GCSE Maths Practice: order-of-operations-bidmas

Question 2 of 10

In this word-based BIDMAS problem, a quantity decreases, gains energy raised to a power, and is finally scaled, testing full order-of-operations reasoning.

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\( \begin{array}{l}\text{A system starts with 10 units of energy. It loses 3 units, then}\text{ gains }2^3\text{ times 5 more.}\\ \text{What is the final energy?}\end{array} \)

Choose one option:

Translate descriptive steps into an expression and follow BIDMAS carefully to maintain correct order.

Translating Real-World Problems into BIDMAS Expressions

Higher-tier questions often disguise mathematical operations inside word problems. The challenge is to extract each part of the description, convert it into symbols, and then apply the correct order of operations. This approach checks whether you understand how mathematics models everyday events such as growth, loss, or scaling.

How to Decode a Word Problem

  1. Identify the base quantity. In most questions, there will be a starting amount or value to which changes are applied.
  2. Translate actions into operations. Words like increase, add, or gain suggest addition. Terms such as remove or loss suggest subtraction. Phrases like times larger, doubles, or scaled by represent multiplication. References to squared or cubed indicate powers.
  3. Build the expression. Place operations in the order they are described but remember that BIDMAS, not sentence order, decides which is done first.
  4. Evaluate systematically. Complete powers first, then multiplication or division, followed by addition or subtraction.

Writing a clear algebraic or numerical expression from the story is the skill that separates higher-level reasoning from simple computation.

Common Misinterpretations

  • Adding or subtracting before handling a power or multiplier.
  • Forgetting that real-world descriptions rarely match the operation order directly.
  • Assuming time order equals calculation order — in BIDMAS, mathematical priority always wins.

For example, if energy doubles every second and then a constant is subtracted, the doubling (multiplication or power) still happens before subtraction, even if the subtraction is mentioned first.

Practical Connections

This kind of reasoning appears in physics, business, and computing. In physics, formulas often add or subtract energy terms after powers or squares are applied (as in kinetic energy, \(E=\frac{1}{2}mv^2\)). In finance, compound growth works with percentages that act as powers before additional costs or deductions are applied. In coding or spreadsheet work, order of operations ensures consistent automation of these models.

How to Approach Exam Questions

1. Read slowly and highlight numbers and operation keywords.
2. Write an expression directly underneath the question in mathematical form.
3. Check that powers and brackets are placed where the words imply grouping.
4. Solve in BIDMAS order, showing each stage clearly.
5. Re-read the question to confirm that your operations make sense contextually.

FAQs

Q1: Why do word problems feel harder than pure equations?
A: Because they test interpretation skills as well as computation. Once you translate the story correctly, the maths is the same.

Q2: How do I know if something should be inside brackets?
A: If two or more operations apply to the same part of the description (for example, “the sum of” or “the total before scaling”), group them with brackets before multiplying or dividing.

Q3: Can I use BIDMAS in every real-life context?
A: Yes. The order of operations is a universal logic system used in every applied formula.

Study Tip

When practising, rewrite short stories into algebraic expressions yourself. The ability to convert words into BIDMAS structure trains analytical thinking and prepares you for both non-calculator reasoning questions and modelling tasks in higher maths and science.