Higher June 2022 Paper 5 Q17
17 Charlie is making some wooden frames.
Charlie has a strip of wood 1.6 m long and 2 cm wide.
Not to scale
Each frame will be made from four pieces of wood cut from the strip to form a rectangle, as shown below.
Not to scale
The width of each frame is \(x\) cm.
The length of each frame is \(2x\) cm.
The area enclosed by each frame must be 96 cm2.
Work out the maximum number of frames Charlie can make from the 1.6 m length of wood.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 3 frames with correct working | 6 | “Correct working” requires B5 | |
| Algebraic method: B5 for [one frame =] 52 [cm] with \(x = 10\) and \(2x^2 - 12x - 80\) [= 0] or better or M3 for \(2x^2 - 12x - 80\) [= 0] or better A1 for [\(x\) =] 10 or M2 for \((2x - 4)(x - 4)\) [= 96] oe or better seen or B1 for \(2x - 4\) or \(x - 4\) seen | For B5 and M3A1 isw for use of \(x = -4\) For B5 or M3 allow equivalent 3 term quadratic e.g. \(2x^2 - 12x = 80\) Allow equivalents for M2 e.g. \(2 \times 2 \times 2x + 2 \times 2(x - 4) + 96 = 2x^2\) May be on diagram | ||
| OR | |||
| Trial and improvement: B5 for [one frame =] 52 [cm] with \(x = 10\) and 16 by 6 [= 96] shown or B4 for \(x = 10\) and 16 by 6 [= 96] selected or B3 for selects 6 by 16 [= 96] | B3 not just for seeing 6 by 16 it must be selected in some way e.g. ringed, underlined, used | ||
| If 0, 1 or 2 scored, instead award SC3 for [one frame =] 52 [cm] with no or insufficient working If 0 or 1 scored, instead award SC2 for \(x = 10\) with no or insufficient working | |||