Transcript Document
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:
Stem and Diagram
7 15 Stem (tens) 38 13 41 23 22 45 Leaf (units) 20 17 The data below represents test results for 16 students in year 11.
8 11 5 17 24 30 3 4 0 1 2
Interpreting
Stem (tens) 1 0 5 5 7 Leaf (units) 2 1 4 6 7 8 3 1 2 2 2 5 7 8 4 3 7 5 1 4 8
Key 2 | 3 = 23 (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
60 55 50 45 40 140 85 80 75 70 65 60 55 50 0 150 20 160 170
Height (cm)
180 190 40 60 80 100
Number of cigarettes smoked in a week
120
Correlation
Decide whether each of the following graphs shows, positive correlation 25 5 0 0 20 15 10 negative correlation 25 20 15 10 5 0 0 5 5 10 10 15 15 20 20
A
25 8 6 12 10 4 2 0 0 25
C
20 15 10 5 25 0 0 2 5 4 10 6 15 8 20
B
10 12
D
25 zero correlation 5 0 0 15 10 25 20 5 20 10 15 20
E
25 10 5 20 15 25 0 0
F
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?
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 Number of People 260 24 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
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 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) 4
r
+ 6
r
3) 5
a
x 4
b
4) 4
c
+ 3
d
– 2
c
+
d
5) 4
x
x 3
x
6)
r
x
r
x
r
x
r
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 = 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 f) 3c
2
g) x
2
Plotting graphs of linear functions
y
= 2
x
+ 5
x y
= 2
x
+ 5 –3 –2 –1 0 1 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
2 3 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(3
n
– 4) + 3(3
n
+ 5) Expand and simplify: 3(3
b
+ 2) - 3(2
b
- 5)
Expanding DOUBLE brackets
(x + 4)(x + 2)
x x 4 x 2
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
.
a
4 ×
a
2 =
4a
5 × 2
a
= When we
divide
two terms with the
same base
the indices are
subtracted
.
a
5 ÷
a
2 = 4
p
6 ÷ 2
p
4 = When we
have brackets
you need to
multiply
the indices .
(
y
3 ) 2 = (
q
2 ) 4 =
You Try
1)
a
2 x
a
3 = 3) 3
h
2 x 4
h
= 5)
a
5 ÷
a
3 = 7) 10
h
2 ÷ 5
h
3 = 9)
a
5 x
a
3 =
a
2 11) (
m
3 ) -4 = 2)
m
2 x
m
-4 = 4) 3
g
-5 x 2
g
-3 = 6)
m
3 ÷
m
= 8) 12
g
5 ÷
3g
-3 = 10) (
a
2 ) 3 = 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 + 3 2 (e) 6 x 4 – 3 x 5 (f) 35 – 4 x 3
B ( ) I x
2
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
0.000
7 506 6.3528
34.026
0.005708
150.932
0.00007835
to 1 s. f.
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 What is × 8 4 5 ?
5 What is × 6 2 5 ?
Dividing Fractions
2 What is ÷ 3 4 5 ?
3 What is ÷ 5 6 7 ?
Adding and Subtracting Fractions
What is 1 2 + 1 3 ?
What is 3 5 + 3 4 ?
Fractions
How to score HIGH marks
Where to start with topics…….
2 nd 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
5 th 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 + 12x 2 Trial and Improvement Once you have the this situation….
X 2.7
2.8 ----- Too small ----- Too big
Circles
x 9.7
2
= 295.5924528
Pythagoras
8
2
+ 11
2
= 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
(b) Write your answer to part (a) to 3 decimal places ..........................(1)
(Total 3 marks)