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 7. The content follows the official curriculum structure and exam pattern.

Integers — Class 7 Olympiad (2025-26)

About Integers — Class 7 Olympiad

Perform operations on integers, apply properties of addition and multiplication, and solve integer-based Olympiad puzzles. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 1). 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 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Integers — solved examples for Class 7 Olympiad

Example 1easy

An integer P is 7 units to the left of -3 on the number line. Another integer Q is 5 units to the right of P. What is the value of Q?

A)-15
B)-1
C)-5
D)-10

Step-by-step solution

P is 7 units to the left of -3. This means P = -3 - 7.
Calculating P: P = -10.
Q is 5 units to the right of P. This means Q = P + 5.
Calculating Q: Q = -10 + 5 = -5.

Answer: -5

Example 2medium

Find the value of P = 1 - 2 + 3 - 4 + 5 - 6 + ... + 99 - 100 + 101.

A)-50
B)51
C)-51
D)50

Step-by-step solution

Group the terms in pairs: (1 - 2) + (3 - 4) + (5 - 6) + ... + (99 - 100) + 101.
Each pair sums to -1: (-1) + (-1) + (-1) + ... + (-1) + 101.
There are (100 / 2) = 50 such pairs. So, the sum of these pairs is 50 × (-1) = -50.
Add the last term: -50 + 101 = 51.

Answer: 51

Example 3hard

Let P = (1 - 100) × (2 - 100) × (3 - 100) × ... × (200 - 100). What is the value of P?

A)A) A very large negative number
B)B) 0
C)C) -100!
D)D) 100!

Step-by-step solution

The product P consists of terms in the form (n - 100) where n ranges from 1 to 200.
As 'n' goes from 1 to 200, one of the terms will be (100 - 100).
Since (100 - 100) = 0, and any number multiplied by zero is zero, the entire product P will be 0.
$P = (1-100) × ... × (100-100) × ... × (200-100) = ... × 0 × ... = 0$

Answer: B) 0

Practice questions on Integers

Q1.easy
If 'm' and 'n' are two distinct integers such that |m| = |n|, then which of the following statements must be true?
1. A)m + n = 0
2. B)m × n > 0
3. C)m - n = 0
4. D)m is positive and n is negative
Show answer
Answer: m + n = 0
Hint: If two distinct integers have the same absolute value, what does that imply about their relationship?
Q2.easy
What is the sum of all integers between -10 and 10 (exclusive)?
1. A)-10
2. B)0
3. C)10
4. D)20
Show answer
Answer: 0
Hint: Look for pairs of numbers that add up to zero within the given range.
Q3.easy
A submarine is at 250 metres below sea level. It then ascends 75 metres and later descends 120 metres. What is its final position relative to sea level?
1. A)195 m
2. B)-195 m
3. C)295 m
4. D)-295 m
Show answer
Answer: -295 m
Hint: Represent positions below sea level with negative integers and movements upwards with positive integers.
Q4.medium
Evaluate: ((-17) × 98) + ((-17) × 2) - ((-17) × 100).
1. A)0
2. B)-1700
3. C)17
4. D)-17
Show answer
Answer: 0
Hint: Look for a common factor in all three terms and apply the distributive property of multiplication over addition/subtraction.
Q5.medium
A submarine starts at 250 meters below sea level. It then ascends 120 meters, and later descends 180 meters. If the sea level is represented by 0, what is the final depth of the submarine?
1. A)-310 meters
2. B)-290 meters
3. C)-190 meters
4. D)-350 meters
Show answer
Answer: -310 meters
Hint: Represent 'below sea level' with negative integers and 'ascends' as addition, 'descends' as subtraction.
Q6.medium
How many integers 'x' satisfy the condition |x - 5| < 3?
1. A)5
2. B)6
3. C)7
4. D)8
Show answer
Answer: 5
Hint: The condition |A| < B means -B < A < B. Convert the absolute value inequality into a compound inequality.
Q7.hard
If x is an integer, what is the smallest possible value of |x - 5| + |x + 3|?
1. A)A) 0
2. B)B) 2
3. C)C) 8
4. D)D) 10
Show answer
Answer: C) 8
Hint: Think of |a - b| as the distance between 'a' and 'b' on the number line. The expression asks for the sum of distances from 'x' to 5 and from 'x' to -3.
Q8.hard
A sequence of integers is defined by a₁ = 1, and aₙ = aₙ₋₁ - (-1)ⁿ for n > 1. What is the value of a₁₀₀?
1. A)A) -1
2. B)B) 0
3. C)C) 1
4. D)D) 100
Show answer
Answer: B) 0
Hint: Calculate the first few terms of the sequence to identify a repeating pattern or a trend.
Q9.hard
Calculate the value of 17 × (-23) + 17 × (-12) - 17 × 5 - 17 × (-10).
1. A)A) -510
2. B)B) -340
3. C)C) 170
4. D)D) 510
Show answer
Answer: A) -510
Hint: Look for common factors in the terms and apply the distributive property to simplify the calculation.

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.