OCR MEI C2 2005 June — Question 6 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2005
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Functions
TypeSolve exponential equation using logarithms
DifficultyModerate -0.8 This is a straightforward two-part question requiring a standard exponential graph sketch and a routine logarithmic calculation (x = log 50/log 2). Both parts are basic textbook exercises with no problem-solving required, making it easier than average but not trivial since it does require correct application of logarithms.
Spec1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b

6 Sketch the graph of \(y = 2 ^ { x }\).
Solve the equation \(2 ^ { x } = 50\), giving your answer correct to 2 decimal places.

AnswerMarks Guidance
Correct curve thro' y axis \((0, 1)\) indicated on sketch or tableG1 \(y, y' \& y''\) all positive independent
5.64B2 for other versions of \(5.64(3....)\) or B1 for other ans \(5.6\) to \(5.7\) or M1 for \(x\log 2 = \log 50\) and M1 for \(x = \log 50 \div \log 2\) 5
Correct curve thro' y axis $(0, 1)$ indicated on sketch or table | G1 $y, y' \& y''$ all positive independent | 
5.64 | B2 for other versions of $5.64(3....)$ or B1 for other ans $5.6$ to $5.7$ or M1 for $x\log 2 = \log 50$ and M1 for $x = \log 50 \div \log 2$ | 5
6 Sketch the graph of $y = 2 ^ { x }$.\\
Solve the equation $2 ^ { x } = 50$, giving your answer correct to 2 decimal places.

\hfill \mbox{\textit{OCR MEI C2 2005 Q6 [5]}}