Foundation June 2022 Paper 3 Q28
28 The diagram shows rectangle \(STUV\).
\(TQU\) and \(SRV\) are straight lines.
All measurements are in cm.
The area of trapezium \(QUVR\) is \(A\) cm2
Show that \(A = 2x^2 + 20x\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Complete chain of reasoning | M1 | for (area of trapezium \(TQRS =\)) \(0.5 \times 4x \times (2x + 3x)\) or for (area of rectangle \(TUVS =\)) \(4x \times (3x + 5)\ (= 12x^2 + 20x)\) |
| M1 | for (area of trapezium \(QUVR =\)) \(4x(3x + 5) - 0.5 \times 4x \times (2x + 3x)\) | |
| C1 | for correct algebraic processing and simplification to the given form |
Additional guidance
Evidence for the award of marks may be seen on the diagram
Alternative methods may be seen.
Alternative 1
| Answer | Mark | Mark scheme |
|---|---|---|
| M1 | for (\(QU =\)) \(3x + 5 - 2x\ (= x + 5)\) | |
| M1 | for (area of trapezium \(QUVR =\)) \(0.5 \times 4x \times (\text{``}x + 5\text{''} + 5)\) or \(0.5 \times 4x \times (x + 10)\) | |
| C1 | for correct algebraic processing and simplification to the given form |
Alternative 2
| Answer | Mark | Mark scheme |
|---|---|---|
| M1 | for (area of triangle =) \(0.5 \times (3x - 2x) \times 4x\) or for (area of rectangle =) \(4x \times 5\) | |
| M1 | for (area of trapezium \(QUVR =\)) \(\text{``}0.5 \times (3x - 2x) \times 4x\text{''} + \text{``}4x \times 5\text{''}\) | |
| C1 | for correct algebraic processing and simplification to the given form |
Accept \(x\) for \((3x - 2x)\)