREFUL OF SCALES

17. Scales Plot (10, 1000) (3, 500) (8, 600) (11, 750)

18. Scales Plot (10, 1000) (3, 500) (8, 600) (11, 750)

19. 60 55 Weight (kg) 50 45 40 140 150 160 170 180 190 Height (cm) Describe the Correlation Positive

20. 85 80 75 Life expectancy 70 65 60 55 50 0 20 40 60 80 100 120 Number of cigarettes smoked in a week Describe the Correlation Negative

21. A D B C E F Correlation Decide whether each of the following graphs shows, • positive correlation • negative correlation • zero correlation

22. Positive correlation Negative correlation The line of best fit Use a clear RULER Roughly equal number of points above and below the line. Does not have to pass through the origin.

23. Using the lines of best fit 72 • Use the equation to estimate the life expectancy for someone who smokes 10 cigarettes a week. 10 • The estimated life expectancy is 72 years

24. This graph shows the relationship between student’s results in a non-calculator and a calculator paper 85 80 75 Calculator paper 70 65 60 55 50 0 20 40 60 80 100 Non calculator paper If a student scored 74 in the Calculator paper, what would be a good estimate for their non calculator paper? 76

25. The table shows this information for two more Saturdays. Plot this information on the scatter graph. What type of correlation does this scatter graph show? Draw a line of best fit on the scatter graph. The weather forecast for next Saturday gives a maximum temperature of 17. Estimate the number of people who will visit the softball playground. On another Saturday, 350 people were recorded to have visited the playground. Estimate the maximum outside temperature on that day.

27. Negative Correlation 215 - 255 235 10.5 – 12.5 11.5

28. Frequency Polygons Plot the MID POINT with the frequency Join points with a ruler. Modal Class = Group with highest frequency 20≤h<30

29. Frequency Polygons

30. You Try 60 students take a science test. The test is marked out of 50. This table shows information about the students’ marks 30<m≤40 • What is the modal class? • Draw a frequency polygon to represent this information

31. You Try x x x x x

32. Test 1 - Data

33. Simplifying Substitution Session 2 - Algebra Expanding Brackets Rules of Indices

34. Collecting together like terms Simplify these expressions by collecting together like terms. 1) a + a + a + a + a = 5a 2) 4r + 6r =10r 3) 5a x 4b = 20ab 4) 4c + 3d – 2c + d = 2c + 4d 12x2 5) 4x x 3x = r4 6) r x r x rx r =

35. Rules of Negatives Multiplying/Dividing Same sign + Positive Different sign – Negative 3 x 4 = -3 x -4 = -3 x 4 = 3 x -4 = 12 12 -12 -12 Adding/Subtracting – THINK NUMBER LINE Look at “touching” signs Same sign + Positive Different sign – Negative 20 +– 6 = 20 – 6 20 - - 6 = -20 - + 6 = = 14 20 + 6 = 26 - 20 - 6 = -26

36. Substitution BE CAREFUL OF NEGATIVES 4a + 3b a = 5 b = -2 REMEMBER BIDMAS 4 x 5 + 3 x -2 Rules of negatives 20 + - 6 20 – 6 = 14

37. a = 3, c = 2, x = -4 Practice: • 5c • 3x • 4c + 5a • c – x • 5a + 2x • 3c2 • x2 5 x 2 = 10 3 x -4 = -12 4 x 2 + 5 x 3 = 8 + 15 = 23 2 - - 4 = 2 + 4 = 6 5 x 3 + 2 x - 4 = 15 + - 8 = 15 – 8 = 7 3 x 22 = 3 x 4 = 12 -42 = -4 x -4 = 16

38. Substitution for Linear Graphs x –3 –2 –1 0 1 2 3 y = 2x + 5 You will be given an equation and asked to complete the table of values. y = 2x + 5 We can use a table as follows: -1 3 5 7 9 11 1

39. Plotting graphs of linear functions y = 2x + 5 y 1) Plot the points on a coordinate grid. 2) Draw a line through the points. 3) Use you graph to estimate: (i) y when x = - 1.5 (ii) x when y = 8 3 2 1 2 3 x 1

40. Plotting graphs of linear functions Use you graph to estimate: (i) y when x = - 1.5 y=2 (ii) x when y = 8 x=1.5

41. 4 6 8 -2 y = 2x + 2 x x Use your graph to estimate the value of y when x = -1.5 x x x x y = -1

42. Linear Graphs – NO Table Given – Make one x On the grid draw the graph of x + y = 4 for values of x from -2 to 5 x x x x x x x

43. Expanding Brackets Look at this algebraic expression: 3(4x – 2) To expand or multiply out this expression we multiply every term inside the bracket by the term outside the bracket. 3(4x – 2) = 12x – 6

44. Practice Expand these expressions: • 3(x + 5) • 12(2x – 3) • 4x(x + 1) • 5a(4 – 7a) 3x + 15 24x – 36 4x2 + 4x 20a – 35a2

45. Expanding Brackets and Simplifying Expand and simplify: 2(3n – 4) + 3(3n + 5) 2(3n – 4) + 3(3n + 5) = – 8 + 15 6n + 9n = 6n + 9n – 8 + 15 = 15n + 7

46. Expanding Brackets and Simplifying Expand and simplify: 3(3b + 2) - 3(2b - 5) 3(3b + 2) - 3(2b - 5) = + 6 + 15 9b - 6b = 9b - 6b + 6 + 15 = 3b + 21

47. Expanding DOUBLE brackets (x + 4)(x + 2)

48. Expanding DOUBLE brackets x2 + 4x + 2x + 8 Simplify x2 + 6x + 8

49. Expanding two brackets Expand these algebraic expressions: (x + 5)(x + 2) = x2 + 5x + 2x + 10 = x2 + 7x + 10 (x + 2)(x – 3) = x2 + 2x - 3x - 6 = x2 – x - 6

50. When we multiply two terms with the same base the indices are added. Indices – Multiplying For example, a4 × a2 = (a × a × a × a) × (a × a) = a6 = a(4 + 2) 4a5 × 2a = 4 x 2 (a × a × a × a × a ) × (a) = 8 a6