Worksheet analyzing temperature trends using a line graph.

To solve the problems presented in the image, let's break them down step by step.

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Problem 1: Looking at graphs

#### Task:
- The graph shows the temperature recorded each hour.
- At what time was the temperature at $40^\circ$?
- By how much did the temperature fall between 6 am and 8 am?

#### Solution:
1. At what time was the temperature at $40^\circ$?
- Look at the graph and find the point where the temperature line intersects the $40^\circ$ mark on the vertical axis.
- From the graph, we can see that the temperature reaches $40^\circ$ at 2 pm.

2. By how much did the temperature fall between 6 am and 8 am?
- At 6 am, the temperature is approximately $35^\circ$.
- At 8 am, the temperature is approximately $30^\circ$.
- The change in temperature is:
\[
30^\circ - 35^\circ = -5^\circ
\]
- The temperature fell by 5 degrees.

#### Final Answers:
- At what time was the temperature at $40^\circ$: 2 pm
- By how much did the temperature fall between 6 am and 8 am: 5 degrees

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Problem 2: Kate's test scores

#### Task:
- What was Kate's score in Week 2?
- In which two consecutive weeks did Kate's score increase?
- What was Kate's lowest score?
- How much did her score improve between Week 5 and Week 7?

#### Solution:
1. What was Kate's score in Week 2?
- From the graph, locate Week 2 on the horizontal axis and read the corresponding value on the vertical axis.
- Kate's score in Week 2 is 6.

2. In which two consecutive weeks did Kate's score increase?
- Look for segments of the graph where the line is going upwards (indicating an increase).
- The score increases between:
- Week 1 to Week 2: From 5 to 6.
- Week 3 to Week 4: From 4 to 5.
- Week 5 to Week 6: From 7 to 8.
- Week 6 to Week 7: From 8 to 9.
- The two consecutive weeks with an increase are Week 5 to Week 6 and Week 6 to Week 7.

3. What was Kate's lowest score?
- Identify the lowest point on the graph.
- Kate's lowest score is 4, which occurs in Week 3.

4. How much did her score improve between Week 5 and Week 7?
- In Week 5, Kate's score is 7.
- In Week 7, Kate's score is 9.
- The improvement is:
\[
9 - 7 = 2
\]
- Her score improved by 2 points.

#### Final Answers:
- What was Kate's score in Week 2: 6
- In which two consecutive weeks did Kate's score increase: Week 5 to Week 6 and Week 6 to Week 7
- What was Kate's lowest score: 4
- How much did her score improve between Week 5 and Week 7: 2 points

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Problem 3: Temperature in Chelmsford

#### Task:
- What was the temperature in April?
- Overall, what is happening to the temperature between April and August?
- How much did the temperature increase between May and July?
- Which two months had the same maximum temperature?

#### Solution:
1. What was the temperature in April?
- Locate April on the horizontal axis and read the corresponding temperature on the vertical axis.
- The temperature in April is approximately 10°C.

2. Overall, what is happening to the temperature between April and August?
- Observe the trend of the graph from April to August.
- The temperature generally increases from April to August, reaching a peak in July and then slightly decreasing in August.

3. How much did the temperature increase between May and July?
- In May, the temperature is approximately 15°C.
- In July, the temperature is approximately 25°C.
- The increase is:
\[
25 - 15 = 10
\]
- The temperature increased by 10°C.

4. Which two months had the same maximum temperature?
- Identify the peaks in the graph.
- The maximum temperature occurs in both July and August, with a value of approximately 25°C.

#### Final Answers:
- What was the temperature in April: 10°C
- Overall, what is happening to the temperature between April and August: The temperature generally increases.
- How much did the temperature increase between May and July: 10°C
- Which two months had the same maximum temperature: July and August

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Final Summary of All Answers:

1. Problem 1:
- At what time was the temperature at $40^\circ$: 2 pm
- By how much did the temperature fall between 6 am and 8 am: 5 degrees

2. Problem 2:
- What was Kate's score in Week 2: 6
- In which two consecutive weeks did Kate's score increase: Week 5 to Week 6 and Week 6 to Week 7
- What was Kate's lowest score: 4
- How much did her score improve between Week 5 and Week 7: 2 points

3. Problem 3:
- What was the temperature in April: 10°C
- Overall, what is happening to the temperature between April and August: The temperature generally increases.
- How much did the temperature increase between May and July: 10°C
- Which two months had the same maximum temperature: July and August

---

Final Boxed Answers:
\[
\boxed{
\begin{array}{l}
\text{Problem 1:} \\
\text{2 pm, 5 degrees} \\
\text{Problem 2:} \\
6, \text{Week 5 to Week 6 and Week 6 to Week 7}, 4, 2 \text{ points} \\
\text{Problem 3:} \\
10^\circ \text{C}, \text{The temperature generally increases.}, 10^\circ \text{C}, \text{July and August}
\end{array}
}
\]