1. Welcome to the Revision Conference Name: School:

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

3. Comment on these sampling techniques
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
You want to work out what proportion of a magazine is pictures. You count the number of pictures on the first 3 pages
This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

4. Questionnaires – Important Points
Normally 2 parts to an exam question:
Questionnaire involves:
A question
Response boxes
Critique a questionnaire – say what is wrong
Improve a questionnaire
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)
This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

5. Questionnaires Critique & Improve:
“How much money do you spend on magazines?”
State TWO criticisms:
Improve this questionnaire:
This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

6. Questionnaires Critique & Improve: “How many pizzas have you eaten?”
State TWO criticisms:
Improve this questionnaire:
This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

7. Questionnaires Critique & Improve: “How many DVDs do you watch?”
State TWO criticisms:
Improve this questionnaire:
This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

8. The data below represents test results for 16 students in year 11.
Stem and Diagram 4 3 2 1
Leaf (units)
Stem (tens)
Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What percentage smoke more than 20 a fortnight?” as well as the averages and range. 8

9. Interpreting 1 5
3 7 4 3 2
Leaf (units)
Stem (tens)
Key
2 | 3 = 23
Mode
Median
Range

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

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

12. Describe the Correlation40 45 50 55 60
140
150
160
170
180
190
Height (cm)
Weight (kg) 50 55 60 65 70 75 80 85 20 40
100
120
Number of cigarettes smoked in a week
Life expectancy

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

14. This graph shows the relationship between student’s results in a non-calculator and a calculator paper
If a student scored 74 in the Calculator paper, what would be a good estimate for their non calculator paper? 50 55 60 65 70 75 80 85 20 40
100
Non calculator paper
Calculator paper
Pupils would benefit from a print out of the graph. The approximate equation of the line is y = –0.21x Note that the gradient is roughly (73 – 52) /100 not 73/100.

15. The table shows this information for two more Saturdays.
Maximum outside temperature (C) 15 24
Number of People
260 80
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.

16. This data is fictional. However, some research does suggest links between smoking and a number of fatal diseases such as cancer. For further details, see the ASH website (

17. Frequency Polygons Plot the MID POINT with the frequency
Join points with a ruler.
Modal Class

18. You Try
60 students take a science test. The test is marked out of 50. This table shows information about the students’ marks
Science Mark
0<m≤10
10<m≤20
20<m≤30
30<m≤40
40<m≤50
Frequency 4 13 17 19 7
What is the modal class?
Draw a frequency polygon to represent this information

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

20. Collecting together like terms
Simplify these expressions by collecting together like terms.
1) a + a + a + a + a
2) 4r + 6r
3) 5a x 4b
4) 4c + 3d – 2c + d
5) 4x x 3x
Whenever possible make comparisons to arithmetic by substituting actual values for the letters. If it is true using numbers then it is true using letters. For example, in 1) we could say that is equivalent to 5 × 7.
For example 1) and example 2), remind pupils that in algebra we don’t need to write the number 1 before a letter to multiply it by 1. 1a is just written as a and 1b is just written as b.
For example 3), explain that when there are lots of terms we can write like terms next to each other so that they are easier to collect together. The numbers without any letters are added together separately.
In example 4) emphasize that n² is different from n, this can be demonstrated by thinking about possible values for n, and because they are different they cannot be collected together. 4n – 3n is n and n² stays as it is.
If we can’t collect together any like terms, as in example 5), we write ‘cannot be simplified’.
6) r x r x r x r

21. 3 x 4 = -3 x -4 = -3 x 4 = 3 x -4 = 20 +– 6 = 20 - - 6 = -20 - + 6 =
Rules of Negatives
Multiplying/Dividing
Same sign + Positive
Different sign – Negative
3 x 4 =
-3 x -4 =
-3 x 4 =
3 x -4 =
Adding/Subtracting
Look at “touching” signs
Same sign + Positive
Different sign – Negative
20 +– 6 = = =
Start by asking pupils to simplify x + x + x + x + x. This is 5 lots of x, which is written as 5x.
Next ask pupils how we could simplify x × x × x × x × x. Make sure there is no confusion between this repeated multiplication and the previous example of repeated addition.
If x is equal to 2, for example, x + x + x + x + x equals 10, while x × x × x × x × x equals 32.
Some pupils may suggest writing xxxxx. While this is not incorrect, neither has it moved us on very far. Point out the problems of readability, especially with high powers.
When we write a number or term to the power of another number it is called index notation. The power, or index (plural indices), is the superscript number, in this case 5. The number or letter that we are multiplying successive times, in this case, x, is called the base.
Practice the relevant vocabulary: x2 is read as ‘x squared’ or ‘x to the power of 2’; x3 is read as ‘x cubed’ or ‘x to the power of 3’; x4 is read as ‘x to the power of 4’.

