Part 1: Number

• > indicates that the number on the left is greater than on the right
• < indicates that the number on the right is greater than on the left
• ≤ indicates the number on the left is less than or equal to the number on the right
• = means the number on the left equals the number on the right
• ≥ means the number on the left is greater than or equal the number on the right
• When adding/subtracting fractions together they must have the same denominator
• To multiply fractions: multiply the numerators and denominators together
• To divide fractions: flip the second fraction and then multiply the two resulting fractions together
• The inverse of addition is subtraction, and vice versa
• The inverse of multiplication is division and vice versa.
• BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction
• A factor is a number which divides into another number exactly, without leaving a remainder.
• The easiest way to find factors is to start with 1 and work your way up
• The highest common factor (HCF) is the common factor of highest value.
• Common factor = a number that is a factor of all numbers of interest
• Prime number = a number which is divisible by only 1 and itself.
• Systematic listing is a technique used to work out all possible combinations or outcomes in a particular situation
• For larger groups we use the product rule instead of systematic listing to work out all possible combinations
• To apply the product rule, we count how many objects there are in each group and multiply these
• A power is a number that tells another number and (called the base) how many times it needs to multiply by itself
• Sometimes we cannot simplify a root, so we can leave it as it is. This form is called surd form.
• If the power has a minus (-) sign in front of it, the base must be flipped
• Standard form has the format $A\cdot10^n$
• Decimals:

  • 1st column = tenths
  • 2nd column = hundredths
  • 3rd column = thousandths
  • etc..
• A terminating decimal is one in which the end of the numbers beyond the decimal point is easy to identify e.g. 3.5
• Recurring decimals = when the end of the numbers beyond the decimal point is not identifiable e.g. 0.77777777...
• A ratio tells us the proportions of how things are shared. For example, a ratio of 1: 1 means that the objects are shared equally, whereas a ratio of 2: 1 means that twice as many objects are in the first group compared to the second group.
• The percentage sign can be interpreted as ‘out of 100’
• There are three main ways to round a number:

  1. Rounding to the nearest unit, ten, hundred, thousand
  2. Rounding to a certain number of decimal places.
  3. Rounding to a certain number of significant figures.
• Rounding loses some accuracy because we are approximating the number, but it is often more practical
• A question may specify the number of decimal places (d.p.) that are required in the answer. This means that we will need to round the digit that is to the right of the number of decimal places required.
• Unlike decimal places, significant figures can be used for all numbers, not just decimals.
• We can use the upper and lower limits of accuracy to write the error interval, which shows how far away the actual value could be from the estimated value.