1. Decimal Places Write 32. 5616 correct to 1 dp = 32. 6 Write 400
Decimal Places Write correct to 1 dp = Write correct to 2 dp = Write correct to 2 dp = 26.15

2. Significant figures Write 67.49 correct to 3 sig figs = 67.5
because you start counting from the 6
Write 2649 correct to 3 sig figs = 2650
(don’t forget to put ZERO)
Write correct to 2 sig figs = 0.047
because you start counting from the first
non zero digit

3. Perimeter is the distance around the OUTSIDE of a shape.
Area is the space INSIDE a shape – count the squares or use a formula.
If you are asked to estimate the area - count squares MORE than ½ as 1cm², ignore if less than ½.

4. Area of Triangle = b x h (Half a rectangle) Area of parallelogram = b x h Area of trapezium = (a + b) x h

5. Volume of cuboid = l x w x h
height
width
length
There may be a link with Pythagoras or Density = Mass ÷ Volume
with area or volume questions.

6. Pythagoras’ Theorem
c² = a² + b²
                           

7. Labelling a circle
Tangent
Sector
Radius
Diameter
Chord
Circumference

8. Circumference of a Circle
It’s easy as a, b, c,
C = π x D
Area of a Circle
A = π x r x r

9. Remember UNITS! Perimeter/Circumference = cm, m Area = cm², m²
Volume = cm³, m³
High/Int tier only:
Think: m² to cm² we multiply by 100 x 100
or multiply by 100²
and m³ to cm³ we multiply by 100³

10. Area of triangle = 1 ab sinC 2
Higher Tier only:
Arc length = θ x πD
360
Area of sector = θ x πr2
360
Area of triangle = 1 ab sinC 2
Area of segment = Area sector –
Area of triangle

11. Parallel, e. g. (lines never meet) Perpendicular, e. g
Parallel, e.g. (lines never meet) Perpendicular, e.g. (90º) Horizontal, e.g. _____________ Vertical, e.g

12. Triangles: Angles add up to 180º
2D Shapes
Triangles: Angles add up to 180º
3 sides different sides same sides same
3 angles different angles same angles same

13. Rhombus Parallelogram Kite
Quadrilaterals: Angles add up to 360º
Square Rectangle Trapezium
Rhombus Parallelogram Kite
(squashed square) (squashed rectangle)

14. Angles
Angles on a straight line add to 180 °
Angles at a point add to 360°
Vertically opposite angles are equal
Parallel lines – look for Z, F and C angles

15. Pyramid Tetrahedron Cone (square based) (triangular based pyramid)
Cube Cuboid Triangular prism
Pyramid Tetrahedron Cone (square based) (triangular based pyramid)
Sphere
Cylinder

16. Polygons e.g. SUM OF EXTERIOR ANGLES is ALWAYS 360°
Triangle Quadrilateral Pentagon Hexagon
SUM OF EXTERIOR ANGLES is ALWAYS 360°
SUM OF INTERIOR ANGLES = (n-2) x 180°
(where n = number of sides)
REGULAR means all sides and angles are equal.

17. Congruent shapes are exactly the same shape and size
Congruent shapes are exactly the same shape and size Shapes A & B are congruent A B A

18. Mode’s the most (Common)
Median’s the middle (put in order first)
Mean you add up and divide
Range = High - Low

19. Multiply midpoints by frequencies (fx) Total fx column
Estimate of mean:
Find midpoints
Multiply midpoints by frequencies (fx)
Total fx column
Estimate of mean = Total fx Total f
May be asked to draw a frequency polygon here

20. Example 1.
During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below.
midpoint(x)
mp x f 2 4 5 7 10 27
0 - 10
frequency
minutes Late 5
135 15
150 25
175 35
175 45
180 55
110
Mean estimate = 925/55 = 16.8 minutes

21. Plot MIDPOINT against frequency
Frequency Polygons –
Plot MIDPOINT against frequency
Remember to label the axes
Grouped frequency diagrams –
Bar charts with NO gaps

22. Work out the scale on both axes of graphs BEFORE you start the question Write all angles or measurements you find on the diagram as you go along as well as showing workings in the answer space If there is no diagram drawn for a question about shapes, draw one it may well gain you marks

