| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compound growth applications |
| Difficulty | Moderate -0.8 This is a straightforward application of geometric sequences with clear scaffolding across four parts. Part (i) is basic calculation, (ii) uses the standard GP formula, (iii) requires summing a GP (formula given in exam), and (iv) connects to arithmetic sequences. All techniques are routine for C2 level with no novel problem-solving required, making it easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) £28 000, £31 360, £35 123.20 ratio = 1.12 | B1 B1 | 2 marks |
| (ii) \(28000(1.12)^9 = 77646.21\) | M1 A1 | 2 marks |
| (iii) Use of \(\frac{a(r^n-1)}{r-1}\) \(= \frac{28000(1.12^{10}-1)}{1.12-1} = 491 364.58\) | M1 A1 A1 | 3 marks |
| (iv) Use of \(\frac{n}{2}(2a + (n-1)d)\) \(= \frac{10}{2}(70000 + 9d) = 491 364.58\) \(\Rightarrow d = 3141.44\) | M1 A1 M1 A1 A1 | 5 marks |
**(i)** £28 000, £31 360, £35 123.20 ratio = 1.12 | B1 B1 | 2 marks
**(ii)** $28000(1.12)^9 = 77646.21$ | M1 A1 | 2 marks
**(iii)** Use of $\frac{a(r^n-1)}{r-1}$ $= \frac{28000(1.12^{10}-1)}{1.12-1} = 491 364.58$ | M1 A1 A1 | 3 marks
**(iv)** Use of $\frac{n}{2}(2a + (n-1)d)$ $= \frac{10}{2}(70000 + 9d) = 491 364.58$ $\Rightarrow d = 3141.44$ | M1 A1 M1 A1 A1 | 5 marks11 When Fred joined a computer firm his salary was $\pounds 28000$ per annum. In each subsequent year he received an annual increase of $12 \%$ of his previous year's salary.\\
(i) State Fred's salary for each of his first 3 years with the company. State also the common ratio of the geometric sequence formed by his salaries.\\
(ii) How much did Fred earn in the tenth year?\\
(iii) Show that the total amount Fred earned over the ten years was between $\pounds 400000$ and £500000.\\
(iv) When Fred joined the computer firm, his brother Archie set up a plumbing business. He earned $\pounds 35000$ in his first year and each year earned $\pounds d$ more than in the previous year. At the end of ten years, he had earned exactly the same total amount as Fred. Calculate the value of $d$.
\hfill \mbox{\textit{OCR MEI C2 Q11 [12]}}