22. 5c 3x 4c + 5a c – x 5a + 2x 3c2 x2 a = 3, c = 2, x = -4 Substitution
Example
Practice:
4a + 3b 5c 3x
4c + 5a
c – x
5a + 2x
3c2 x2
a = 5
b = -2
Start by asking pupils to simplify x + x + x + x + x. This is 5 lots of x, which is written as 5x.
Next ask pupils how we could simplify x × x × x × x × x. Make sure there is no confusion between this repeated multiplication and the previous example of repeated addition.
If x is equal to 2, for example, x + x + x + x + x equals 10, while x × x × x × x × x equals 32.
Some pupils may suggest writing xxxxx. While this is not incorrect, neither has it moved us on very far. Point out the problems of readability, especially with high powers.
When we write a number or term to the power of another number it is called index notation. The power, or index (plural indices), is the superscript number, in this case 5. The number or letter that we are multiplying successive times, in this case, x, is called the base.
Practice the relevant vocabulary: x2 is read as ‘x squared’ or ‘x to the power of 2’; x3 is read as ‘x cubed’ or ‘x to the power of 3’; x4 is read as ‘x to the power of 4’.

23. Plotting graphs of linear functions
y = 2x + 5 x
y = 2x + 5 –3 –2 –1 1 2 3
1) Complete the table and plot the points y
2) Draw a line through the points
3) Use you graph to estimate:
(i) y when x = - 1.5
(ii) x when y = 8
This slide summarizes the steps required to plot a graph using a table of values. 3 2 1 1 2 3 x

24. Use your graph to estimate the value of
y = 2x + 2
Use your graph to estimate the value of
y when x = -1.5

25. Linear Graphs – NO Table Given – Make one
On the grid draw the graph of x + y = 4 for values of
x from -2 to 5
Explain that when we construct a table of values, the value of y depends on the value of x. That means that we choose the values for x and substitute them into the equation to get the corresponding value for y.
The minimum number of points needed to draw a straight line is two, however, it is best to plot several extra points to ensure that no mistakes have been made.
The points given by the table can then be plotted to give the graph of the required function.

26. 3(x + 5) 12(2x – 3) 4x(x + 1) 5a(4 – 7a) 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) =
3(x + 5)
12(2x – 3)
4x(x + 1)
5a(4 – 7a)
The lines shown in orange show which terms we are multiplying together.

27. Expanding Brackets and Simplifying
Expand and simplify:
2(3n – 4) + 3(3n + 5)
Expand and simplify:
3(3b + 2) - 3(2b - 5)
In this example, we have two sets of brackets. The first set is multiplied by 2 and the second set is multiplied by 3.
We don’t need to use a grid as long as we remember to multiply every term inside the bracket by every term outside it.
Talk through the multiplication of (3n – 4) by 2 and (3n + 5) by 3.
Let’s write the like terms next to each other.
When we collect the like terms together we have 6n + 9n which is 15n and – = 7.

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

29. Expanding two brackets
Expand these algebraic expressions:
(x + 5)(x + 2) =
(x + 2)(x - 3) =
In this example, we need to multiply everything in the second bracket by 3 and then everything in the second bracket by t. We can write this as 3(4 – 2t) + t(4 – 2t). As pupils become more confident, they can leave this intermediate step out.

30. Indices a4 × a2 = 4a5 × 2a = a5 ÷ a2 = 4p6 ÷ 2p4 = (y3)2 = (q2)4 =
When we multiply two terms with the same base the indices are added.
a4 × a2 =
4a5 × 2a =
When we divide two terms with the same base the indices are subtracted.
a5 ÷ a2 =
4p6 ÷ 2p4 =
When we have brackets you need to multiply the indices.
Stress that the indices can only be added when the base is the same.
(y3)2 =
(q2)4 =

31. You Try a5 x a3 = a2 1) a2 x a3 = 2) m2 x m-4 = 3) 3h2 x 4h =
4) 3g-5 x 2g-3 =
5) a5 ÷ a3 =
6) m3 ÷ m =
7) 10h 2 ÷ 5h 3 =
8) 12g5 ÷ 3g-3 =
a5 x a3 =
You may wish to ask pupils to complete this exercise individually before talking through the answers. 9)
10) (a2)3 = a2
11) (m3)-4 =
12) (g-5)-3 =

32. Session 3 - Shape
Transformations
Pythagoras’ Theorem

33. There are two ways you have to answer this question:
Pythagoras
There are two ways you have to answer this question:
(1) Finding the longest side
(2) Finding a shorter side
Stress that the indices can only be added when the base is the same.

34. Pythagoras
Stress that the indices can only be added when the base is the same.

35. Draw and label these lines
Stress that the indices can only be added when the base is the same.

36. Transformations
Stress that the indices can only be added when the base is the same.

37. Find Reflections State pairs of triangles and the equation of the line
Stress that the indices can only be added when the base is the same.
Now reflect the black triangle in the line x = y

38. Translation Can describe in words: Or as a VECTOR
Stress that the indices can only be added when the base is the same.

