CAIE P2 2022 March — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2022
SessionMarch
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |linear| = |linear| (both linear inside)
DifficultyModerate -0.8 This is a straightforward modulus equation requiring consideration of cases where expressions inside are positive/negative. Standard technique: square both sides or consider sign changes. Simpler than average as it involves only linear expressions with no additional algebraic complexity.
Spec1.02l Modulus function: notation, relations, equations and inequalities
1 Solve the equation \(| 5 x - 2 | = | 4 x + 9 |\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Solve \(5x - 2 = 4x + 9\) to obtain \(x = 11\)B1
Attempt solution of linear equation where signs of \(5x\) and \(4x\) are differentM1
Obtain final value \(x = -\frac{7}{9}\)A1
Alternative method:
State or imply non-modulus equation \((5x-2)^2 = (4x+9)^2\)B1
Attempt solution of 3-term quadratic equationM1
Obtain \(x = -\frac{7}{9}\) and \(x = 11\)A1
Total3 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| Solve $5x - 2 = 4x + 9$ to obtain $x = 11$ | B1 | |
| Attempt solution of linear equation where signs of $5x$ and $4x$ are different | M1 | |
| Obtain final value $x = -\frac{7}{9}$ | A1 | |
| **Alternative method:** | | |
| State or imply non-modulus equation $(5x-2)^2 = (4x+9)^2$ | B1 | |
| Attempt solution of 3-term quadratic equation | M1 | |
| Obtain $x = -\frac{7}{9}$ and $x = 11$ | A1 | |
| **Total** | **3** | |

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1 Solve the equation $| 5 x - 2 | = | 4 x + 9 |$.\\

\hfill \mbox{\textit{CAIE P2 2022 Q1 [3]}}
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Q1 3 Q2 5 Q3 5 Q4 7 Q5 8 Q6 10 Q7 12