Higher November 2024 Paper 2 Q12
12
Show clear algebraic working. (3)
| Scheme | Marks |
|---|---|
eg \(\dfrac{3(3x + 2) - 5(2x + 1)}{15}\;(= x)\) oe eg \(\dfrac{1 - x}{15}\;(= x)\) or \(\dfrac{3(3x + 2)}{15} - \dfrac{5(2x + 1)}{15}\;(= x)\) or \(3(3x + 2) - 5(2x + 1) = x \times 5 \times 3\) oe or \(\dfrac{3}{5}x + \dfrac{2}{5} - \dfrac{2}{3}x - \dfrac{1}{3}\;(= x)\) | M1 |
eg \(9x + 6 - 10x - 5 = 15x\) oe or \(1 - x = 15x\) oe eg \(9x + 6 = 15x + 10x + 5\) or \(\dfrac{-x + 1}{15} = \dfrac{15x}{15}\) or \(-\dfrac{16}{15}x = -\dfrac{1}{15}\) | M1 |
Working required Answer: \(\dfrac{1}{16}\) | A1 |
| (3) |
Notes
M1: Writing fractions over a common denominator or removing denominator or writing each term separately – if student has expanded/multiplied at this stage, then allow one of the 4 terms on the LHS incorrect.
If the student has removed the denominator at this stage then a correct method must be shown or implied
M1: An equation with no brackets or fractions
or
an equation with a common denominator for all terms with numerators simplified
(allow one error for the 4 terms on the LHS only (they may have moved these to the RHS) across the 2 M marks and ft for simplifying)
A1: oe 0.0625 (allow 0.062 or 0.063)
dep on M1
| Scheme | Marks |
|---|---|
| \(f^2 = \dfrac{a + bc}{c - d}\) | M1 |
| eg \(cf^2 - df^2 = a + bc\) | M1 |
| eg \(cf^2 - bc = a + df^2\) | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(c = \dfrac{a + df^2}{f^2 - b}\) | A1 |
| (4) | |
| (7 marks) |
Notes
M1: for squaring both sides in a correct equation
M1: for multiplying by the denominator and expanding in a correct equation
M1: for isolating terms in \(c\) on one side and other terms the other in a correct equation
A1: oe eg \(c = \dfrac{-a - df^2}{b - f^2}\)