Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the sum of −8 and 5.
Correct! −8 + 5 = −3.
(2) Write the difference between −12 and −4.
Perfect! −12 − (−4) = −12 + 4 = −8.
(3) Write the integer that is 10 more than −15.
Excellent! −15 + 10 = −5.
(4) Find the additive inverse of 0.
Great! The additive inverse of 0 is 0 itself.
(5) Write the integer between −2 and 0.
Correct! The only integer between −2 and 0 is −1.
Short Answer Questions (2 Marks Each)
Answer each question with proper working
(1) Find the value of −25 + 17.
Perfect! Start at −25, move 17 units right to get −8.
(2) Subtract −6 from −9.
Excellent! Subtracting a negative becomes addition.
(3) Add: −10 + (−7).
Correct! Adding two negative numbers gives a negative result.
(4) The temperature was 5°C in the morning. By night, it dropped by 13°C. Represent the night temperature as an integer.
Perfect! The night temperature is −8°C.
(5) A lift is on the 3rd floor. It goes down 7 floors. Which floor is it on now (if the ground floor is 0)?
Excellent! The lift is on floor −4 (4 floors below ground level).
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) A submarine is at 150 m below sea level. It dives 100 m deeper and then rises 75 m. Represent its final position as an integer.
Perfect! Final position: −175 m below sea level.
(2) A mountaineer is at a height of 825 m above sea level. He descends 1200 m. Represent his new position as an integer and state whether it is above or below sea level.
New position: −375 m (below sea level)
(3) Evaluate: −8 + 5 − 7 + (−4).
Excellent! The final answer is −14.
(4) Using a number line, show and find (−6) + (−3) − (−5).
Result: (−6) + (−3) − (−5) = −4
(5) The temperature on Monday was 4°C. On Tuesday, it dropped by 7°C, and on Wednesday, it increased by 5°C. Find the temperature on Wednesday.
Perfect! The temperature on Wednesday is 2°C.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) −12 + (−5) =
(a) −17 (b) 7 (c) −7 (d) 17
Correct! Adding two negative numbers: −12 + (−5) = −17.
(2) 8 − (−9) =
(a) 1 (b) 17 (c) −1 (d) −17
Correct! 8 − (−9) = 8 + 9 = 17.
(3) The sum of −15 and 9 is:
(a) −6 (b) 6 (c) −24 (d) 24
Correct! −15 + 9 = −6.
(4) If −x = 12, then x =
(a) −12 (b) 12 (c) 0 (d) 1
Correct! If −x = 12, then x = −12.
(5) (−3) − (−8) =
(a) −11 (b) 5 (c) 11 (d) −5
Correct! (−3) − (−8) = −3 + 8 = 5.
(6) Which of these is the largest?
(a) −2 (b) 0 (c) 3 (d) −5
Correct! 3 is the largest among −2, 0, 3, and −5.
(7) The opposite of a rise of 20 m is:
(a) 20 m (b) −20 m (c) 0 m (d) 200 m
Correct! The opposite of a rise of 20 m is a fall of 20 m (−20 m).
(8) (−7) + 12 =
(a) −19 (b) 5 (c) −5 (d) 19
Correct! (−7) + 12 = 5.
(9) −25 − (−30) =
(a) 55 (b) −55 (c) 5 (d) −5
Correct! −25 − (−30) = −25 + 30 = 5.
(10) The additive inverse of −100 is:
(a) 100 (b) −100 (c) 0 (d) 1
Correct! The additive inverse of −100 is 100.
Complex Integer Operations True or False
Determine whether these statements are True or False:
Integers - Hard Quiz
🎉 Outstanding Mastery! Advanced Integer Excellence Achieved:
You have successfully conquered the "Integers (Hard)" worksheet and mastered:
(1) Complex Multi-step Operations: Solving challenging problems with multiple addition and subtraction steps
(2) Advanced Real-world Applications: Tackling sophisticated scenarios involving submarines, mountaineers, elevators, and temperature changes
(3) Negative Variable Understanding: Working with expressions like −x = 12 and solving for unknown values
(4) Large Number Computations: Confidently handling integers with absolute values over 100
(5) Sequential Problem Solving: Managing problems with multiple sequential changes (dive, rise, descend, etc.)
(6) Comparative Analysis: Ordering integers and identifying largest/smallest values across positive and negative ranges
(7) Floor and Elevation Concepts: Understanding below-ground levels and their integer representations
(8) Temperature Change Analysis: Tracking complex temperature variations over multiple time periods
(9) Advanced Number Line Applications: Using number lines for complex multi-step operations
(10) Strategic Problem Decomposition: Breaking down complex word problems into manageable calculation steps
(11) Sign Pattern Recognition: Identifying and applying patterns in operations with multiple negative numbers
(12) Contextual Integer Interpretation: Understanding when answers represent above/below references, gains/losses, etc.
(13) Advanced Verification Skills: Checking complex calculations using multiple methods
(14) Mathematical Modeling: Representing real-world situations with appropriate integer expressions
(15) Computational Fluency: Achieving speed and accuracy with challenging integer calculations
(16) Problem-solving Confidence: Approaching complex integer problems with systematic strategies
Exceptional achievement! You've mastered advanced integer operations with sophisticated mathematical reasoning!