Decimal Places Write 32. 5616 correct to 1 dp = 32. 6 Write 400 Decimal Places Write 32.5616 correct to 1 dp = 32.6 Write 400.295 correct to 2 dp = 400.30 Write 26.154 correct to 2 dp = 26.15

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 0.0473 correct to 2 sig figs = 0.047 because you start counting from the first non zero digit

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.

Area of Triangle = b x h (Half a rectangle) 2 Area of parallelogram = b x h Area of trapezium = (a + b) x h 2

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.

Pythagoras’ Theorem c² = a² + b²                            

Labelling a circle Tangent Sector Radius Diameter Chord Circumference

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

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

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

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

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

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

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

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

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.

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

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

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

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 50 - 60 4 40 - 50 5 30 - 40 7 20 - 30 10 10 - 20 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

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

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

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

Box and whisker plots - Higher/Intermediate Tier only:

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

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

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

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?

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

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

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%.

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.

Higher/Int Tier only: Converting a number into standard form a) 5 600 000 = 5.6 × 106 b) 0.0465 = 4.65 × 10-2 Remember to write x 10 …

Be very careful when multiplying out brackets with lots of negative signs: 7(3n − 2) − 4(6 − 5n) - x - = + = 21n − 14 − 24 + 20n Expand = 21n + 20n - 14 - 24 Collect like terms = 41n − 38 Simplify

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

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

(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).

Venn diagrams  

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

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. £2.40 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!

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!!

Good luck!!