Foundation June 2025 Paper 2 Q13
13 Ingrid records the number of minutes she uses her mobile phone over four weeks.
\[140 \qquad 168 \qquad 205 \qquad 192\](a) Work out the range. [1 mark]
(b) Ingrid records the number of minutes for a fifth week.
The mean for all five weeks is 178 minutes.
Work out the number of minutes used in the fifth week. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| 65 | B1 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: works with total | ||
| \(178 \times 5\) or 890 or \((140 + 168 + 205 + 192 + x) \div 5\) or \((705 + x) \div 5\) | M1 | oe any letter |
| their \(890 - (140 + 168 + 205 + 192)\) or their \(890 - 705\) or \((705 + x) \div 5 = 178\) | M1dep | oe |
| 185 | A1 | SC2 3 hrs 5 (minutes) |
| Alternative method 2: works with differences from new mean | ||
| \(140 - 178\) and \(168 - 178\) and \(205 - 178\) and \(192 - 178\) or \(-38\) and \(-10\) and 27 and 14 or 38 and 10 and \(-27\) and \(-14\) | M1 | subtractions may be the other way round |
| \(-7\) or 7 | M1dep | |
| 185 | A1 | SC2 3 hrs 5 (minutes) |
| Alternative method 3: works from the mean of the 4 given values | ||
| \(178 - (140 + 168 + 205 + 192) \div 4\) or \(178 - 705 \div 4\) or \(178 - 176.25\) or 1.75 or \(-1.75\) | M1 | oe eg \(4 \times 178 - 705\) subtraction may be the other way round |
| \(4 \times\) their 1.75 or 7 or \(-7\) | M1dep | oe |
| 185 | A1 | SC2 3 hrs 5 (minutes) |
| Alternative method 4: trial and improvement | ||
| Trial of any value with mean correctly evaluated | M1 | |
| Trial of 185 with mean evaluated to 178 | M1dep | eg \((140 + 168 + 205 + 192 + 185) \div 5 = 178\) |
| 185 | A1 | SC2 3 hrs 5 (minutes) |
| Alternative method 5: numerical solution of \((140 + 168 + 205 + 192 + x) \div 5 = 178\) | ||
| \(178 - (140 + 168 + 205 + 192) \div 5\) or \(178 - 705 \div 5\) or \(178 - 141\) or 37 | M1 | oe |
| their \(37 \times 5\) | M1dep | oe |
| 185 | A1 | SC2 3 hrs 5 (minutes) |
Additional guidance
| M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| In alt 4 ignore trials which are not evaluated or are evaluated incorrectly | |
| In alt 4 accept if the mean is given to the next or previous integer eg trial of 178 \((140 + 168 + 205 + 192 + 178) \div 5 = 176\) (or 177 or 176.6) | M1 |
| Accept working in hours and minutes for M2 178 \(=\) 2hrs 58mins 140 \(=\) 2hrs 20mins 168 \(=\) 2hrs 48mins 205 \(=\) 3hrs 25mins 192 \(=\) 3hrs 12mins | |
| SC2 is for 185 in hours and minutes |