## Question 9(i):

| Answer | Mark | Guidance |
|--------|------|----------|
| $0.5 \times 2.5 \times (1 + 2(-3 + 2\sqrt{6.5}) + 3)$ | M1* | Attempt $y$-values at $x = 0, 2.5, 5$ only. M0 if additional $y$-values found, unless not used. $y_1$ can be exact or decimal (2.1 or better). Allow M1 for using incorrect function as long as still clearly $y$-values intended to be original function eg $-3 + 2\sqrt{x+4}$ (from $\sqrt{(x+4)} = \sqrt{x} + \sqrt{4}$) |
| $= 10.2$ | M1d* | Attempt correct trapezium rule, inc $h = 2.5$. Fully correct structure reqd, including placing of $y$-values. The 'big brackets' must be seen, or implied by later working. Could be implied by stating general rule in terms of $y_0$ etc, as long as these have been attempted elsewhere and clearly labelled. Using $x$-values is M0. Can give M1, even if error in evaluating $y$-values as long correct intention is clear |
| | A1 | Obtain 10.2, or better. Allow answers in range [10.24, 10.25] if $>3$sf. A0 if exact surd value given as final answer. Answer only is 0/3. Using 2 separate trapezia can get full marks. Using anything other than 2 strips of width 2.5 is M0. Using trapezium rule on result of an integration attempt is 0/3 |
| | [3] | |

---

## Question 9(ii):

| Answer | Mark | Guidance |
|--------|------|----------|
| $(5 \times 3) - 10.2 = 4.8$ | M1 | Attempt area of rectangle $-$ their (i). As long as $0 <$ their (i) $< 15$ |
| | A1FT | Obtain 4.8, or better. Allow for exact surd value as well. Allow answers in range [4.75, 4.80] if $> 2$sf |
| | [2] | |

---

## Question 9(iii):

| Answer | Mark | Guidance |
|--------|------|----------|
| $x = \frac{1}{4}(y^2 + 6y - 7)$ | M1 | Attempt to write as $x = f(y)$. Must be correct order of operations, but allow slip with inverse operations eg $+/-$, and omitting to square the $\frac{1}{2}$. Allow $y^2 + 9$ from an attempt to square $y+3$, even if $(y+3)^2$ is not seen explicitly first. Allow maximum of 1 error |
| | A1 | Obtain $x = \frac{1}{4}(y^2 + 6y - 7)$ aef. Allow A1 as soon as any correct equation seen in format $x = f(y)$, eg $x = \frac{1}{4}(y+3)^2 - 4$ or $x = \frac{1}{4}(y^2+6y+9) - 4$, and isw subsequent error |
| $\text{area} = \left[\frac{1}{12}y^3 + \frac{3}{4}y^2 - \frac{7}{4}y\right]_1^3$ | M1* | Attempt integration of $f(y)$. Expand bracket and increase in power by 1 for at least two terms (allow if constant term disappears). Independent of rearrangement attempt so M0M1 is possible. Can gain M1 if their $f(y)$ has only two terms, as long as both increase in power by 1. Allow M1 for $k(y+3)^3$, any numerical $k$, as the integral of $(y+3)^2$ or M1 for $k(\frac{1}{2}(y+3))^3$ from $(\frac{1}{2}(y+3))^2$ oe if their power is other than 2 |
| | A1 | Obtain $\frac{1}{12}y^3 + \frac{3}{4}y^2 - \frac{7}{4}y$ aef. Or $\frac{1}{12}(y+3)^3 - 4y$. A0 if constant term becomes $-\frac{7}{4}x$ not $-\frac{7}{4}y$ |
| | B1 | State or imply limits are $y = 1, 3$. Stated, or just used as limits in definite integral. Allow B1 even if limits used incorrectly (eg wrong order, or addition). Allow B1 even if constant term is $-\frac{7}{4}x$ (or their $cx$) |
| $= \frac{15}{4} - (-\frac{11}{12})$ | M1d* | Attempt correct use of limits. Correct order and subtraction. Allow M1 (BOD) if $y$ limits used in $-\frac{7}{4}x$ (or their $cx$), but M0 if $x = 0, 5$ used. Minimum of two terms in $y$. Only term allowed in $x$ is their $c$ becoming $cx$. Allow processing errors eg $(\frac{1}{12} \times 3)^3$ for $\frac{1}{12} \times 3^3$. Answer is given so M0 if $\frac{14}{3}$ appears with no evidence of use of limits. Minimum working required is $\frac{15}{4} + \frac{11}{12}$. Allow M1 if using decimals (0.92 or better for $\frac{11}{12}$). M0 if using lower limit as $y=0$, even if $y=3$ is also used. Limits must be from attempt at $y$-values, so M0 if using 0 and 5 |
| $= \frac{14}{3}$ **AG** | A1 | Obtain $\frac{14}{3}$. Must come from exact working ie fractions or recurring decimals - correct notation required so A0 for 0.9166... A0 if $-\frac{7}{4}x$ seen in solution |
| | [7] | **SR** for candidates who find the exact area by first integrating onto the $x$-axis: **B4** obtain area between curve and $x$-axis as $10\frac{1}{3}$; **B1** subtract from 15 to obtain $\frac{14}{3}$; And, if seen in the solution, **M1A1** for $x = f(y)$ as above |

The pages you've shared only contain **Appendix 1** (Guidance for Marking C2) and the OCR contact/back page — these are **not question-specific mark scheme pages**. They contain only general marking guidance (accuracy rules, extra solutions policy, solving equations guidance, etc.) and no individual question mark allocations.

To extract question-by-question mark scheme content in the format you've requested, I would need the **main mark scheme pages** for the 4722 June 2014 paper, which would typically show:

- Question numbers
- Working/answers
- Mark codes (M1, A1, B1, etc.)
- Examiner guidance notes

Could you share those pages? They would typically appear **before** the Appendix page shown here.