How many practice questions are available for Integers?

SparkEd Math offers 60+ practice questions for Integers across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Integers content free on SparkEd Math?

Yes! All Integers content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Integers differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Integers problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Integers content aligned with the Olympiad syllabus?

Yes, all Integers questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 6. The content follows the official curriculum structure and exam pattern.

Integers — Class 6 Olympiad (2025-26)

About Integers — Class 6 Olympiad

Work with positive and negative integers, understand absolute value, and solve challenging integer arithmetic puzzles. This topic is part of the Olympiad Class 6 mathematics syllabus (chapter: Module 4). On this page you can practice 59 questions across three difficulty levels — 20 easy, 20 medium, and 19 hard — each with a visual step-by-step solution, plus a timed 34-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Integers — solved examples for Class 6 Olympiad

Example 1easy

A submarine is at a depth of 250 metres below sea level. It ascends 120 metres, then descends 180 metres. Finally, it ascends another 50 metres. What is the final depth of the submarine relative to sea level?

A)160 metres below sea level
B)260 metres below sea level
C)200 metres below sea level
D)210 metres below sea level

Step-by-step solution

Initial depth is 250 metres below sea level, so we represent it as -250 m.
Ascends 120 metres: -250 + 120 = -130 m.
Descends 180 metres: -130 - 180 = -310 m.
Ascends another 50 metres: -310 + 50 = -260 m. So, the final depth is 260 metres below sea level.

Answer: 260 metres below sea level

Example 2medium

An integer 'x' satisfies the condition |x - 5| < 3. How many possible integer values can 'x' take?

Step-by-step solution

The inequality |x - 5| < 3 implies that -3 < x - 5 < 3.
Add 5 to all parts of the inequality to isolate 'x': -3 + 5 < x - 5 + 5 < 3 + 5.
This simplifies to 2 < x < 8.
The integers satisfying this condition are 3, 4, 5, 6, 7. Counting these values, there are 5 possible integers.

Answer: 5

Example 3hard

Given three distinct integers P, Q, and R. We know that |P| = 5, |Q| = 7, and |R| = 3. If P is a negative integer, Q is a positive integer, and R is a negative integer, what is the value of P + Q - R?

A)A) -5
B)B) 9
C)C) -1
D)D) 5

Step-by-step solution

From |P| = 5 and P is negative, we get P = -5.
From |Q| = 7 and Q is positive, we get Q = 7.
From |R| = 3 and R is negative, we get R = -3.
Now, substitute these values into the expression: P + Q - R = (-5) + 7 - (-3) = -5 + 7 + 3 = 2 + 3 = 5.

Answer: D) 5

Practice questions on Integers

Q1.easy
If 'a' is an integer such that |a| < 5 and a ≠ 0, how many possible values can 'a' take?
1. A)4
2. B)8
3. C)9
4. D)10
Show answer
Answer: 8
Hint: The absolute value |a| represents the distance of 'a' from zero on the number line. Remember that 'a' cannot be zero.
Q2.easy
Consider the sequence: 10, 7, 4, 1, -2, ... What is the 8th term in this sequence?
1. A)-8
2. B)-11
3. C)-14
4. D)-17
Show answer
Answer: -11
Hint: Observe the pattern of change between consecutive terms to find the common difference.
Q3.easy
If 'p' is the smallest integer greater than -15, and 'q' is the largest integer less than -8, what is the value of p - q?
1. A)-6
2. B)6
3. C)7
4. D)-7
Show answer
Answer: 6
Hint: Carefully identify 'p' and 'q' by thinking about their positions on the number line.
Q4.medium
Consider the expression: 12 - [(-8) + 5 × (-2)] ÷ (-3). What is its value?
1. A)18
2. B)12
3. C)8
4. D)6
Show answer
Answer: 6
Hint: Follow the order of operations (BODMAS/PEMDAS) carefully, paying attention to signs of integers.
Q5.medium
A submarine is at 350 meters below sea level. It ascends 120 meters, then descends 80 meters. Finally, it ascends another 200 meters. What is its final position relative to sea level?
1. A)110 m below sea level
2. B)10 m below sea level
3. C)10 m above sea level
4. D)110 m above sea level
Show answer
Answer: 110 m below sea level
Hint: Represent 'below sea level' with negative integers and 'ascends' with positive changes, 'descends' with negative changes.
Q6.medium
Observe the pattern: -10, -7, -2, 5, ___, 23. What is the missing integer?
1. A)12
2. B)14
3. C)16
4. D)18
Show answer
Answer: 14
Hint: Calculate the difference between consecutive terms to find the rule of the sequence. The differences might follow a pattern themselves.
Q7.hard
Consider a product 'P' of 15 non-zero integers. If exactly 7 of these integers are negative and the rest are positive, what is the sign of P? Also, if 'S' is the sum of these 15 integers, can we determine the sign of S?
1. A)A) P is positive, S is positive
2. B)B) P is negative, S is negative
3. C)C) P is negative, S cannot be determined
4. D)D) P is positive, S cannot be determined
Show answer
Answer: C) P is negative, S cannot be determined
Hint: Recall the rules for multiplying integers with different signs. For the sum, consider various combinations of magnitudes for positive and negative numbers.
Q8.hard
Three distinct integers A, B, and C have a sum of -10. The sum of A and B is -3. The sum of B and C is -8. What is the value of A - C?
1. A)A) 5
2. B)B) -1
3. C)C) 1
4. D)D) -5
Show answer
Answer: C) 1
Hint: Use the given sums to find the individual values of A, B, and C, or cleverly manipulate the equations to find A-C directly.
Q9.hard
Which of the following expressions has the largest value?
1. A)A) -|-5| - |-3|
2. B)B) -(-5) + |-3|
3. C)C) |5 - 3| - |-5|
4. D)D) -|(-5) × 3| + |5|
Show answer
Answer: B) -(-5) + |-3|
Hint: Carefully evaluate each expression step-by-step, paying close attention to absolute values and signs before performing arithmetic operations.

These are 9 of the 59 questions available for Integers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.