| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Linear transformation to find constants |
| Difficulty | Moderate -0.5 This is a standard data-plotting and linear regression question requiring students to plot points, draw a line of best fit, find its equation (y = mx + c form), and use it for predictions. While it involves logarithms and multiple parts (5 marks typical), each step is routine and follows a well-practiced procedure with no conceptual challenges or novel problem-solving required. Slightly easier than average due to its procedural nature. |
| Spec | 1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form2.02c Scatter diagrams and regression lines |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| i \(0.6(0..), 0.8(45..), [1], 1.1(76..), 1.3(0..), 1.6(0..)\) | T1 | Correct to 2 d.p. Allow 0.6, 1.3 and 1.6 |
| Points plotted correctly f.t. | P1 | |
| Ruled line of best fit | L1 | tol. 1 mm |
| ii \(b =\) their intercept | M1 | |
| \(a =\) their gradient | M1 | |
| \(-11 \leq b \leq -8\) *and* \(21 \leq a \leq 23.5\) | A1 | |
| iii 34 to 35 m | 1 | |
| iv \(29 =\) "22"\(\log t -\) "9" | M1 | |
| \(t = 10^{"1.727..."}\) | M1 | |
| 55 [years] approx | A1 | accept 53 to 59 |
| v For small \(t\) the model predicts a negative height (or \(h = 0\) at approx 2.75) | 1 | |
| Hence model is unsuitable | D1 |
# Question 10:
| Answer/Working | Mark | Guidance |
|---|---|---|
| **i** $0.6(0..), 0.8(45..), [1], 1.1(76..), 1.3(0..), 1.6(0..)$ | T1 | Correct to 2 d.p. Allow 0.6, 1.3 and 1.6 |
| Points plotted correctly f.t. | P1 | |
| Ruled line of best fit | L1 | tol. 1 mm | **[3]** |
| **ii** $b =$ their intercept | M1 | |
| $a =$ their gradient | M1 | |
| $-11 \leq b \leq -8$ *and* $21 \leq a \leq 23.5$ | A1 | | **[3]** |
| **iii** 34 to 35 m | 1 | | **[1]** |
| **iv** $29 =$ "22"$\log t -$ "9" | M1 | |
| $t = 10^{"1.727..."}$ | M1 | |
| 55 [years] approx | A1 | accept 53 to 59 | **[3]** |
| **v** For small $t$ the model predicts a negative height (or $h = 0$ at approx 2.75) | 1 | |
| Hence model is unsuitable | D1 | | **[2]** |
---(i) On the insert, complete the table and plot $h$ against $\log _ { 10 } t$, drawing by eye a line of best fit.\\
(ii) Use your graph to find an equation for $h$ in terms of $\log _ { 10 } t$ for this model.\\
(iii) Find the height of the tree at age 100 years, as predicted by this model.\\
(iv) Find the age of the tree when it reaches a height of 29 m , according to this model.\\
(v) Comment on the suitability of the model when the tree is very young.
\hfill \mbox{\textit{OCR MEI C2 2009 Q10 [12]}}