**Question 1: The temperature of a patient at a hospital is shown in the graph below, which is updated every hour.**

(a) What was the patient’s temperature at 1 pm?

(b) When was the patient’s temperature 38.5°C?

(c) During the time period specified, the patient's temperature was the same twice. What were the dates of the two events?

(d) What was the temperature at 1:30 pm? How did you arrive at your answer?

(e) During which time periods did the patient's temperature increase?

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**Solution:**

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(a) The patient's temperature was 36.5°C at 1 pm.

(b) At 12:00 pm, the patient's temperature was 38.5°C.

(c) The patient's temperature was 36.5°C at 1 pm and 2 pm.

(d) The temperature at 1:30 pm was 36.5°C. We have taken the midpoint between 1 and 2 pm, which is 1:30 pm, and proceeded perpendicularly upwards to the 36.5°C horizontal line.

(e) The temperature increased from 9 am to 10 am and from 10 am to 11 am.

**Question 2. The following line graph depicts a manufacturing company's annual sales numbers.**

(a) How much did they sell in (i) 2002 and (ii) 2006?

(b) How much did they sell in (i) 2003 and (ii) 2005?

(c) Calculate the difference in sales between 2002 and 2006.

(d) When compared to the year before, which year saw the highest difference in sales?

**Solution: **

(a) Sales in 2002 totalled 4 crores, whereas sales in 2006 totalled 8 crores.

(b) In 2003, the sales were at 7 crores, and in 2005, the sales were at 10 crores.

(c) In 2002, sales were at 4 crore rupees.

In 2006, sales were at 8 crores.

8 – 4 crore = 4 crore. So, 4 crore is the difference.

(d) The highest change in sales occurred in 2005 when compared to the prior year.

**Question 3. Two distinct plants, plant A and plant B, were grown under similar laboratory circumstances for a botany experiment. For three weeks, their heights were measured at the end of each week. The following graph depicts the outcomes.**

(a) After (i) 2 weeks (ii) 3 weeks, how tall was plant A?

(b) After (i) 2 weeks (ii) 3 weeks, how tall was plant B?

(c) During the third week, how much did plant A grow?

(d) From the end of the second week to the end of the third week, how much did plant B grow?

(e) Plant A grew the most during which week?

(f) Plant B grew the least during which week?

(g) Did the two plants reach the same height during any of the weeks depicted? Specify.

**Solution:**

(a) Plant A grew to a height of 7 cm after two weeks and 9 cm after three weeks.

(b) Plant B grew to a height of 7 cm after two weeks and 10 cm after three weeks.

(c) Plant A grew from 7 to 9 cm tall, a difference of 2 cm.

(d) From 7 cm, Plant B grew to 10 cm. So, Plant B grew by 3 cm.

(e) Plant A grew the most in the second week, reaching a height of 5 cm.

(f) Plant B grew the least in the first week.

(g) Yes, at the end of the second week, both plants had reached the same height of 7 cm.

**Question 4. The temperature forecast and actual temperature for each day of the week are shown in the graph below.**

(a) On which days did the forecasted and actual temperatures coincide?

(b) What was the highest temperature predicted for the week?

(c) During the week, what was the lowest actual temperature?

(d) Which day's actual temperature saw the biggest difference from the anticipated temperature?

**Solution:**

(a) The forecast temperature on Tuesday, Friday, and Sunday were the same as the actual temperature. That is, 20°C, 15°C, and 35°C, respectively.

(b) The maximum temperature for the week was anticipated to be 35°C.

(c) During the week, the lowest real temperature was 17.5°C.

(d) The actual temperature, 22.5°C - 15°C = 7.5°C, deviated the greatest from the expected temperature on Thursday.

**Question 5. Draw linear graphs using the tables provided.**

(a) The number of days a hillside city was able to recover in various years.

Year |
2003 |
2004 |
2005 |
2006 |

Days |
8 |
10 |
5 |
12 |

(b) The number of men and women in a village varies by year (in thousands).

Year |
2003 |
2004 |
2005 |
2006 |
2007 |

Number of men |
12 |
12.5 |
13 |
13.2 |
13.5 |

Number of women |
11.3 |
11.9 |
13 |
13.6 |
12.8 |

**Solution:**

**Question 6. To deliver a parcel to a merchant, a courier boy travels on bicycle from one town to another. The graph below depicts his distance from the town at various moments.**

(a) On the time axis, what is the scale used?

(a) How long did it take the person to travel?

(c) How distant is the merchant's location from the town?

(c) Did the person make a pit stop along the way? Explain?

(e) When was he the fastest on the bike?

**Solution:**

(a) Time-axis scale, which is the x-axis is 4 units = 1 hour.

(b) The entire journey time taken by the person is 3 hours 30 minutes.

(c) The merchant's location is 22 kilometres away from the town.

(d) Yes, the horizontal part of the graph clearly indicates this. From 10 am to 10:30 am, the individual was at a halt.

(e) Between 8 and 9 am He rode the fastest.

**Question 7. Is it possible to make a time-temperature graph like this? Justify your response.**

**Solution:**

(i) It depicts a temperature-time graph in which the temperature rises as time passes.

(ii) It depicts a temperature-time graph in which the temperature decreases as time passes.

(iii) It does not depict a temperature-time graph. This is impossible because the temperature is increasing at a consistent rate.

(iv) It depicts a temperature-time graph in which the temperature remains constant as time passes.

- Rational Numbers
- Linear Equations in One Variable
- Understanding Quadrilaterals
- Practical Geometry
- Data Handling
- Squares and Square Roots
- Cubes and Cube Roots
- Comparing Quantities
- Algebraic Expressions and Identities
- Visualizing Solid Shapes
- Mensuration
- Exponents and Powers
- Direct and Inverse Proportions
- Factorization
- Playing With Numbers