Higher June 2024 Unit 1 Q4
4. The diagram below shows a shape made by joining two rectangles together.
The area of the whole shape is 89 cm2.
Diagram not drawn to scale
Form and solve an equation to find the value of \(x\). [5]
| Scheme | Marks | Comments |
|---|---|---|
| Sight of \(7(x + 8)\) or equivalent AND Sight of \(3(x + 1)\) or equivalent. | B1 | Check diagram for answers Brackets must be seen unless implied in later correct working. |
| \(7(x + 8) + 3(x + 1) = 89\) or equivalent. | B1 | FT ‘their expressions’ provided of equivalent difficulty. Equating the sum of their two area expressions to 89. |
| \(7x + 56 + 3x + 3 = 89\) | B1 | Correct expansion in an equation. |
| \(10x = 30\) | B1 | FT only from \(ax \pm b \pm cx \pm d = k\), provided working with area. |
| \(x = 3\) | B1 | FT from any equation of the form \(fx = g\). Answer must be > –1 on FT. Accept an answer rounded, truncated or as an improper fraction (if not whole number) on FT. Mark final answer. If the first B0 or B1 awarded, then award an additional SC2 for \(x = 3\) clearly identified as a final answer if no correct equation shown. Award full marks if \(x = 3\) given and correct equation shown. If an incorrect equation shown and correct answer on FT given (with or without workings shown), award the final B0B1B1 marks. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Sight of \(7(x + 8 + 3)\) or equivalent AND Sight of \(3(7 - 1 - x)\) or equivalent. | B1 | Check diagram for answers. Brackets must be seen unless implied in later correct working. |
| \(7(x + 8 + 3) - 3(7 - 1 - x) = 89\) or equivalent. | B1 | FT ‘their expressions’ provided of equivalent difficulty. Equating the difference of their two area expressions to 89. |
| \(7x + 77 - 18 + 3x = 89\) | B1 | Correct expansion in an equation. |
| \(10x = 30\) | B1 | FT only from \(ax \pm b \pm cx \pm d = k\), provided working with area. |
| \(x = 3\) | B1 | FT from any equation of the form \(fx = g\). Answer must be > –1 on FT. Accept an answer rounded, truncated or as an improper fraction (if not whole number) on FT. Mark final answer. If the first B0 or B1 awarded, then award an additional SC2 for \(x = 3\) clearly identified as a final answer if no correct equation shown. Award full marks if \(x = 3\) given and correct equation shown. If an incorrect equation shown and correct answer on FT given (with or without workings shown), award the final B0B1B1 marks. |