GCSE Maths Practice: integers-and-directed-numbers

Question 3 of 10

This question turns a mixed-operation expression into a sports-style scoring problem involving repeated losses.

‹ ›

\( \begin{array}{l}\text{A team starts with a score of } -5.\\\text{They lose 2 points in each of 6 rounds.}\\\text{What is their total score after all rounds?}\end{array} \)

Choose one option:

Convert repeated changes into multiplication, then apply addition or subtraction in the correct order.

Applying BIDMAS in Competitive Scenarios

Numbers can represent more than just quantities—they can show gains and losses. In sports, business, and games, negative values often stand for penalties or points lost. This question explores how order of operations applies when calculating overall performance using both positive and negative scores.

Scenario

Imagine a quiz competition where a team starts with a score of −5 because of an earlier penalty. During the next six rounds, they lose 2 points in each round for incorrect answers. To find their total score after all rounds, the situation is represented by the expression (−5) + (−2 × 6). This combines an initial negative value with a repeated loss.

Without a clear grasp of BIDMAS, it’s easy to make mistakes here. Many students might add the numbers directly, but the multiplication must happen first. The group of six rounds involves a repeated event (a consistent −2 penalty), so the total for that section must be calculated before adding it to the starting score.

Step-by-Step Method

  1. Recognise operations: The expression contains multiplication and addition.
  2. Follow BIDMAS: Multiplication comes before addition.
  3. Multiply the repeated penalty: Multiply −2 by 6 to find the total points lost in the rounds.
  4. Combine with the starting penalty: Add the new total loss to the initial negative value.

This process shows how multiple negative changes can accumulate to produce a larger overall decrease—a concept that occurs frequently in real data situations.

Worked Examples (Different from the Question)

  • Example 1: A gamer loses 3 lives at the start and then 4 more for each of 2 levels. Expression: (−3) + (−4 × 2).
  • Example 2: A company begins £10,000 in debt and loses £2,000 each quarter for 3 quarters. Expression: (−10,000) + (−2,000 × 3).
  • Example 3: A basketball player starts with −8 points after penalties, then loses 5 points in each of 2 fouls. Expression: (−8) + (−5 × 2).

Common Mistakes

  • Performing addition before multiplication, which changes the total completely.
  • Forgetting that a negative multiplied by a positive gives a negative total.
  • Writing −2 × 6 as +12, which confuses sign rules.

Real-World Applications

Beyond sports, this same principle appears in accounting, science, and statistics. When calculating repeated decreases (like energy loss, depreciation, or negative growth), multiplying the repeated rate first gives the total change before adding other factors. This ensures results are consistent and reflect the true pattern of variation.

FAQs

Q1: Why must the multiplication happen first?
A: Multiplication represents repeated action. BIDMAS ensures those repeated effects are calculated before combining them with single changes.

Q2: What happens if both numbers are negative?
A: Two negatives multiplied together become positive, because a double reversal changes direction.

Q3: How do I check my result’s sign quickly?
A: If every number represents a loss or penalty, the result will remain negative.

Study Tip

When solving contextual questions, write down the story as an equation first. Identify repeated changes (for multiplication) and single changes (for addition or subtraction). Then apply BIDMAS carefully. Practising with everyday examples like finances, temperature, or game scoring will help you visualise how negative values combine and reinforce your fluency for GCSE exam questions and real-world numeracy.