CAIE P2 2017 June — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |f(x)| compared to |g(x)| with parameters: equation or inequality only
DifficultyStandard +0.3 This is a straightforward modulus equation requiring the standard technique of considering critical points and cases. While it involves a parameter 'a', the algebraic manipulation is routine: squaring both sides gives (x+a)² = (2x-5a)², leading to a simple factorization. This is slightly above average difficulty only because of the parameter, but remains a standard textbook exercise with no novel insight required.
Spec1.02l Modulus function: notation, relations, equations and inequalities

1 Solve the equation \(| x + a | = | 2 x - 5 a |\), giving \(x\) in terms of the positive constant \(a\).

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
State or imply non-modulus equation \((x+a)^2 = (2x-5a)^2\) or pair of linear equationsB1 SR B1 for \(x = 6a\)
Attempt solution of quadratic equation or of pair of linear equationsM1 Allow M1 if \(\frac{4}{3}\) and 6 seen
Obtain, as final answers, \(6a\) and \(\frac{4}{3}a\)A1
Total:3
## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| State or imply non-modulus equation $(x+a)^2 = (2x-5a)^2$ or pair of linear equations | B1 | SR **B1** for $x = 6a$ |
| Attempt solution of quadratic equation or of pair of linear equations | M1 | Allow **M1** if $\frac{4}{3}$ and 6 seen |
| Obtain, as final answers, $6a$ and $\frac{4}{3}a$ | A1 | |
| **Total:** | **3** | |

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1 Solve the equation $| x + a | = | 2 x - 5 a |$, giving $x$ in terms of the positive constant $a$.\\

\hfill \mbox{\textit{CAIE P2 2017 Q1 [3]}}