Welcome to the
Revision Conference
Name:
School:
Session 1 - Data
Sampling & Questionnaires
Stem-and-leaf
Scatter Graphs
Frequency Polygons
Sampling
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
Questionnaires – Important Points
Normally 2 parts to an exam question:
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)
Questionnaires
Critique & Improve:
“How much money do you spend on magazines?”
State TWO criticisms:
Improve this questionnaire:
Questionnaires
Critique & Improve:
“How many pizzas have you eaten?”
State TWO criticisms:
Improve this questionnaire:
Questionnaires
Critique & Improve:
“How many DVDs do you watch?”
State TWO criticisms:
Improve this questionnaire:
The data below represents test
results for 16 students in year 11.
Stem and Diagram
7
15
38
13
Stem
(tens)
0
1
2
3
4
41
23
22
45
Leaf (units)
20
17
8
11
5
17
24
30
Interpreting
Stem
(tens)
Leaf (units)
Key
2 | 3 = 23
1 0 5 5 7
2 1 4 6 7 8
(a) Mode
3 1 2 2 2 5 78
4 3 7
(b) Median
5 1 4 8
(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)
Weight (kg)
Describe the Correlation
60
55
50
45
40
140
150
160
170
Height (cm)
180
190
Life expectancy
85
80
75
70
65
60
55
50
0
20
40
60
80
100
Number of cigarettes smoked in a week
120
Correlation
Decide whether each of the
following graphs shows,
25
A
20
B
12
10
15
8
positive correlation
6
10
4
5
2
0
0
5
10
15
20
25
0
0
2
4
6
8
10
12
25
25
C
20
D
20
15
15
negative correlation
10
10
5
5
0
0
0
5
10
15
20
25
20
5
10
15
20
25
25
25
E
20
zero correlation
0
F
20
15
15
10
10
5
5
0
0
5
10
15
20
25
0
0
5
10
15
20
25
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?
Calculator paper
85
80
75
70
65
60
55
50
0
20
40
60
Non calculator paper
80
100
The table shows this information for two more Saturdays.
Maximum outside temperature (C) 15
24
Number of People
80
260
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
13
17
19
7
4
(a) What is the
modal class?
(a) Draw a
frequency
polygon to
represent this
information
Session 2 - Algebra
Simplifying
Substitution
Expanding Brackets
Rules of Indices
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
6) r x r x r x r
Rules of Negatives
Multiplying/Dividing
Same sign + Positive
Different sign – Negative
3x4
-3 x -4
-3 x 4
3 x -4
Adding/Subtracting
Look at “touching” signs
Same sign + Positive
Different sign – Negative
20 +– 6 =
20 - - 6 =
-20 - + 6 =
=
=
=
=
Substitution
Example
4a + 3b
a=5
b = -2
Practice:
a = 3, c = 2, x = -4
a) 5c
b) 3x
c) 4c + 5a
d) c – x
e) 5a + 2x
2
f) 3c
g) x2
Plotting graphs of linear functions
y = 2x + 5
x
–3
–2
–1
0
1
2
3
y = 2x + 5
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
3
2
1
1
2 3
x
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 of
x from -2 to 5
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) =
(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)
Expanding DOUBLE brackets
(x + 4)(x + 2)
x
x
2
x
4
Expanding two brackets
Expand these algebraic expressions:
(x + 5)(x + 2) =
(x + 2)(x - 3) =
Indices
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.
(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 =
5
3
9) a x a =
10) (a2)3 =
a2
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
BIDMAS
Long Multiplication
Place Value
Estimating
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 x
A +
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 = 5934
Calculate:
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
Rounding to ONE significant figure
to 1 s. f.
4 890 351
6.3528
34.026
0.0007506
0.005708
150.932
0.00007835
Estimate:
43 x 2.6 =
(3.01 + 8.7)2.2 =
Estimate:
7 .8  5 .3
10 . 3
68  401
198
What if you need to divide by a decimal?
Work out an estimate for the value of
6.37 x 1.9
0.145
412  5 . 904
0 . 195
5 . 79  312
0 . 523
Multiplying Fractions
3
4
What is
×
8
5
What is
?
5 2
×
6 5
?
Dividing Fractions
4
2
What is
÷
?
5
3
What is
6
3
÷
?
7
5
Adding and Subtracting Fractions
What is
What is
1
1
+
?
2
3
3
3
+
?
5
4
Fractions
How to score HIGH marks
Where to start with topics…….
2nd March NON Calculator
5th March CALCULATOR
• Estimating (round to 1 significant figure)
•Trial and Improvement
• Place Value
•Use your calculator to work out……
• Solving Linear Equations
•Rounding - decimal places and sig figs
• Long Multiplication and Division
•Area and circumference of a circle
•Volume and surface area of cylinders
• Fractions Operations (+, - , x, ÷)
• Indices
•Pythagoras’ Theorem
• Substitution
•Currency Conversions
• 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
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….
X
2.7
2.8
----- Too small
----- 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
6 . 27  4 . 52
4 . 81  9 . 63
(a) Write down all the figures on your calculator
display.
1.962631579
.......................... (2)
(b) Write your answer to part (a) to 3 decimal
places
..........................(1)
(Total 3 marks)