Higher June 2018 Paper 3 Q19
19 Here are two right-angled triangles.
Given that
\(\tan e = \tan f\)
find the value of \(x\).
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{5}{3}\) | P1 | for process to derive an equation in \(x\), eg \(\dfrac{x}{4x - 1} = \dfrac{6x + 5}{12x + 31}\) |
| P1 | for complete process to remove fractions, eg \(x(12x + 31) = (6x + 5)(4x - 1)\) | |
| P1 | for process to reduce to a quadratic equation, eg \(12x^2 - 17x - 5 = 0\) | |
| P1 | for process to solve the quadratic equation by factorisation or use of quadratic formula, eg \((4x + 1)(3x - 5) = 0\) | |
| A1 | for \(\dfrac{5}{3}\) oe |
Additional guidance
Must be correct use of brackets
Award for correct LHS only.
Award for correct LHS only.
Accept substitution into the formula;
\(\dfrac{-(-17) \pm \sqrt{(-17)^2 - 4 \times 12 \times -5}}{2 \times 12}\)
Accept answers in the range 1.66 to 1.67 as equivalent