http://www.youtube.com/watch?v=XKCZn5MLKvk
Numbers:
- Multiples- numbers in the 4 times table are called multiples of 4
- Square numbers- numbers raised to the power 2
e.g. 3^2 = 3 x 3 = 9
- Cube numbers- numbers raised to the power 3
e.g. 3^3= 3 x 3 x 3= 27
- To find the LCM of two numbers, write each number as a product of its prime factors
(e.g. 50= 2 x 5^2)
then multiply the figures with the highest power for each prime factor.
- To find the HCF, write each number as a product of its prime factors and then multiply the figures with the lowest power.
- the reciprocal of a number x is 1/x
A number times it's reciprocal equals 1.
The reciprocal of a number can be shown using an index of -1. for example 7^-1= 1/7
Basics:
You need to be very comfortable on knowledge of time, years, ect:
a century- a period of 100 years. Because there is no year 0, the epoch started with year 1, so a century always starts with a number 1 (1601,1701,1801,1901,2001...2101) A century always begins on january 1st of the year ending with '01.'
The 21st century began on the 1st January 2001 and will end on 31st December 2100
The 20th century began on the 1st January 1901 and ended on 31st December 2000...ect...
Days in each month of the year:
Shapes:
This will be useful for both QR and AR sections. It will save a lot of time to be familiar with number of sides and angles of certain groups of shapes.
Quadrilaterals- A quadrilateral is any 2 dimensional four sided shape made of straight lines. www.mathsisfun.com/quadrilaterals.html
Polygons- www.mathsisfun.com/geometry/polygons.html
Regular polygons are polygons in which all sides and angles are equal.
Averages:
Range- is the difference between the highest and lowest values
Cumulative frequency tables and Averages:
Converting a percentage to a raw result:
-times the percentage by the amount its out of e.g.:
So as you can see in that example, the total marks you can get in maths was 80. The average of the percentages was 74.5%
and they converted this into raw marks by multiplying 74.5 x 80
How to find out the original percentage of an unknown amount:
Original value x ( 1 + or - %) = Final value
So for example, if an item of clothing has gone up 20% , and now the price is £15, what was the original price before the remark?
15 x (1+ 0.2) = £18
(can be simplified to 1.2)
e.g. the total rainfall for sept was 570cm,
to find out what a 45% increase of this is:
570 x 1.45% = 826.5 cm
e.g. the total rainfall for sept was 570cm,
to find out what a 45% increase of this is:
570 x 1.45% = 826.5 cm
Q.The weight of exonium 23% less than deranium. What is it's weight? (from the table the weight of deranium is 232)
A. The weight of exonium = 232 x (1-0.23) =178.6
Final value/ (1+/-%) = Original value
e.g. we know from the table that the production of machine 1 is 400 accepted and 20% rejected. We need to find out the original value to find out the total production os machine 1 (including the amount rejected)
so using the equation above;
Final value/ (1+/-%) = Original value
400 / (1-0.2) = 500
Examples:
Q. At it's highest point (308.5m), the tallest building is 18.6% than the next tallest building. What is the height of the second tallest building?
A. Using the equation, we can see that the final value is given. So to work out the original value,
308.5/1.186 = 260.1 m
To find out how much a 'Whole' is from a percentage:
Divide the given amount by the percentage of how much that given amount represents
savings = income- expenditure
Geometry
Circles:
circumference= π x diameter
area =π r^2
Ratio:
How to turn a percentage into a ratio (pie chart)
In this example, the question asks how much of a pie chart would size C get (in the table size C was 24% of the population).
So to find the proportion of something given in a percentage multiply the percentage by the whole.
Measurement:
Density= mass/volume
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