Higher June 2017 Paper 3 Q26
26 Here is an L-shape.
All dimensions are in centimetres.
Not drawn accurately
The area of the L-shape is 65 cm\(^2\)
Work out the value of \(x\). [6 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(10(3x + 1)\) or \(\;9x\) or \(\;x(9 - 3x - 1)\) or \(x(8 - 3x)\) or \(\;(10 - x)(3x + 1)\) or \(\;x(3x + 1)\) or \(\;(10 - x)(9 - 3x - 1)\) | M1 | oe One correct area expression in \(x\) May be implied |
| \(10(3x + 1) + x(9 - 3x - 1)\) or \(\;9x + (10 - x)(3x + 1)\) or \(\;(10 - x)(3x + 1) + x(9 - 3x - 1) + x(3x + 1)\) or \(\;10 \times 9 - (10 - x)(9 - 3x - 1)\) | M1dep | oe Fully correct unsimplified expression for area |
| \(30x + 10 + 9x - 3x^2 - x\) or \(9x + 30x + 10 - 3x^2 - x\) or \(30x + 10 - 3x^2 - x + 9x - 3x^2 - x + 3x^2 + x\) or \(90 - 90 + 30x + 10 + 9x - 3x^2 - x\) or \(\;38x + 10 - 3x^2\) | M1dep | oe dep on M1 M1 Full expansion All brackets removed |
| \(3x^2 - 38x + 55\ (= 0)\) | A1 | oe 3-term equation |
| \((3x - 5)(x - 11)\) \(\dfrac{--38 \pm \sqrt{(-38)^2 - 4 \times 3 \times 55}}{2 \times 3}\) or \(\dfrac{38 \pm \sqrt{1444 - 660}}{6}\) or \(\dfrac{38 \pm \sqrt{784}}{6}\) | M1 | oe their 3-term quadratic factorised correctly or correct substitution in formula for their 3-term quadratic equation |
| \(\dfrac{5}{3}\) or \(1\dfrac{2}{3}\) or 1.66(6...) or 1.67 | A1 | oe \(x = 11\) included is A0 |
Additional guidance
| \(3x^2 = 38x - 55\) | M1M1M1A1 |