1. 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

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

3. 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

4. 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. 4

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

6. 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

7. 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 7

8. 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 8

9. 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 9

10. 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 10

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

12. £5600 x 1.018515 Percentage Increase by Multiplier

13. Currency exchange

14. 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

15. 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%

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

17. Surds

18. 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

19. Plans and Elevations

20. Nets of 3d shapes

21. 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 21

22. Prisms – Area of front x length
VOLUME
Prisms – Area of front x length 22

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

24. Parallel lines- look for FUZ: Corresponding Interior Alternate
ANGLES
Parallel lines- look for FUZ:
Corresponding
Interior
Alternate
Bearings measure clockwise from North 24

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

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

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

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

29. 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 29

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

31. 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

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

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

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

35. Volume of a sphere – find the radius

36. 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

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

38. 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 38

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