Higher Tier WJEC GCSE Revision PPT(20 secs)

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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
ESTIMATE OF THE MEAN
•2 extra columns
•Use mid point of groups
•Mid point x frequency
•Big total divided by
little total
QUESTIONNAIRES
•Look for a time
limit in the question
•Overlap between
the choices
•Any missing
choices?
CUMULATIVE FREQUENCY
•Running total
•Plot end points against
cumulative frequency
•Measure median and
quartiles
HISTOGRAMS
•Frequency density is
freq divided by class
width
•The area of a bar is
the frequency
TREE DIAGRAMS
• Each V adds to 1
• Multiply alon g
the branches
FREQUENCY DIAGRAMS
Frequency polygon
= join midpoints
of bar chart
Frequency diagram =
bar chart
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
•Negative powers – work out +
power and turn upside down
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
FRACTIONS OF
Eg
239 of 100
Total
•Fraction of – divide by the
bottom, times by the top.
PERCENTAGES
•1% - divide by 100
•10% - divide by 10
• % change is change / original x 100%
CALCULATOR WORK + ESTIMATION
• Work
out the top
•Work out the bottom
•Top divided by the bottom
Estimate means
round the numbers
first
RATIO
• RATIO 2:3 MEANS 2+3 = 5
PARTS
• FIND THE VALUE OF 1
PART
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
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
VOLUME
•Prisms – Area of front x
length
ANGLES
•Parallel lines- look for
FUZ:
Corresponding
Interior
Alternate
•Bearings measure
clockwise from North
CIRCLE THEOREM
xo
xo
o
DIAMETER
ao
o
2xo
a + b = 180°
x + y = 180°
yo
Angle at centre is twice the
angle at the circumference.
yo
Angle made by a diameter is 90°.
Opposite angles in a cyclic
quadrilateral add up to 180°
xo
yo
RADIUS
xo
yo
xo
yo
Angles subtended by an arc
or a chord in the same
segment are equal.
xo
Alternate segment theorem.
Angle between a tangent and
a radius make 90°
bo
SIMILAR SHAPES
Congruent
means exactly
the same
Length scale factor = x
Area scale factor = x2
Volume scale factor = x3
PYTHAGORAS
• TAKE
THE 2 NUMBERS
•SQUARE
•SQUARE
•ADD OR SUBTRACT
•SQUARE ROOT
TRAVEL GRAPH
Away from
home
Journey
home
Stops
Distance
Speed
Time
POLYGON ANGLES
Interior angle is
180 – exterior angle
ENLARGEMENT
Scale factor x3
Count across and up
from the centre
Times this by 3 from the
centre
Negative enlargement
goes the opposite way
VECTORS
• Go from A to B
• Only use a and b
• -a+b or b-a
TRIG
Opp
Sin
Opp
Adj
Hyp
•
•
•
•
•
Cos
Hyp
Right angle triangle
Label sides
Pick correct triangle
Cover up the side you want
If finding angle use the 2ndF
button
Tan
Adj
Write
SOHCAHTOA
on the formula
page of the
paper
CIRCLES
Area = pi x rad2
Circumference = pi x diameter
Leave in terms of pi means treat
pi as a letter
CONES AND SPHERES
Everything you need to know is
on the formula sheet on the
paper
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
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
STRAIGHT LINES
• Look
neg
at the gradient – positive or
•Gradient is up divided by the
across
• Line is y=mx+c, where m is the
gradient and c the intercept
INEQUALITIES
-2 not included,
empty circle
3 included,
filled circle
• Integer means whole
number
• Solve like an equation
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
PLOTTING GRAPHS
• Complete table of
values
• Plot points on grid
• Join points together
to make a graph
PROPORTION
• Bring in k
• Y = k x2
• Work out k
• If inverse proportion,
• Y=k
x2
TRANSFORMING GRAPHS
Inside the brackets – changes x coords the opposite way
Outside the brackets, changes y coords the same way
TYPES OF GRAPHS
Quadratic graph y = x2
Cubic graph
Y = x3
x2 + y2 = r2
Reciprocal graph
Y=1/x
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)
To find the gradient when x=4
1. Mark the point
2. Draw tangent
3. Find the gradient of the line
Pick 2 points on the line
Gradient = up / across
1. Draw line 2x -3y = 6 by making a table
2. Pick a point not on the line
Take the x and y numbers and put into the
inequality. See if the inequality is true or
false for that side

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