Algebra, number and structure
What you must understand
This domain covers fluent work with numbers and with simple algebraic expressions. You need confident arithmetic with integers, fractions, decimals and percentages, including order of operations (brackets, then powers, then multiplication and division left to right, then addition and subtraction). Know how to convert between fractions, decimals and percentages, to find a percentage of a quantity, to increase or decrease by a percentage, and to work with ratios and rates such as speed and unit price.
In algebra, understand that a pronumeral stands for a number. Be able to substitute values into formulas, simplify expressions by collecting like terms, expand simple brackets, and solve linear equations by doing the same operation to both sides. Rearranging a familiar formula to make another variable the subject is a common requirement.
Traps to watch
- Ignoring order of operations, especially with negative numbers and powers.
- Percentage increase and decrease applied to the wrong base, or adding percentages that are taken of different amounts.
- Sign errors when subtracting negative numbers or expanding a bracket preceded by a minus.
- Cancelling terms across a plus sign, which is invalid - only factors may be cancelled.
- Forgetting units when working with rates, or mixing units such as minutes and hours.
Worked example
A jacket costs $80 and is discounted by 15%, then a further 10% is taken off the sale price. The first discount gives 80 × 0.85 = $68. The second gives 68 × 0.90 = $61.20. Note the total reduction is 23.5%, not 25%, because the second discount applies to the reduced price. Rule of thumb: successive percentage changes multiply, they do not add.