OCR MEI C2 2010 June — Question 9 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2010
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeModel y=ax^b: linearise and find constants from graph/data
DifficultyStandard +0.3 This is a straightforward application of logarithms to find parameters in a power law. Students substitute both points, take logs of both equations, then solve the resulting linear system. While it requires multiple steps and careful algebraic manipulation, the method is standard and commonly practiced in C2, making it slightly easier than average.
Spec1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form
The points \((2, 6)\) and \((3, 18)\) lie on the curve \(y = ax^n\). Use logarithms to find the values of \(a\) and \(n\), giving your answers correct to 2 decimal places. [5]
AnswerMarks Guidance
\(\log 18 = \log a + n \log 3\) and \(\log 6 = \log a + n \log 2\)M1* Or correct use of \(18 = a \times 3^n\) and \(6 = a \times 2^n\)
\(\log 18 - \log 6 = n(\log 3 - \log 2)\)DM1 Or \(3 = \left(\frac{3}{2}\right)^n\)
\(n = 2.71\) to \(2\) d.p. c.a.o.A1 Or \(n = \frac{\log 3}{\log 1.5} = 2.71\) c.a.o.
\(\log 6 = \log a + 2.70951...\log 2\) o.e.M1
\(a = 0.92\) to \(2\) d.p. c.a.o.A1 Or \(6 = a \times 2^{2.70951...}\) o.e. \(= 0.92\) c.a.o. 
$\log 18 = \log a + n \log 3$ and $\log 6 = \log a + n \log 2$ | M1* | Or correct use of $18 = a \times 3^n$ and $6 = a \times 2^n$
$\log 18 - \log 6 = n(\log 3 - \log 2)$ | DM1 | Or $3 = \left(\frac{3}{2}\right)^n$
$n = 2.71$ to $2$ d.p. c.a.o. | A1 | Or $n = \frac{\log 3}{\log 1.5} = 2.71$ c.a.o.
$\log 6 = \log a + 2.70951...\log 2$ o.e. | M1 | 
$a = 0.92$ to $2$ d.p. c.a.o. | A1 | Or $6 = a \times 2^{2.70951...}$ o.e. $= 0.92$ c.a.o.
The points $(2, 6)$ and $(3, 18)$ lie on the curve $y = ax^n$.

Use logarithms to find the values of $a$ and $n$, giving your answers correct to 2 decimal places. [5]

\hfill \mbox{\textit{OCR MEI C2 2010 Q9 [5]}}
This paper (12 questions)
View full paper
Q1 2 Q2 4 Q3 5 Q4 4 Q5 4 Q6 5 Q7 2 Q8 5 Q9 5 Q10 13 Q11 13 Q12 10