# Question 1:

## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $S_{th} = 64980 - \frac{7150 \times 110}{9} = -22408.9...$ → $-\mathbf{22400}$ | M1 A1 | M1 for at least one correct expression (condone transcription error). 1st A1 for $S_{hh}$ = awrt 1 490 000 or $S_{th}$ = awrt −22 400 |
| $S_{hh} = 7171500 - \frac{7150^2}{9} = 1491222.2...$ → $\mathbf{1\,490\,000}$ | A1 | 2nd A1 for $S_{th} = -22400$ AND $S_{hh} = 1490000$ only. Allow no labels but mis-labelling $S_{th}$ as $S_{hh}$ etc loses final A1 |

## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $r = \frac{-22408.9}{\sqrt{1491222 \times 371.56}} = -0.95200068...$ → awrt $-\mathbf{0.952}$ | M1 A1 | M1 for attempt at correct formula. Allow minor transcription errors of 2 or 3 digits. Must have their $S_{hh}$, $S_{th}$ and given $S_{tt}$ (3sf or better) in correct places. Condone missing "−". Award M1A0 for awrt −0.95 with no expression seen. M0 for $\frac{64980}{\sqrt{7171500 \times 7.864}}$ |

## Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Yes as $r$ is close to $-1$ (if $-1 < r < -0.5$) or Yes as $r$ is close to 1 (if $1 > r > 0.5$) | B1ft | Must comment on supporting AND state: high/strong/clear (negative or positive) correlation. "Points lie close to a straight line" is B0 since there is no evidence of this. If $-0.5 \leq r \leq 0.5$ allow "no since $r$ is close to 0". If $|r| > 1$ award B0 |

## Part (d)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $b = \frac{-22408.9}{1491222.2} = -0.015027...$ (allow $\frac{-56}{3725}$) → awrt $-0.015$ | M1 A1 | 1st M1 for correct expression for $b$. Follow through their $S_{hh}$ & $S_{th}$. Condone missing "−". 1st A1 for awrt −0.015 or allow exact fraction from rounded values |
| $a = \frac{110}{9} - \text{"their } b\text{"} \times \frac{7150}{9} = (12.2 - -0.015 \times 794.4) = 24.1604...$ so $t = \mathbf{24.2 - 0.015h}$ | M1, A1 | 2nd M1 for correct method for $a$. Follow through their value of $b$. 2nd A1 for correct equation for $t$ and $h$ with $a$ = awrt 24.2 and $b$ = awrt −0.015. No fractions |

## Part (e)
| Answer/Working | Marks | Guidance |
|---|---|---|
| 0.015 is the drop in temp (in ${}^0$C), for every 1(m) increase in height above sea level | B1 | Must mention $h$ (or height) and $t$ (or temperature) and their (1 sf) value of $b$ in a correct comment |

## Part (f)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Change $= ("24.2 - 0.015" \times 500) - ("24.2 - 0.015" \times 1000)$ or $500 \times "0.015"$ $= \pm 7.5$ (awrt $\pm 7.5$) (only ft a value < 100) | M1 A1ft | M1 for correct expression seen based on their equation. Allow transcription error of 1 digit. If answer is $500 \times$ their $b$ to 2sf and $< 100$ (M1A1). If answer is $500 \times$ their $b$ to 2sf and $\geq 100$ (M1A0) |

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