Transcript Higher Tier NUMERACY WJEC GCSE Revision

MEAN FROM A TABLE
•Multiply frequency
by the value
•Divide this total by
total frequency
Total
Mean
How many
ESTIMATE OF THE MEAN
•2 extra columns
•Use mid point of groups
•Mid point x frequency
•Big total divided by
little total
Basic Averages
• Modal class is the mode
group
• Median is the middle one
• Mean is total divided how
many?
Mean
Total
How many?
STRATIFIED SAMPLING
Eg
239 of 100
Total
•Fraction of – divide by the
bottom, times by the top.
FREQUENCY DIAGRAMS
Frequency polygon
= join midpoints
of bar chart
Frequency diagram =
bar chart
Venn Diagrams
Everything in the
rectangle is part of
the universal set
AuB is everything in
either A, B or both
AI means not A
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
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)
(b)
32
8
4
2
10
4
2
2
60
2
5
6
2
3
2
2
ANSWER = 2 X 2 X 2 X 2 X 2
5
=2
ANSWER = 2 X 2 X 3 X 5
2
=2 X3X5
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
PERCENTAGES
•1% - divide by 100
•10% - divide by 10
• % change is change / original x 100%
Percentage Increase by Multiplier
100% + 1.85% = 101.85%
= Multiplier 1.0185
£5600 x 1.018515
Currency exchange
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
Income tax
• 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
20%
£40000 £31865 =
£8135
40%
CALCULATOR WORK + ESTIMATION
• Work
out the top
•Work out the bottom
•Top divided by the bottom
Estimate means
round the numbers
first
Surds
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
Plans and Elevations
Nets of 3d shapes
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
Density Formula Triangles
Mass
Density
Population
Volume
Pop density
Area of
country
ANGLES
•Parallel lines- look for
FUZ:
Corresponding
Interior
Alternate
•Bearings measure
clockwise from North
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
Area of Isosceles Triangle
Use Pythagoras to find the
height
Then use base x height / 2
for the area
TRAVEL GRAPH
Away from
home
Journey
home
Stops
Speed is how
far you travel
in 1 hour
Distance
Speed
Time
BEARINGS
ANG
LE
MEASURED
FROM THE
(North line must be on zero degrees on a protractor)
NORTH LINE
MEASURED IN A CLOCKWISE
DIRECTION
MUST BE WRITTEN AS THREE
Find the bearing of B from A
N
A
054
° B
FIGURES
Tessellations
Shapes tessellate when the angles at
the point they meet add to 360 deg
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
Circle Area – Work backwards
We are given the
area, find the radius
CONES AND SPHERES
Everything you need to know is
on the formula sheet on the
paper
Volume of a sphere – find the radius
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
Collect like terms
Don’t forget that you cannot add an x2
term and an x term
Nth Term
Find the nth term of the following sequences and then
calculate the 100th term.
a) 3, 7, 11, 15, …
+4
+4
+4
100th term =
4x100 -1
100th term =
399
Nth term so
far = 4n
Start
number is Nth term
1 is 4n - 1
PROPORTION
• Bring in k
• Y = k x2
• Work out k
• If inverse proportion,
• Y=k
x2