| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward application of arithmetic and geometric sequence formulas with clear structure and standard calculations. Part (i) requires summing an arithmetic sequence over 24 terms using the standard formula. Part (ii) is a simple conceptual explanation of constant ratio. Part (iii) involves calculating a geometric series sum and comparing values. All steps are routine with no problem-solving insight required, making it easier than average but not trivial due to the multi-part nature and need for careful calculation. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Arithmetic sequence with \(a=50\), \(d=20\) | M1 | Using appropriate formula for sum of arithmetic sequence with \(a=50\), \(d=20\) |
| \(S_{24} = \dfrac{24}{2}(2\times50+(24-1)20)\) | Allow for total written out in full | |
| \(= £6720\) | A1 [2] | Allow full credit for any correct method |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Each month is 12% more than the previous, so multiplied by 1.12 giving a geometric sequence with \(a=50\), \(r=1.12\) | E1 [1] | Clear argument must include the value 1.12 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Geometric sequence with \(a=50\), \(r=1.12\) | M1 | Using appropriate formula for sum of geometric sequence; allow for total written out in full |
| \(S_{24} = \dfrac{50(1.12^{24}-1)}{0.12}\) | ||
| \(= £5907.76\), which is less than Aleela | A1, E1 [3] | Allow any suitable rounding; FT their values |
## Question 6(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Arithmetic sequence with $a=50$, $d=20$ | M1 | Using appropriate formula for sum of arithmetic sequence with $a=50$, $d=20$ |
| $S_{24} = \dfrac{24}{2}(2\times50+(24-1)20)$ | | Allow for total written out in full |
| $= £6720$ | A1 [2] | Allow full credit for any correct method |
## Question 6(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Each month is 12% more than the previous, so multiplied by 1.12 giving a geometric sequence with $a=50$, $r=1.12$ | E1 [1] | Clear argument must include the value 1.12 |
## Question 6(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Geometric sequence with $a=50$, $r=1.12$ | M1 | Using appropriate formula for sum of geometric sequence; allow for total written out in full |
| $S_{24} = \dfrac{50(1.12^{24}-1)}{0.12}$ | | |
| $= £5907.76$, which is less than Aleela | A1, E1 [3] | Allow any suitable rounding; FT their values |
---6 Aleela and Baraka are saving to buy a car. Aleela saves $\pounds 50$ in the first month. She increases the amount she saves by $\pounds 20$ each month.\\
(i) Calculate how much she saves in two years.
Baraka also saves $\pounds 50$ in the first month. The amount he saves each month is $12 \%$ more than the amount he saved in the previous month.\\
(ii) Explain why the amounts Baraka saves each month form a geometric sequence.\\
(iii) Determine whether Baraka saves more in two years than Aleela.
Answer all the questions\\
Section B (77 marks)
\hfill \mbox{\textit{OCR MEI Paper 1 2018 Q6 [6]}}