Higher June 2021 Paper 1 Q3
3
Diagram NOT accurately drawn
The diagram shows the shape \(ABCDE\).
The area of the shape is 91.8 cm2
Work out the value of \(x\).
(4)
| Scheme | Marks |
|---|---|
\(8 \times x\ (= 8x)\) or \(14 \times x\ (= 14x)\) or \((14 - 8) \times x\ (= 6x)\) or \(\tfrac{1}{2} \times (14 - 8) \times (13 - x)\ (= 39 - 3x)\) or \(\dfrac{13 + x}{2} \times (14 - 8)\ (= 39 + 3x)\) or \(\tfrac{1}{2} \times 13 \times (14 - 8)\ (= 39)\) or \(\dfrac{8 + 14}{2} \times x\ (= 11x)\) or \(14 \times 13\ (= 182)\) or \(8 \times (13 - x)\ (= 104 - 8x)\) or \(\left(\dfrac{8 + 14}{2} \times (13 - x)\right)\ (= 143 - 11x)\) oe | M1 |
\(14x + 6 \times \tfrac{1}{2} \times (13 - x)\) oe eg \(8x + \dfrac{x + 13}{2} \times 6\) or \(\dfrac{8 + 14}{2} \times x + \dfrac{13 \times (14 - 8)}{2}\) or \(\text{“182”} - \left(\dfrac{8 + 14}{2} \times (13 - x)\right)\) or \(11x + 39\) oe | M1 |
| eg \(11x + 39 = 91.8\) or \(14x + 39 - 3x = 91.8\) or \(182 - 143 + 11x = 91.8\) or \(16x + 6x + 78 = 183.6\) oe | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 4.8 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: one correct area linked to the shape
M1: ft from correct working expression for total area of shape – with no parts omitted or duplicated
Adding up parts of given shape
or large rectangle subtracting trapezium (or subtracting (rectangle + triangle))
M1: fully correct equation with no fractions (allow 91.8 or multiples of 91.8 but no other decimals) and no brackets
A1: or \(4\dfrac{4}{5}\) oe or \(\dfrac{24}{5}\) oe