Ratio, Proportion and Rates of Change (AQA)

Ratios

Ratios

Show the relationship between two (or more) numbers, written as a:b or a/b.

Simplifying Ratios

Ratios can be simplified like fractions by dividing both parts by their greatest common factor.

Simplifying Ratios with Decimals/Fractions

Multiply the ratio by a number to get whole numbers, then simplify further if possible.

Simplifying Ratios in Different Units

Convert units to the same type, simplify, and express as a ratio.

Writing Ratios as Fractions of a Whole

Express ratios as parts of a whole, finding total amount and fractions for each part.

Scale Factors

Numbers that scale quantities, used in maps and scaled diagrams.

Percentages

Show a number as parts per hundred, written as a fraction or decimal.

Calculating Percentages of Amounts

Convert percentage to decimal/fraction, then multiply by the amount.

Increasing/Decreasing by Percentages

Add or subtract the percentage of the amount to increase or decrease it.

Reverse Percentages

Find the original value after an increase or decrease using percentages.

Interest Rates

Money paid back at a percentage when borrowing or loaning.

Simple Interest

Calculate interest by finding a percentage of the principal for a period and adding it.

Compound Interest

Interest where added interest also earns interest, using a multiplier method.

Proportions

Two equal ratios used to find missing values, set up as fractions.

Scale Factors

Used to compare sizes of shapes, find length scale factor, and calculate area/volume scale factors.

Proportionality

Write equations with proportions using a constant of proportionality.

Direct Proportions

Relationship where values increase together with a constant multiplier.

Indirect Proportions

Relationship where one value increases while the other decreases.

Exponential Growth and Decay

Graphs with exponential growth for >1 and decay for 0< <1.