Welcome to the

Revision ConferenceName:School:

Session 1 - Data

Stem-and-leaf

Scatter Graphs

Frequency Polygons

Sampling & Questionnaires

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

Sampling

Comment on these sampling techniques

You want to work out what proportion of a magazine is pictures. You count the number of pictures on the first 3 pages

Normally 2 parts to an exam question:

Questionnaires – Important Points

Critique a questionnaire – say what is wrong

Improve a questionnaire

Questionnaire involves:

(1) A question

(2) Response boxes

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)

Critique & Improve:

Questionnaires

“How much money do you spend on magazines?”     

State TWO criticisms:

Improve this questionnaire:

Critique & Improve:

Questionnaires

“How many pizzas have you eaten?”     

State TWO criticisms:

Improve this questionnaire:

Critique & Improve:

Questionnaires

“How many DVDs do you watch?”     

State TWO criticisms:

Improve this questionnaire:

0

4

3

2

1

Leaf (units)Stem (tens)

Stem and Diagram

7 38 41 22 20 8 524

15 13 23 45 17 11 1730

The data below represents test results for 16 students in year 11.

Interpreting

0 5 5 71

1 4 85

3 7 4

1 2 2 2 5 7 8 3

1 4 6 7 82

Leaf (units)Stem (tens) 2 | 3 = 23

Key

(a) Mode

(b) Median

(a) Range

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

Scales

Plot

(10, 1000)

(3, 500)

(8, 600)

(11, 750)

Describe the Correlation

40

45

50

55

60

140 150 160 170 180 190Height (cm)

Wei

gh

t (k

g)

50

55

60

65

70

75

80

85

0 20 40 60 80 100 120Number of cigarettes smoked in a week

Lif

e e

xp

ect

ancy

Correlation

positive correlation

negative correlation

zero correlation

0

5

10

15

20

25

0 5 10 15 20 25

A

0

2

4

6

8

10

12

0 2 4 6 8 10 12

B

0

5

10

15

20

25

0 5 10 15 20 25

C

0

5

10

15

20

25

0 5 10 15 20 25

D

20

0

5

10

15

20

25

0 5 10 15 20 25

E

0

5

10

15

20

25

0 5 10 15 20 25

F

Decide whether each of the following graphs shows,

50

55

60

65

70

75

80

85

0 20 40 60 80 100

Non calculator paper

Cal

cula

tor

pap

er

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?

The table shows this information for two more Saturdays.

Maximum outside temperature (C) 15 24

Number of People 260 80

1. Plot this information on the scatter graph.

1. What type of correlation does this scatter graph show?

1. Draw a line of best fit on the scatter graph.

The weather forecast for next Saturday gives a maximum temperature of 17.4. Estimate the number of people who will visit the softball playground.

On another Saturday, 350 people were recorded to have visited the playground.

5. Estimate the maximum outside temperature on that day.

Frequency Polygons

Plot the MID POINT with the frequency

Join points with a ruler.

Modal Class

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

(a) What is the modal class?

(a) Draw a frequency polygon to represent this information

Session 2 - Algebra

Simplifying

Expanding Brackets

Substitution

Rules of Indices

Simplify these expressions by collecting together like terms.

1) a + a + a + a + a

3) 5a x 4b

4) 4c + 3d – 2c + d

5) 4x x 3x

6) r x r x r x r

Collecting together like terms

2) 4r + 6r

Rules of Negatives

Multiplying/Dividing

Same sign + PositiveDifferent sign– Negative

20 +– 6 = 20 - - 6 =-20 - + 6 =

3 x 4 =-3 x -4 =-3 x 4 =3 x -4 =

Adding/Subtracting

Look at “touching” signsSame sign + PositiveDifferent sign– Negative

Substitution

4a + 3b

a = 5b = -2

a = 3, c = 2, x = -4Example Practice:

a) 5cb) 3xc) 4c + 5ad) c – xe) 5a + 2xf) 3c2

g) x2

Plotting graphs of linear functions

y = 2x + 5

1) Complete the table and plot the points

2) Draw a line through the points

3) Use you graph to estimate:(i) y when x = - 1.5(ii) x when y = 8

y

x

x

y = 2x + 5

–3 –2 –1 0 1 2 3

1

1

2

2

3

3

y = 2x + 2

Use your graph to estimate the value of

y when x = -1.5

Linear Graphs – NO Table Given

– Make one

On the grid draw the graph of x + y = 4 for values ofx from -2 to 5

Look at this algebraic expression:

