A school runs a quiz night to raise money for charity. In the quiz, a correct answer scores +5 points, a wrong answer scores \(-2\) points, and an unanswere...
Question 1 Report
A school runs a quiz night to raise money for charity. In the quiz, a correct answer scores +5 points, a wrong answer scores \(-2\) points, and an unanswered question scores 0 points. One team answers all 12 questions in the final round: 7 correct, 3 wrong, and 2 unanswered.
- Work out the team's total score. (3)
- A second team scores \(-4\). Find the difference between the two teams' scores. (2)
Answer Details
This question tests applying a scoring rule to directed numbers and then comparing two totals.
(a) Each correct answer scores \(+5\) and each wrong answer scores \(-2\), while unanswered questions score 0. With 7 correct, 3 wrong and 2 unanswered:
\[7 \times 5 = 35, \qquad 3 \times (-2) = -6\] \[35 + (-6) + 0 = 29\]The team's total score is \(29\). [3] (1 for \(7\times5=35\), 1 for \(3\times(-2)=-6\), 1 for the total 29)
(b) The difference between the two teams' scores is found by subtracting the second team's score from the first:
\[29 - (-4) = 29 + 4 = 33\]The difference between the two teams' scores is \(33\) points. [2] (1 for setting up \(29-(-4)\), 1 for the value 33)
When a scoring rule mixes positive and negative points, calculate each category's contribution separately before adding them together, so a sign is not lost partway through a longer sum.
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