Foundation November 2021 Paper 2 Q17
17.
(a) Solve \(6x - 1 = 5 + x\). [2]
(b)
Abby, Ben and Ceri are solving a puzzle.
Abby takes \(x\) seconds.
Ben takes 5 seconds more than Abby.
Ceri takes twice as long as Ben.
Ceri takes 116 seconds to solve the puzzle.
Use an algebraic method to find how long Abby takes to solve the puzzle.
You must show all your working. [3]
Abby takes ……………… seconds
| Scheme | Marks | Comments |
|---|---|---|
| \(6x - x = 5 + 1\) oe | B1 | |
| \(x = \dfrac{6}{5}\) oe, ISW | B1 | FT from \(ax = 6\), \(a \neq 1\) or \(5x = b\) accept \(\frac{6}{a}\) or \(\frac{b}{5}\) but if on FT either simplifies to an integer the answer must be given as an integer. ‘\(x\) =’ can be omitted but must not be wrong if there. Correct answer implies first B1. Final answer of \(x = \dfrac{-6}{-5}\) is B0. Maximum of 1 mark if not fully correct |
| Scheme | Marks | Comments |
|---|---|---|
| A correct equation e.g. \(2x + 10 = 116\) \(2(x + 5) = 116\) \(x + 5 = 58\) \(x = 116 \div 2 - 5\) | B2 | B1 for \(2(x + 5)\) or \(2x + 10\) |
| 53 | B1 | If no marks award: SC2 for \(x = 55.5\) following \(2x + 5 = 116\) SC1 for \(2x + 5 = 116\) |
| (5) |