## Question 7:

### Part (i):
| Answer | Mark | Guidance |
|--------|------|----------|
| State $y>3$ or $f(x)>3$ or $f>3$ or 'greater than 3' | B1 | Must be $>$ not $\geq$; allow $3<y<\infty$ |

### Part (ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| Obtain expression or eqn involving $\ln\!\left(\frac{y-3}{4}\right)$ or $\ln\!\left(\frac{x-3}{4}\right)$ | M1 | Or equivs such as $\ln\!\left(\frac{4}{y-3}\right)$ or $\ln\!\left(\frac{4}{x-3}\right)$ |
| Obtain $\ln\!\left(\frac{4}{x-3}\right)$ or $-\ln\!\left(\frac{x-3}{4}\right)$ | A1 | Or equiv |
| State domain is $x>3$ or equiv | B1FT | Following answer to part (i) (but with adjustment so that reference is to $x$) |
| State range is all real numbers or equiv | B1 | |

### Part (iii):
| Answer | Mark | Guidance |
|--------|------|----------|
| Obtain correct first iterate | B1 | Showing at least 3 dp; B0 if initial value not 3 but then M1A1A1 available |
| Show correct iteration process | M1 | Showing at least 3 iterates in all; may be implied by plausible converging values; M1 available if based on equation with just a slip in $x=f(x)$ but M0 if based on clearly different equation |
| Obtain at least 3 correct iterates | A1 | Allowing recovery after error; iterates to only 3 dp acceptable; values may be rounded or truncated |
| Obtain (3.168, 3.168) | A1 | Each coordinate required to exactly 3 dp; award A0 if fewer than 4 iterates shown; part (iii) consisting of answer only gets 0 out of 4. $[3 \to 3.199148 \to 3.163187 \to 3.169162 \to 3.168155 \to 3.168324]$ |

### Part (iv):
| Answer | Mark | Guidance |
|--------|------|----------|
| State $P$ is point where the curves meet | B1 | Or equiv |

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