Enhanced Curriculum Support

SecA

1. Find the answers to the following terms:

(a) 35 – (20) = ?

(b) 72 – (90) = ?

(c) (-15) – (-18) = ?

(d) (-20) – (13) = ?

(e) 23 – (-12) = ?

(f) (-32) – (-40) = ?

2. Fill in the following blanks with >, < or = sign (greater, lesser or equal sign)

(a) (-3) + (-6), (-3) – (-6)

(b) (-21) – (-10), (- 31) + (-11)

(c) 45 – (-11), 57 + (-4)

(d) (-25) – (-42), (-42) – (-25)

3. Write four negative integers which are greater than – 20.

SecB

1. For the below following statements, write True (T) or False (F). If the statement is false, then correct the state­ment.

(a) -8 is present to the right of- 50 on a number line.

(b) – 100 is present to the right of – 50 on a number line.

(c) The smallest negative integer is said to be – 1.

(d) – 26 is larger than the number -25.

SecC

1. Write all the integers present between the given pairs (also write them in increasing order):

(a) 0 and – 7 (negative)

(b) – 4 and 4

(c) – 8 and – 15

(d) – 30 and – 23.

2. The temperature in a freezer is -18°C. If the temperature increases by 7°C, then decreases by 5°C, what is the final temperature?

SecD

1. A person has $150 in their bank account. Over the week, they perform the following transactions: they withdraw $35, deposit $50, withdraw $70, and deposit $40. Calculate the final balance in the account at the end of the week. Also, discuss how understanding integers helps in keeping track of these transactions.

2.Represent the following numbers as integers with their appropriate signs.

(a) An aeroplane is flying at the height of two thousand metres above the surface.

(b) A submarine is travelling at a depth of eight hundred metres below sea level.

(c) A deposit of rupees two hundred.

(d) A withdrawal of rupees seven hundred.

3. Write the opposites in the following values given below:

(a) An increase in weight

(b) Distance of 30 km north

(c) Distance of 80 m east

(d) Loss of Rupees 700

(e) 100 metres above sea level

Problem1

Situation: Alex has a busy week ahead. On Monday, he finished his homework early, so he gained 2 extra hours of free time (+2 hours). On Tuesday, he had a lot of chores, which took 3 hours longer than expected (-3 hours). On Wednesday, he managed his time well and gained 1 extra hour (+1 hour).

1. How many hours does Alex have left by the end of Wednesday?

2. What does this situation teach you about time management and balancing responsibilities?

Problem2

Situation: Your class has a charity project where you can earn points by helping others. Helping someone with their homework earns you +5 points. However, missing a deadline on your own work results in -3 points. Last week, you helped 3 classmates but missed 2 deadlines.

1. What is your total score for the week?

2. How does this situation help you understand the importance of helping others while also managing your own responsibilities?

Problem3

Situation: You are hiking up a mountain. You start at an elevation of 0 meters (sea level). On the first day, you climb 500 meters (+500 meters). On the second day, you descend into a valley 200 meters below your starting point (-200 meters). On the third day, you climb back up 400 meters (+400 meters).

1. What is your final elevation after the third day?

2. How does this scenario help you appreciate the challenges of hiking and understanding elevation changes in nature?

Problem4

Situation: In a soccer match, your team gains 3 points for every goal scored (+3 points) but loses 1 point for every foul committed (-1 point). If your team scored 5 goals and committed 2 fouls, what is the final score?

1. What does this scenario teach you about teamwork, effort, and how every action can affect the overall outcome?

Problem5

Situation: Imagine you had a really good start to your day, so your happiness level is at +5. But then, you had a disagreement with a friend, which brought your happiness level down by 4 points (-4). Later, you received some good news, raising your happiness by 3 points (+3).

1. What is your happiness level now?

2. How does this scenario help you understand the concept of emotional balance and how to manage your feelings?

Q1

1. What is the opposite of -7?

2. If the temperature drops from 3°C to -2°C, by how many degrees did the temperature decrease?

3. What is the integer that is 5 less than -3?

4. If you add a positive integer to a negative integer, can the result be positive? Explain briefly.

Q2

1. A diver is 20 meters below sea level. If he rises by 15 meters, what is his new position relative to sea level? Explain your answer.

2. If the product of two integers is positive, what can you say about the signs of the two integers? Explain.

3. Calculate the sum of -6, +3, and -8, and briefly explain your steps.

Q3

1. A hiker starts at an elevation of 200 meters above sea level. On the first day, she climbs 350 meters. On the second day, she descends 420 meters, and on the third day, she climbs 180 meters. What is her final elevation? Explain your calculations.

