Unit 1 Revision Cards Higher Tier

Converting fractions to decimals:

Divide e.g. 1/2 = 1÷2

Converting decimals to percentages = x by 100 e.g. 0.5 x 100 = 50%

Converting pecentages to decimals = ÷ by 100 e.g. 50% ÷ 100 = 0.5

Find percentage = x% of £y = 0.x multiplied by y

Express as a percentage = give xp as pecentage of yp = (x ÷ y) x 100

Percentage off = £x - y% = x multiplied by 0.y

Compound interest

Formula = n (1 + r/100) to the power of n

n = initial amount

r/100 = percentage change

to the power of n = number of years

Depreciation

Formula = n (1 - r/100) to the power of n

n = initial amount

r/100 = percentage change

to the power of n = number of years

To reduce ratios, divide by the HCF e.g 6:3 = 2:1

For decimals, multiply to get whole numbers e.g. 1.5:4 = 3:8

For mixed units, convert all sides to the smallest unit 200g:3kg = 200g:3000g

To reduce to 1:n divide all sides by the smallest side e.g. 4:20 = 1:5

To share ratios, add the parts, then divide the share amount by the total parts, before multiplying each side by 1 part e.g.divide £9100 in the ratio 2:4:7

2+4+7 = 13 parts

9100/13 = £700

£700 x 2 =£1400        £700 x 4 = £2800       £700 x 7 = £4900

Answer = £1400 : £2800 : £4900

To estimate, round everything off to easy numbers, then calculate e.g.

419 + 203 = 400 + 200 = 600

To round decimal places, locate the number of decimal places, locate the digit to the right, and round off using this digit e.g.

26.387 to 2 decimal places:    26.387 = 26.39

Significant figures are all digits in place after the first zero, including zeros!

The first sig. fig. is the first digit which isn't a zero. All other sig. figs. follow on e.g.

0.03079 Significant figures are after the zero

A probability of zero will never happen.

A probability of one will certainly happen.

Probabilities can be fractions, decimals or percentages.

Probabilities always add up to one.

Sample space diagrams are an easy way of listing potential outcomes.

To work out the probability of A and B happening, multiply the probabilities.

To work out the probability of A or B happening, add the probabilities.

Always multiply along the branches to get the end result. All end results must add to one.

You don't always need to draw the whole diagram. Be careful you understand that in conditional probability what happens on the branches second or more on the tree depends on what happens on the previous branches.

At least is always 1 - other outcome(s)

I couldn't paste an example - sorry! :)

Choose a research question, e.g. How many people go to the beach?

Choose an appropriate source of data.

Primary data is mainly surveys, interviews and experiments. It has not been processed. Secondary data is mainly newspapers, magazines, internet, databases, books, historical records etc. It can also come from the Office of National Statistics. It has usually been processed and presented in a percentage, graph, table etc.

Choose a method of collecting the data.

There are two types of data - qualitative and quantitative.

Qualitative data is wordy and hard to analyse e.g. eye colour, gender.

Quantitative data is measured with numbers e.g. shoe size, height.

Discrete data is whole numbers e.g. no. of people.

Continuous data can be decimals e.g weight.

If you split data into class intervals, they must not overlap.

The population is the group you are finding out about. You choose a sample from this group, which is easier and more efficient than surveying the whole group.

You can use your data to make estimates and conclusions about the whole population.

A sample frame is a list or map of all members of the population.

Samples should be chosen at random, with no bias or preference.

Simple random sampling chooses random members from the sample frame.

Stratified sampling chooses members of the sample frame in proportion to the total population, when they are split into categories.

Stratified sampling = no. in category/no. in population x sample size

To avoid bias, only choose members of the sample frame, and select the sample at random. A bigger sample will be more accurate, but is less practical to collect.