QCE Year 11 Essential Maths practice exams with worked answers

Almost every practical calculation is built from the four basic operations: addition, subtraction, multiplication and division. The skill is deciding which operation a situation needs. Words such as total, altogether and increase usually signal addition. Words such as difference, change and left over signal subtraction. Each, per and times usually signal multiplication, while share, split equally and how many fit signal division.

Before touching a calculator, read the problem twice, underline the numbers and units, and write a short plan such as "cost of coffees + cost of muffins, then divide by the number of staff".

When an expression contains more than one operation, the answer depends on the order in which you work. Mathematicians agree on one order so that everyone gets the same result. Remember it as BODMAS (or BIDMAS, or PEMDAS in some books):

1. Brackets (and anything grouped, such as the top and bottom of a fraction bar) first.
2. Orders (indices): squares, cubes and square roots next.
3. Division and Multiplication together, working from left to right.
4. Addition and Subtraction together, working from left to right.

The most common confusion is thinking that multiplication always comes before division, or addition always before subtraction. They do not. Division and multiplication share the same level, so you move left to right. For example, 24 ÷ 4 × 3 is 6 × 3 = 18, not 24 ÷ 12 = 2. In the same way, 10 − 3 + 2 is 7 + 2 = 9, not 10 − 5 = 5.

Setting your working out clearly makes errors easier to find. Write one line per step, copy down everything you have not yet used, and change only the part you are working on. Keep the equals signs lined up under each other. If an answer involves money, keep two decimal places during the working and round only at the end.

Practical problems often hide a bracket. If three friends each pay for a meal and a drink, the total is 3 × (meal + drink), not 3 × meal + drink. Where the problem describes a combined amount that is then multiplied or divided, you will need a bracket, and your calculator needs it too.