CAIE P1 2022 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicSolving quadratics and applications
TypeSolving simple rational equations
DifficultyModerate -0.8 This is a straightforward rational equation requiring multiplication by (x-1), rearranging to standard quadratic form, and solving using the quadratic formula or factorization. It's a routine procedural question with clear steps, making it easier than average for A-level, though not trivial since it requires careful algebraic manipulation and checking the domain restriction.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.02f Solve quadratic equations: including in a function of unknown
1 Solve the equation \(3 x + 2 = \frac { 2 } { x - 1 }\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\((3x+2)(x-1)=2 \Rightarrow 3x^2-x-4\ [=0]\)M1 OE Multiply by denominator and obtain a quadratic
\((3x-4)(x+1)[=0]\)M1 Solve by factorising, formula or completing the square
\([x=]\ -1, \dfrac{4}{3}\)A1 Allow 1.33; If M1 M0, SC B1 possible for two correct answers
Total: 3 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $(3x+2)(x-1)=2 \Rightarrow 3x^2-x-4\ [=0]$ | M1 | OE Multiply by denominator and obtain a quadratic |
| $(3x-4)(x+1)[=0]$ | M1 | Solve by factorising, formula or completing the square |
| $[x=]\ -1, \dfrac{4}{3}$ | A1 | Allow 1.33; If M1 M0, SC B1 possible for two correct answers |
| **Total: 3** | | |

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1 Solve the equation $3 x + 2 = \frac { 2 } { x - 1 }$.\\

\hfill \mbox{\textit{CAIE P1 2022 Q1 [3]}}
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Q1 3 Q2 6 Q3 5 Q4 6 Q5 6 Q6 6 Q7 7 Q8 8 Q9 8 Q10 10