Moderate -0.8 This is a straightforward rational equation requiring only algebraic manipulation: find common denominator, simplify, and solve the resulting quadratic. It's simpler than average A-level questions as it involves routine techniques with no conceptual challenges or multi-step problem-solving.
Multiply throughout by \((x + 1)(x - 1)\) or combining fractions and multiply up oe (can retain denominator throughout). Condone a single computational error provided that there is no conceptual error. Do not condone omission of brackets unless it is clear from subsequent work that they were assumed.
A1
Any fully correct multiplied out form (including say, if 1's correctly cancelled)
DM1
Dependent on first M1. For any method leading to both solutions. Collecting like terms and forming quadratic \(= 0\) and attempting to solve *(provided that it is a quadratic and \(b^2 - 4ac \geq 0)\). Using either correct quadratic equation formula (can be error when substituting), factorising (giving correct \(x^2\) and constant terms when factors multiplied out), completing the square oe soi.*
A1
For both solutions www.
SC B1
For \(x = 0\) (or \(x = 3\)) without any working
SC B2
For \(x = 0\) (or \(x = 3\)) without above algebra but showing that they satisfy equation
SC M1A1M0 SCB1
For first two stages followed by stating \(x = 0\)
SC M1A1M0 SCB1
For first two stages and cancelling \(x\) to obtain \(x = 3\) only.
[4]
# Question 1
M1 | Multiply throughout by $(x + 1)(x - 1)$ or combining fractions and multiply up oe (can retain denominator throughout). Condone a single computational error provided that there is no conceptual error. Do not condone omission of brackets unless it is clear from subsequent work that they were assumed.
A1 | Any fully correct multiplied out form (including say, if 1's correctly cancelled)
DM1 | Dependent on first M1. For any method leading to both solutions. Collecting like terms and forming quadratic $= 0$ and attempting to solve *(provided that it is a quadratic and $b^2 - 4ac \geq 0)$. Using either correct quadratic equation formula (can be error when substituting), factorising (giving correct $x^2$ and constant terms when factors multiplied out), completing the square oe soi.*
A1 | For both solutions www.
SC B1 | For $x = 0$ (or $x = 3$) without any working
SC B2 | For $x = 0$ (or $x = 3$) without above algebra but showing that they satisfy equation
SC M1A1M0 SCB1 | For first two stages followed by stating $x = 0$
SC M1A1M0 SCB1 | For first two stages and cancelling $x$ to obtain $x = 3$ only.
[4]