Hard Level Worksheet Questions

Part A: Subjective Questions

Interactive Integers Worksheet (Hard Level) Hard Level Worksheet Questions

(1) What integer is 7 less than the negative of –12?

Awesome! Negative of -12 is 12, and 12 - 7 = 5.

(2) Fill in the blank so that the sum of (–15), (–10), and is zero.

Great job! (-15) + (-10) + 25 = 0.

(3) Identify the smallest 3-digit negative integer.

Perfect! -999 is the smallest 3-digit negative integer.

(4) Write a positive integer which when added to –24 gives –6.

Excellent! -24 + 18 = -6.

(5) If (–a) + (–b) = –(a + b), what is (–3) + (–7)?

Super! Using the rule: -(3 + 7) = -10.

(6) Which property is violated in subtraction: a – b ≠ b – a?

That's correct! Subtraction is not commutative.

(7) State the sign of the product of 8 negative integers.

Well done! Even number of negatives gives positive.

(8) How many integers are there between –25 and –13 (excluding both)?

Brilliant! From -24 to -14, there are 11 integers.

(9) Fill in the blank: (–10) × (–1) × 0 × (–5) =

You nailed it! Any product with 0 equals 0.

(10) A number is multiplied by –1 thrice. Will the result be positive or negative?

Perfect! Odd number of (-1) multiplications gives negative.

Drag each example to its correct integer property:

(1) Fill in the blanks so that the equation holds:

(a) + (–9) + 6 = 0

(b) –12 – (–x) = –5 → Find x. x =

(2) Arrange the following integers in ascending order and find the mean: –8, 5, –3, –10, 0, 2

(a) Ascending order: , , , , ,

(b) Mean=

(3) A submarine is at –150 m below sea level. It descends 75 m more and then rises by 90 m. Find its final position.

Initial position = m

After descending 75 m: -150 (-75) = m

After rising 90 m: -225 + 90 = m

Final position = m below sea level

{.m-green}Excellent! The submarine is at -135 m.

(4) Solve: (–4) × [(–6) + (–3)] – 2 × (–5)

By solving we get

Outstanding! The answer is 46.

(1) A lift is at 3rd floor. Each floor is 4 meters high. The lift goes down 7 floors and then up 9 floors.

(a) Represent each movement using integers:

Initial position: 3rd floor = 3 × 4 = meters above ground

Going down 7 floors = meters down

Position after going down: - = meters (below ground)

Going up 9 floors: 9 × 4 = meters up

(b) What is the final position of the lift in meters?

Final position = meters above ground level

Perfect! The lift is 20 meters above ground.

(2) The temperature at 5 AM was –4°C. It increased by 2°C every hour till 11 AM and then decreased by 1°C per hour for the next 6 hours.

(a)What was the temperature at 11 AM?

Initial temperature at 5 AM = °C

From 5 AM to 11 AM = hours

Temperature increase = °C

Temperature at 11 AM = °C

(b) What was the final temperature at 5 PM?

From 11 AM to 5 PM = hours

Temperature decrease = °C

Final temperature at 5 PM = °C

Excellent! Temperature at 11 AM was 8°C and at 5 PM was 2°C.

(3) Solve and verify using integer laws:

(a) –3 × [2 + (–5)] – 4 × (–2 + 6)

(b) (–8 + 4) – [(–6) – 3]

(4) A diver descended 15 m every minute for 4 minutes and then rose 10 m per minute for 3 minutes.

(a) Represent the situation using integers. {.reveal(when="blank-15")}Descent: 15 m/min × 4 min = m down

Representing descent as negative: m

Rise = 3 × 10 =

(b) What is the final position of the diver relative to the starting point?

Rise = m up

Representing rise as positive: m

Final position = m

Fantastic! The diver is 30 m below the starting point.

Part B: Objective Questions

Test your understanding with these challenging multiple choice questions:

1. Which of the following is NOT true about integers?

(a) They are closed under multiplication (b) They are closed under subtraction (c) They are closed under division (d) They include 0

Super job! Integers are NOT closed under division (e.g., 1÷2 = 0.5).

2. (–6) ÷ 3 + (–12) ÷ (–4) =

(a) 0 (b) –6 (c) 2 (d) –2

Well done! (-6)÷3 + (-12)÷(-4) = -2 + 3 = 1.

3. A number when multiplied by –1 two times becomes:

(a) Negative (b) Same as original (c) Positive (d) Zero

That's right! Two multiplications by -1 give back the original.

4. The value of: (–2) × 5 + 3 × (–4) =

(a) –22 (b) –2 (c) –6 (d) –10

Correct! (-2)×5 + 3×(-4) = -10 + (-12) = -22.

5. If a student scores +4 marks for each right answer and –1 for each wrong one, which total score is not possible for 10 questions?

(a) 30 (b) 25 (c) 22 (d) 33

Fantastic! 33 is impossible (max is 40 with all correct).

🎉 Exceptional Work! You've Conquered Hard-Level Integers!

Here's what you mastered:

• Advanced integer calculations with multiple operations
• Complex real-world applications (lifts, submarines, temperature, diving)
• Deep understanding of integer properties (commutative, associative, distributive)
• Sign rules for multiple negative numbers
• Nested operations and order of operations with integers
• Problem-solving with constraints and impossible scenarios

Your advanced integer skills prepare you for algebra, coordinate geometry, and higher mathematics!