23. Higher/Intermediate Tier only: Cumulative Frequency
Plot END points against cumulative frequency
‘S’ shaped graph
Interquartile Range
= UQ - LQ

24. Box and whisker plots - Higher/Intermediate Tier only:

25. Histograms (Higher Tier only)
Frequency = AREA of bar and f.d. = f
f = c.w. X f.d. c.w.

26. Metric Units of Measurement
LENGTH: kilometre (km)
metres (m) centimetres (cm)
WEIGHT: tonnes
kilograms (kg)
grams (g)
CAPACITY: litres
millilitres (ml)
Remember:
5 miles ≈ 8km
or 1mile ≈ 1.6km
1kg ≈ 2.2 lbs
1L ≈ 1.75pints

27. Speed = Distance
Time ← must be in hours
Density = Mass ← 1kg = 1000g
Volume ← 1L = 1000cm³
Population density = Population size
Area covered

28. Bearings
3-figure bearings – e.g. if the angle is 36°, you must write it as 036°
You measure starting FROM NORTH in a CLOCKWISE direction and always go FROM somewhere TO somewhere!
If not drawn to scale, can you find Z, F or C angles with parallel north lines?

29. Fractions, decimals, percentages
You need to remember:
50% = ½ = 0.5
25% = ¼ = 0.25
75% = ¾ = 0.75
To find a fraction ÷ by bottom, x by top
e.g. Find 3 of 45 5
45 ÷ 5 = 9
9 x 3 = 27

30. Percentages % means out of 100 First find 10% (÷ 10) 5% (Half 10%) 1% (÷ 100)
High/Int Tier
Don’t forget to use multipliers
e.g. 30% profit = 100% + 30% = 130% or 1.3
40% loss = 100% - 40% = 60% or 0.6

31. More Percentages! Compound Interest:
Remember to add or subtract the interest at the END of EVERY year
or use the formula
Is the question asking for the ‘interest’ or the ‘final amount’?
High/Int Tiers
Reverse Percentages – where you need to find the ORIGINAL amount, first find 1%, then X by 100%.

32. Ratio
Map scales e.g. 1 : 25
means that every 1cm on the map represents
25cm in real life.
Don’t forget to check if you need to convert
to metres for the final answer.

33. Higher/Int Tier only: Converting a number into standard form a) = × 106 b) = × Remember to write x 10 …

34. Be very careful when multiplying out brackets with lots of negative signs:
7(3n − 2) − 4(6 − 5n) x - = +
= 21n − 14 − n Expand
= 21n + 20n Collect like terms
= 41n − Simplify

35. Equations Change side … change sign + becomes a – - becomes a + x becomes a ÷ ÷ becomes a x

36. y = mx + c Straight line graphs Gradient = y x e.g. y = -3x + 9
gradient cut on y axis
Gradient = y x
e.g. y = -3x + 9

37. (All these can only be divided exactly by themselves and one)
Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, …
(All these can only be divided exactly by themselves and one)
1 is NOT prime
Square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, …
e.g. 4² means 4 x 4 = 16
Square root: √ e.g. √9 = 3 √25 = 5
Cube numbers are 1, 8, 27, 64, 125 etc.
e.g. 2³ means 2 x 2 x 2 = 8
Cube roots: e.g. ³√8 = 2 (because 2 x 2 x 2 = 8)
Multiples: e.g. The multiples of 7 are 7, 14, 21, 28, 35 ……
Factors e.g. The factors of 12 are: 1, 12, 2, 6, 3, 4
(all the numbers that divide exactly into 12 with no remainders).

38. Venn diagrams  

39. Electricity Bills Currency Conversions
Remember to change pence to £ BEFORE adding on the standing charge
Currency Conversions
x 1.64
e.g.
£1 ≈ $1.64
÷ 1.64

40. Don’t forget any answers involving money MUST be rounded to 2 d. p. e
Don’t forget any answers involving money MUST be rounded to 2 d.p. e.g. £ If asked to write to an appropriate degree of accuracy round your answers to whole numbers or 1 d.p. and state this in brackets too!

41. And finally!
Underline any key words and read all of the question carefully – including the first paragraph!
Write down any:
UNITS
DEGREES OF ACCURACY
FORMULA
and anything else that may get you extra marks including your WORKINGS OUT!!

42. Good luck!!