Edexcel C3 2010 January — Question 5 3 marks

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2010
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSketch y=|f(x)| for non-linear f(x)
DifficultyModerate -0.3 This is a straightforward graph sketching question requiring knowledge that ln|x| creates an even function with a vertical asymptote at x=0, symmetric about the y-axis, and no x-axis intercepts (since ln|x|=0 only at x=±1). It's slightly easier than average as it combines two basic transformations (modulus and logarithm) with no calculation required beyond identifying x=±1 as intersection points.
Spec1.02l Modulus function: notation, relations, equations and inequalities1.02n Sketch curves: simple equations including polynomials1.06d Natural logarithm: ln(x) function and properties

5. Sketch the graph of \(y = \ln | x |\), stating the coordinates of any points of intersection with the axes.

AnswerMarks Guidance
## Question 5: \(y = \lnx \)
Answer/WorkingMark Guidance
Right-hand branch in quadrants 4 and 1, correct shapeB1
Left-hand branch in quadrants 2 and 3, correct shapeB1
Completely correct sketch with both \((-1, 0)\) and \((1, 0)\) markedB1
## Question 5: $y = \ln|x|$

| Answer/Working | Mark | Guidance |
|---|---|---|
| Right-hand branch in quadrants 4 and 1, correct shape | B1 | |
| Left-hand branch in quadrants 2 and 3, correct shape | B1 | |
| Completely correct sketch with both $(-1, 0)$ and $(1, 0)$ marked | B1 | |

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5. Sketch the graph of $y = \ln | x |$, stating the coordinates of any points of intersection with the axes.\\

\hfill \mbox{\textit{Edexcel C3 2010 Q5 [3]}}