1. SCATTER DIAGRAMS
Plot the points
Line of best fit
Positive and negative correlation

2. SIMPLE PROBABILITY
Probabilities add to 1
Multiply the probability by the number of times

3. Multiply frequency by the value Divide this total by total frequency
MEAN FROM A TABLE
Multiply frequency by the value
Divide this total by total frequency
Total
How many
Mean

4. ESTIMATE OF THE MEAN
2 extra columns
Use mid point of groups
Mid point x frequency
Big total divided by little total

5. Modal class is the mode group
Basic Averages
Modal class is the mode group
Median is the middle one
Mean is total divided how many?
Total
How many?
Mean

6. QUESTIONNAIRES
Look for a time limit in the question
Overlap between the choices
Any missing choices?

7. Cumulative Frequency I
Running total
Plot end points against cumulative frequency
Measure median and quartiles

8. Cumulative Frequency II
Three quarters way
Half way
Quarter way

9. BOX PLOTS Plot 5 measures to draw it.
Lowest value, lower quartile, median, upper quartile, highest value
To compare, 1 comment on the median, 1 comment on the interquartile range (the width of the box)
Remember that there is 25% of the data between each point

10. HISTOGRAMS
Frequency density is freq divided by class width
The area of a bar is the frequency

11. TREE DIAGRAMS
Each V adds to 1
Multiply alon g the branches

12. Fraction of – divide by the bottom, times by the top.
STRATIFIED SAMPLING Eg
of 100
Total
Fraction of – divide by the bottom, times by the top. 12

13. FREQUENCY DIAGRAMS Frequency polygon = join midpoints of bar chart
Frequency diagram = bar chart

14. Venn Diagrams AI means not A
Everything in the rectangle is part of the universal set
AuB is everything in either A, B or both
AI means not A

15. STANDARD FORM It’s a number between 1 and 10 times by a power of 10.
e.g. 450 is 4.5 x 102
Use the exp button on the calculator 15

16. When multiplying times the numbers and add the powers
When dividing divide the numbers and take away the powers
Power of 0 is 1
Fraction powers: ½ is square root, 1/3 is cube root
Negative powers – work out + power and turn upside down 16

17. PRIME FACTOR TREES
PRIME NUMBERS
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …
EXAMPLES
Find the product of prime factors for the following numbers:
(a) 32
(b) 60 8 4 10 6 4 2 2 2 5 2 3 2 2 2
ANSWER = 2 X 2 X 3 X 5
ANSWER = 2 X 2 X 2 X 2 X 2 = =
X 3 X 5 17

18. LCM is a multiple, so is bigger than the start numbers
LCM and HCF
LCM is a multiple, so is bigger than the start numbers
HCF is a factor, so is smaller than the start numbers 18

19. PERCENTAGES
1% - divide by 100
10% - divide by 10
% change is change / original x 100%

20. £5600 x 1.018515 Percentage Increase by Multiplier

21. Currency exchange

22. AER Percentage Rate
As a decimal number eg 15% as 0.15
Per day, week, month etc
With AER you can compare rates over different times as if they were one year

23. Income tax Example Income is £50000 Taxable Income = £40000
Taxable pay =
salary – allowance
Put as much as you can into each “piggy bank” tax rate
Example
Income is £50000
Taxable Income = £40000
Split this into 2 parts
£31865
£ £31865 = £8135
40%
20%

24. CALCULATOR WORK + ESTIMATION
Work out the top
Work out the bottom
Top divided by the bottom
Estimate means round the numbers first

25. RATIO
RATIO 2:3 MEANS 2+3 = 5 PARTS
FIND THE VALUE OF 1 PART

26. BEST VALUE Change £ into pence by x 100
Work out the cost of each per unit
Show all your working out
State the answer at the end

27. Surds

28. Recurring decimal to fraction
Write x out as a long decimal
Keep working 10x, 100x etc until they are the same after the decimal point

29. Height of each bar is the y coordinate
Area under a Curve
Height of each bar is the y coordinate
Find the area of each triangle / trapezium, then find the total
The area under velocity time curve is the distance

30. Plans and Elevations

31. Nets of 3d shapes

32. Rectangle is length x width Triangle is height x base / 2
AREA
Rectangle is length x width
Triangle is height x base / 2
Trapezium is (add parallel sides) x height /2
Compound shapes – split into easier shapes then add together 32

