CAIE P2 2005 November — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2005
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeExponential or logarithmic inequality
DifficultyModerate -0.8 This is a straightforward exponential inequality requiring only taking logarithms of both sides and correctly handling the inequality direction when dividing by a negative logarithm. It's a single-step application of a standard technique with no conceptual complications, making it easier than average but not trivial since students must remember the sign reversal rule.
Spec1.06g Equations with exponentials: solve a^x = b

1 Solve the inequality \(( 0.8 ) ^ { x } < 0.5\).

AnswerMarks Guidance
Use logarithms to obtain a linear inequality in \(x\), or corresponding equationM1
Obtain critical value 3.11, or exact equivalentA1
Obtain answer \(x > 3.11\)A1 √ 3
Use logarithms to obtain a linear inequality in $x$, or corresponding equation | M1 | 
Obtain critical value 3.11, or exact equivalent | A1 | 
Obtain answer $x > 3.11$ | A1 | √ 3
1 Solve the inequality $( 0.8 ) ^ { x } < 0.5$.

\hfill \mbox{\textit{CAIE P2 2005 Q1 [3]}}