stem and leaf diagrams

STEM AND LEAF DIAGRAMS

• Don’t forget to order

• Include a key

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

POWERS

• 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

FRACTIONS OF

• Fraction of – divide by the bottom, times by the top.

COORDINATES

• For 3d coordinates follow the axes as x,y,z

• To find midpoints add the x’s then halve. Do the same for the y’s and z’s.

ANGLES

• Parallel lines- look for FUZ:

CorrespondingInteriorAlternate• Bearings measure

clockwise from North

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

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

• Circle is pi x radius squared

VOLUME

• Prisms – Area of front x length

EXPANDING BRACKETS

• Two brackets together – eyebrows and smiley face are 4 multiplies

FACTORISING BRACKETS

• Pick the x’s to times together

• Pick the numbers to times to the question

• Check the smiley face to see if the x term is right

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

CIRCLE ANGLES

The angle between a tangent and a radius is 90o

SCATTER DIAGRAMS

• Plot the points• Line of best fit• Positive and

negative correlation

SIMPLE PROBABILITY

• Probabilities add to 1

• Multiply the probability by the number of times

MEAN FROM A TABLE

• Multiply frequency by the value

• Divide this total by total frequency

QUESTIONNAIRES

• Look for a time limit in the question

• Overlap between the choices

• Any missing choices?

BOX PLOTS

• Plot 5 measures to draw it

• To compare, 1 comment on the median, 1 comment on the interquartile range (the width of the box)

CUMULATIVE FREQUENCY

• Running total• Plot end points against

cumulative frequency• Measure median and

quartiles

ESTIMATE OF THE MEAN

• 2 extra columns• Use mid point of

groups• Mid point x

frequency• Big total divided by

little total

HISTOGRAMS

• Frequency density is freq divided by class width

• The area of a bar is the frequency

PERCENTAGES

• 1% - divide by 100• 10% - divide by 10• % change is change / original x

100%

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

CALCULATOR WORK

• Work out the top• Work out the bottom• Top divided by the bottom

RATIO

• RATIO 2:3 MEANS 2+3 = 5 PARTS

• FIND THE VALUE OF 1 PART

PYTHAGORAS

• TAKE THE 2 NUMBERS• SQUARE• SQUARE• ADD OR SUBTRACT• SQUARE ROOT

TREE DIAGRAMS

• Each V adds to 1

• Multiply alon g the branches

TRAVEL GRAPH

Away from home

Stops

Journey home

Speed

Distance

Time

POLYGON ANGLES

Interior angle is180 – exterior angle

INEQUALITIES

3 included, filled circle-2 not

included, empty circle

• Integer means whole number

• Solve like an equation

ENLARGEMENT

Scale factor x3

Count across and up from the centre

Times this by 3 from the centre

Negative enlargement goes the opposite way

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

FRACTIONS

TL TR

BL BR

Top of 1st fraction

Bottom of 1st fraction

Top of 2nd

Bottom of 2nd

+ TR+BL BR

- TR – BL BR

X TL BR

÷ TR BL

Works for algebra fractions too

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

VECTORS

• Go from A to B• Only use a and b• -a+b or b-a

PLOTTING GRAPHS

• Complete table of values

• Plot points on grid• Join points together

to make a graph

PROPORTION

• Get 1 by dividing• In this case 1cm = 17.8 /

160• Multiply by his new number

eg 210 x

TRIG

Opp

HypSin

Adj

HypCos

Opp

AdjTan

• 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

CONES AND SPHERES

Everything you need to know is on the formula sheet on the paper