33. Prisms – Area of front x length
VOLUME
Prisms – Area of front x length 33

34. Density Formula Triangles
Mass
Volume
Density
Population
Area of country
Pop density

35. Parallel lines- look for FUZ: Corresponding Interior Alternate
ANGLES
Parallel lines- look for FUZ:
Corresponding
Interior
Alternate
Bearings measure clockwise from North 35

36. SIMILAR SHAPES Congruent means exactly the same
Length scale factor = x
Area scale factor = x2
Volume scale factor = x3

37. PYTHAGORAS
TAKE THE 2 NUMBERS
SQUARE
ADD OR SUBTRACT
SQUARE ROOT

38. Area of Isosceles Triangle
Use Pythagoras to find the height
Then use base x height / 2 for the area

39. Locus This traces the path of a point as it moves
From one point it is a circle
From two points it is the perpendicular bisector of the line joining them
From one line it is a parallel line either side
From 2 lines it is the angle bisector

40. TRAVEL GRAPH Away from home Journey home Stops Distance Speed Time
Speed is how far you travel in 1 hour
Distance
Speed
Time

41. MEASURED FROM THE NORTH LINE
BEARINGS
ANGLE
MEASURED FROM THE NORTH LINE
(North line must be on zero degrees on a protractor)
MEASURED IN A CLOCKWISE DIRECTION
MUST BE WRITTEN AS THREE FIGURES
Find the bearing of B from A N
054° B A 41

42. Tessellations
Shapes tessellate when the angles at the point they meet add to 360 deg

43. TRIG Right angle triangle Label sides
Opp
Adj
Tan
Opp
Hyp
Sin
Adj
Hyp
Cos
Right angle triangle
Label sides
Pick correct triangle
Cover up the side you want
If finding angle use the 2ndF button
Write SOHCAHTOA on the formula page of the paper

44. CIRCLES Area = pi x rad2 Circumference = pi x diameter
Leave in terms of pi means treat pi as a letter

45. Circle Area – Work backwards
We are given the area, find the radius

46. CONES AND SPHERES
Everything you need to know is on the formula sheet on the paper

47. Volume of a sphere – find the radius

48. 1 kg is 2.2 lbs 5 miles is 8 Km 1 litre is 1.75 pints
Conversion Units to Learn
1 kg is 2.2 lbs
5 miles is 8 Km
1 litre is 1.75 pints
1 litre is 1000 cm3

49. Conversion Graph
Plot points from a table
Join to make a straight line
Be prepared to be taken off the graph

50. Collect like terms
Don’t forget that you cannot add an x2 term and an x term

51. SIMULTANEOUS EQUATIONS
Criss cross the numbers in front of x
Times the equation by that number
Change the sign of all the bottom equation
Work out y
Use y to work out x

52. Nth Term
Find the nth term of the following sequences and then calculate the 100th term. a)
3, 7, 11, 15, …
Nth term so far = 4n +4
Start number is -1
Nth term is 4n - 1
Worksheet needs printing
100th term = 4x100 -1
100th term = 399 52

53. STRAIGHT LINES
Form is y=mx+c
To plot the line, take 3
x values and find out the y values that go with them

54. Gradient is up divided by the across
STRAIGHT LINES
Look at the gradient – positive or neg
Gradient is up divided by the across
Line is y=mx+c, where m is the gradient and c the intercept

55. FORM AND SOLVE EQUATION
This one is about angles, so add algebra together and put equal to 360.
If perimeter, do the same but put = perimeter.
Solve by simplifying and solving

56. PLOTTING GRAPHS Complete table of values Plot points on grid
Join points together to make a graph

57. PROPORTION Bring in k Y = k x2 Work out k If inverse proportion, Y = k

58. Circumference of Circle = pi x diameter
Area of Circle = pi x radius2
Fraction of Circle = 60 / 360
Find this fraction of area for sector area and same with circumference for arc length ( divide by bottom, times by top)

59. To find the gradient when x=4
Mark the point
Draw tangent
Find the gradient of the line
Pick 2 points on the line
Gradient = up / across

60. Upper and Lower Bounds 100 / 2 = 50, so do 31500 + and - 50
When you add or multiply, use the 2 biggest or the 2 smallest
When you subtract or divide, cross match them