2. If the temperature in City A is -7°C and it drops by 5°C, while in City B, the temperature is +3°C and it drops by 8°C, which city is colder after the temperature changes?

3. If the sum of three consecutive integers is 6, identify the integers and explain your reasoning.

Q4

1. A submarine starts at 100 meters below sea level and ascends 40 meters. It then descends 60 meters and ascends another 70 meters. Finally, it descends 50 meters. What is the submarine's final position relative to sea level?

2. You are playing a game where moving forward is represented by positive numbers and moving backward by negative numbers. If you start at position 0, then move forward by 8 steps, backward by 5 steps, forward by 7 steps, and finally backward by 9 steps, what is your final position? Describe your thought process.

3. A certain country experiences changes in temperature over three consecutive days: -2°C, +5°C, and -4°C. If the temperature on the first day was -10°C, what was the temperature at the end of the third day? Explain your calculations and how you account for the changes.

A student is working on a project and receives feedback on three assignments. The first feedback adds 10 points, the second subtracts 12 points, and the third adds 8 points to his overall score. If the student's initial score was 75, what is the final score? Discuss how you arrived at your answer.

Q5

1. A mountain climber is planning a three-day hike. On the first day, she ascends 600 meters, on the second day, she descends 350 meters, and on the third day, she ascends another 400 meters. However, due to extreme weather, she is forced to descend 200 meters at the end of the third day. If she started her hike at an elevation of 150 meters above sea level, calculate her final elevation.

2. A company tracks its financial performance over five months. In January, they gained $5,000. In February, they lost $3,500. In March, they made a profit of $7,000. In April, they experienced a loss of $6,000, and in May, they gained $4,500. Calculate the company's net financial position at the end of May, starting from an initial balance of $10,000.

3. You are playing a board game where you start at position 0. The rules are as follows: if you roll an even number, you move forward by that many spaces. If you roll an odd number, you move backward by that many spaces. You roll the following sequence of numbers: 4, 3, 6, 5, 2, 1, 4. Calculate your final position on the board and provide a detailed explanation of each move.

4. Consider the following scenario: A scientist is measuring the depth of the ocean at various points. At point A, the depth is recorded as -500 meters. Moving to point B, the depth increases by 200 meters. At point C, the depth decreases by 300 meters, and at point D, the depth increases by 150 meters. The scientist moves to a final point, E, where the depth decreases by 100 meters. Calculate the depth at point E relative to sea level and explain how these measurements help in understanding the ocean's topography.

Questions

1. The sum of an integer and its additive inverse is always zero.(True/False)

2. The sum of two negative integers is a positive integer.(True/False)

3. On the number line, -15 is to the ……… of zero.

4. The additive inverse of 14 is .

5. Write the digits 0, 1, 2, 3, …., 9 in this order and insert ‘+’ or ‘-‘ between them to get the result 3.

6. Write six distinct integers whose sum is 7.

7. 1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9 = -5 Change one ‘-‘ sign as ‘+’ sign to get the sum 9.

8. Arrange the following integers in the descending order and ascending order: -3, 0, -1, -4, -6

9. Write five integers which are less than -100 but greater than -150.

10. The sum of two integers is 30. If one of the integers is -42, then find the other.

11. If we are at 8 on the number line, in which direction should we move to reach the integer -5,11,0?

Question 1

The level of the surface of oceans or seas is called the sea level. Land and hills are raised and are at some height from the sea level. City A is 10 m below sea level, City B is 28 m below sea level and City C is 14m above sea level.

Based on the figure, answer the following questions:

1. Which of the three cities is at the highest elevation from the sea level?

2. Aditi uses the following rules to represent the elevation of different locations.

The sea level is considered to be zero elevation.

Below sea level is shown using the ‘–’ sign

For example, the elevation of City A is shown as –10.

What would be the elevation of City B?

3. The elevation of City D is 1 m above the elevation of City B. What is the elevation of City D?

4. The elevation of City E is 2 m above the elevation of City B and 4 m below the elevation of City C. What is the elevation oc City E?

Question 2

A child was given 5 quiz tests and the scores of his were recorded as follows :- 3, +7, 0, -2, 6.

Based on the above figure, answer the following questions:

1. What is the lowest score the child got?

2. Which integer lies to the extreme left on the number line?

3. Find the sum of +3, +7, 0, -2, +6.

4. Write the predecessor of positive number and successor of negative number of +3, +7, -2, +6