39. Translations
Stress that the indices can only be added when the base is the same.

40. Rotations
Rotate triangle T 90 anti-clockwise about the point (0,0). Label your new triangle U
Rotate triangle T 180 about point (2,0). Label your new triangle V

41. Describe fully the single transformation which maps triangle
Transformations
Describe fully the single transformation which maps triangle
T to triangle U
3 Marks =
3 THINGS

42. Describe fully the single transformation which maps triangle
Transformations
Describe fully the single transformation which maps triangle
A to triangle B
3 Marks =
3 THINGS

43. DESCRIBING Rotations
Stress that the indices can only be added when the base is the same.

44. Describe (3 marks)

45. Describe fully the single transformation which maps shape P to shape Q
Enlargements
Describe fully the single transformation which maps shape P to shape Q

46. Enlargements
Describe fully the single transformation which maps triangle S to triangle T
Stress that the indices can only be added when the base is the same.

47. Session 4 - Number BIDMAS Long Multiplication Place Value Estimating
Fractions

48. B ( ) I x2 D ÷ M x A + S - 6 x 5 +2 6 + 5 x 2 48 ÷ (14 – 2) 2 + 32
BIDMAS
6 x 5 +2
6 + 5 x 2
48 ÷ (14 – 2)
2 + 32
6 x 4 – 3 x 5
35 – 4 x 3
B ( )
I x2
D ÷
M x
A +
S -
Stress that the indices can only be added when the base is the same.

49. Long Multiplication
Stress that the indices can only be added when the base is the same.

50. One more for you to try…..
46 x 129 =

51. Long Multiplication – Embedded into a word problem
I buy 135 tickets costing £12 each. How much do I spend?

52. Using this information
46 x 129 =
Calculate:
4600 x 129 =
46 x =
460 x =
4.6 x =
4.6 x =
Stress that the indices can only be added when the base is the same.

53. Using this information
46 x 129 = 5934
Calculate:
5934 ÷12.9 =
Estimate:
Stress that the indices can only be added when the base is the same.

54. Using this information
97.6 x 370 = 36112
Calculate:
9.76 x 37
9760 x 3700
÷ 97.6
Stress that the indices can only be added when the base is the same.

55. Rounding to ONE significant figure
to 1 s. f.
6.3528
34.026
Discuss each example, including the use of zero place holders and zeros that are significant figures. The numbers can be modified as required.

56. Estimate:
43 x 2.6 =
( )2.2 =

57. Estimate:

58. What if you need to divide by a decimal?

59. Work out an estimate for the value of
6.37 x 1.9
0.145

60. Multiplying Fractions3 8
What is × ? 4 5 5 6
What is × ? 2
Point out that we could also cancel before multiplying.

61. Dividing Fractions 2 3 4 5 What is ÷ ? 3 5 6 7 What is ÷ ?
Explain that when we are dividing by a fraction we can write an equivalent calculation by swapping the numerator and the denominator around (turning the fraction upside-down) and multiplying.
This works because when we multiply by a fraction we multiply by the numerator and divide by the denominator.
Multiplying by a fraction is straight forward because we simply multiply the numerators together and multiply the denominators together.

62. Adding and Subtracting Fractions
What is + 1 2 3 ?
What is 3 5 + 4 ?
Stress that the indices can only be added when the base is the same.

63. Fractions
Stress that the indices can only be added when the base is the same.

64. Where to start with topics…….
How to score HIGH marks
Where to start with topics…….
2nd March NON Calculator
Estimating (round to 1 significant figure)
Place Value
Solving Linear Equations
Long Multiplication and Division
Fractions Operations (+, - , x, ÷)
Indices
Substitution
Transformations (doing and describing)
Expanding Brackets and factorising
Angles (parallel lines, special triangles)
Simple percentage increase/decrease
Plans and Elevations (& planes of symmetry)
Writing and using formulae
Questionnaires
5th March CALCULATOR
Trial and Improvement
Use your calculator to work out……
Rounding - decimal places and sig figs
Area and circumference of a circle
Volume and surface area of cylinders
Pythagoras’ Theorem
Currency Conversions

65. How to score HIGH marks
What should be my strategy in the exam hall for MATHS?
Depends if you are higher or foundation
If you are entered for higher – it is worth revising some “easy” B grade topics
Tree Diagrams
Cumulative Frequency
Basic Circle Theorems
Right – angle Triangle Trigonometry
Standard Form

66. How to score HIGH marks
If the question asks you to calculate:
AREA – immediately write ……… on the answer line
VOLUME – immediately write …… on the answer line
Factorise “fully” – clue that there is more than one factor
e.g. Factorise fully 8x + 12x2
Trial and Improvement - Once you have the this situation…. X
Too small
Too big

67. Circles
x 9.72 =

68. Pythagoras =
= 185
√185 =

69. 1.962631579 Write down all the figures on your calculator display.
Use your calculator to work out the value of
Write down all the figures on your calculator display.
(2)
(b) Write your answer to part (a) to 3 decimal places
(1)
(Total 3 marks)