| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compound growth applications |
| Difficulty | Moderate -0.3 This is a straightforward geometric sequence application requiring identification of the common ratio (r=1.5), finding the 4th term, summing terms for width calculation, and computing total area using the GP sum formula. All steps are routine C2-level calculations with no novel insight required, making it slightly easier than average. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks |
|---|---|
| \(r = 1.5\), \(u_4 = 1 \times (1.5)^3 = 3.375\) mm | M1 A1 |
| Answer | Marks |
|---|---|
| \(w = 2 \times S_8\); GP, \(a = 1\), \(r = 1.5\) | M1 |
| \(= 2 \times \frac{1[(1.5)^8 - 1]}{1.5 - 1}\) | M1 |
| \(= 98.516 = 98.5\) mm (3sf) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| areas form GP, \(a = \pi \times 1^2 = \pi\), \(r = (1.5)^2 = 2.25\) | B2 | |
| total area \(= \frac{\pi[(2.25)^{10}-1]}{2.25-1} = 8354.8\) mm\(^2\) | M1 A1 | |
| \(= \frac{8354.8}{10^2}\) cm\(^2 = 83.5\) cm\(^2\) (3sf) | A1 | (10) |
# Question 7:
## Part (i):
$r = 1.5$, $u_4 = 1 \times (1.5)^3 = 3.375$ mm | M1 A1 |
## Part (ii):
$w = 2 \times S_8$; GP, $a = 1$, $r = 1.5$ | M1 |
$= 2 \times \frac{1[(1.5)^8 - 1]}{1.5 - 1}$ | M1 |
$= 98.516 = 98.5$ mm (3sf) | A1 |
## Part (iii):
areas form GP, $a = \pi \times 1^2 = \pi$, $r = (1.5)^2 = 2.25$ | B2 |
total area $= \frac{\pi[(2.25)^{10}-1]}{2.25-1} = 8354.8$ mm$^2$ | M1 A1 |
$= \frac{8354.8}{10^2}$ cm$^2 = 83.5$ cm$^2$ (3sf) | A1 | **(10)**
---7.\\
\includegraphics[max width=\textwidth, alt={}, center]{e4afa57d-5be3-42a6-ab35-39b0fdcc1681-2_364_666_1338_568}
The diagram shows part of a design being produced by a computer program.\\
The program draws a series of circles with each one touching the previous one and such that their centres lie on a horizontal straight line.
The radii of the circles form a geometric sequence with first term 1 mm and second term 1.5 mm . The width of the design is $w$ as shown.\\
(i) Find the radius of the fourth circle to be drawn.\\
(ii) Show that when eight circles have been drawn, $w = 98.5 \mathrm {~mm}$ to 3 significant figures.\\
(iii) Find the total area of the design in square centimetres when ten circles have been drawn.\\
\hfill \mbox{\textit{OCR C2 Q7 [10]}}