Higher January 2020 Paper 2R Q19
19
(a) Solve \(\;\dfrac{4 - 3x}{5} - \dfrac{3x - 5}{2} = -3\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
(b) Solve the inequality \(\;5y^2 - 17y \leqslant 40\) (3)
| Scheme | Marks |
|---|---|
eg \(\dfrac{2(4 - 3x)}{10} - \dfrac{5(3x - 5)}{10} = -3\) oe or \(2(4 - 3x) - 5(3x - 5) = -3 \times 2 \times 5\) | M1 |
| \(8 - 6x - 15x + 25 = -30\) oe | M1 |
| Working required Answer: 3 | A1 |
| (3) |
Notes
M1: Correct fractions over common denominator as an equation or Multiplying both sides by 10
M1: A correct equation with no denominators or brackets
A1: dep on M1
| Scheme | Marks |
|---|---|
\((5y + 8)(y - 5)\) (\(\leqslant 0\)) or (\(y\) =) \(\dfrac{-(-17) \pm \sqrt{(-17)^2 - 4 \times 5 \times -40}}{2 \times 5}\) | M1 |
| −1.6, 5 oe | A1 |
| \(-1.6 \leqslant y \leqslant 5\) oe | A1 |
| (3) | |
| (6 marks) |
Notes
M1: Correct method to solve 3 term quadratic – factorising or correct use of formula
A1: Correct critical values
A1: Condone change of variable in place of \(y\) throughout this question.