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
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.
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
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
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)
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 =
Pythagoras
There are two ways you have to answer this question:
(1) Finding the longest side (2) Finding a shorter side
Find Reflections
State pairs of triangles and the
equation of the line
Now reflect the black triangle in the line x = y
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
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
– 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 =
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
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