Expanding Brackets

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) =

(a)3(x + 5)(b)12(2x – 3)(c)4x(x + 1)(d)5a(4 – 7a)

Expanding Brackets and Simplifying

Expand and simplify: 2(3n – 4) + 3(3n + 5)

Expand and simplify: 3(3b + 2) - 3(2b - 5)

xx 4

x

2

(x + 4)(x + 2)

Expanding DOUBLE brackets

Expanding two brackets

Expand these algebraic expressions:

(x + 5)(x + 2) =

(x + 2)(x - 3) =

Indices

a4 × a2 =

When we multiply two terms with the same base the indices are added.When we multiply two terms with the same base the indices are added.

4a5 × 2a =

When we divide two terms with the same base the indices are subtracted.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.When we have brackets you need to multiply the indices.

(y3)2 = (q2)4 =

You Try

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 =a2

9) 10) (a2)3 =

11) (m3)-4 = 12) (g-5)-3 =

Session 3 - Shape

Transformations

Pythagoras’ Theorem

Pythagoras

There are two ways you have to answer this question:

(1) Finding the longest side (2) Finding a shorter side

Pythagoras

Draw and label these lines

Transformations

Find Reflections

State pairs of triangles and the

equation of the line

Now reflect the black triangle in the line x = y

Translation

Can describe in words:

Or as a VECTOR

Translations

Rotations

(a) Rotate triangle T 90 anti-clockwise about the point (0,0). Label your new triangle U

(a) Rotate triangle T 180 about point (2,0). Label your new triangle V

Transformations

Describe fully the single transformation which maps triangle

T to triangle U

3 Marks = 3 THINGS

Transformations

Describe fully the single transformation which maps triangle

A to triangle B

3 Marks = 3 THINGS

DESCRIBING Rotations

Describe (3 marks)

Enlargements

Describe fully the single transformation which maps shape P to shape Q

Enlargements

Describe fully the single

transformation which maps triangle S to

triangle T

Session 4 - Number

Place Value

Estimating

BIDMAS

Long Multiplication

Fractions

BIDMAS

(a) 6 x 5 +2

(b) 6 + 5 x 2

(c) 48 ÷ (14 – 2)

(d) 2 + 32

(e) 6 x 4 – 3 x 5

(f) 35 – 4 x 3

B ( )I x2

D ÷ M xA +S -

Long Multiplication

One more for you to try…..

46 x 129 =

Long Multiplication

– Embedded into a word problem

I buy 135 tickets costing £12 each. How much do I spend?

Using this information

46 x 129 =

Calculate:

(a)4600 x 129 =(b)46 x 12.9 =(c)460 x 1290 =(d)4.6 x 1290 =(e)4.6 x 0.129 =

Using this information

46 x 129 = 5934Calculate:

5934 ÷12.9 =

Estimate:

Using this information

97.6 x 370 = 36112

Calculate:

(a)9.76 x 37

(b)9760 x 3700

(c)361.12 ÷ 97.6

6.3528

34.026

0.005708

150.932

0.00007835

to 1 s. f.

Rounding to ONE significant figure

4 890 351

0.0007506

4 890 351

Estimate:

43 x 2.6 =

(3.01 + 8.7)2.2 =

3.10

3.58.7

Estimate:

198

40168

What if you need to divide by a decimal?

Work out an estimate for the value of

195.0

904.5412

6.37 x 1.9

0.145

523.0

31279.5

Multiplying Fractions

38

What is × ?45

56

What is × ?25

45

What is ÷ ?23

Dividing Fractions

67

What is ÷ ?35

Adding and Subtracting Fractions

What is +12

13

?

What is 35

+34

?

Fractions

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

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

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….

X2.7 ----- Too small2.8 ----- Too big

Circles

x 9.72

= 295.5924528

Pythagoras

82 + 112 = 64 +121= 185

√185 = 13.60147051

Use your calculator to work out the value of

63.981.4

52.427.6

(a) 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)

1.962631579