A sports day timekeeper is allowed to apply a correction, \(n\) seconds, to an old stopwatch reading. The diagram shows the range of values of \(n\) that th...
Question 1 Report
A sports day timekeeper is allowed to apply a correction, \(n\) seconds, to an old stopwatch reading. The diagram shows the range of values of \(n\) that the rules permit.
- Write down the inequality satisfied by \(n\), as shown in the diagram. (2)
- Write down all the integer values of \(n\) that satisfy this inequality. (2)
Answer Details
(a) On the number line, the filled (solid) circle at \(n=-3\) shows this value is included, so the inequality there is \(n\geqslant-3\). The open (unfilled) circle at \(n=4\) shows this value is excluded, so the inequality there is \(n<4\). Combining both, \(-3 \leqslant n < 4\). [2 marks]
(b) The integer values satisfying \(-3 \leqslant n < 4\) are every whole number from \(-3\) up to, but not including, \(4\): \(-3, -2, -1, 0, 1, 2, 3\). [2 marks]
A filled circle always marks an inequality that includes that endpoint ("\(\leqslant\)" or "\(\geqslant\)"), while an open circle marks a strict inequality ("\(<\)" or "\(>\)") that stops just short of it; reading the two ends of the diagram correctly is what fixes both boundary symbols.
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