Course Area
- 1. Square & Square Root
- Square root by division method
- Square root by prime factorization
- Application-based questions
- 2. Cube & Cube Root
- Application-based questions
- 3. H.C.F and L.C.M
- Division and prime factorization
- Application-based questions
- 4. Integers
- Add, subtract, multiply, divide using number line
- Application-based questions
Worksheet Specification Grid
| Bloom's Level | No. of Questions | Marks Distribution | Total Marks |
|---|---|---|---|
| K Knowledge | 2 | 1 + 1 | 2 |
| U Understanding | 3 | 1 + 1 + 2 | 4 |
| A Application | 3 | 2 + 2 + 1 | 5 |
| HA Higher Ability | 2 | 1 + 2 | 3 |
| Total | 10 | — | 14 |
Bloom's Tag Legend:
K Knowledge
U Understanding
A Application
HA Higher Ability
SET 1
Square/Cube Roots · H.C.F / L.C.M · Integers
14 Marks
1
Bindhu studies in class-7. She made a set of numbers as {144, 169, 121, 1728, 13689}.
a.
Select the square of 11 from the given set of numbers. 1K
b.
Find the square root of 13,689 by the division method. 2U
c.
A cube-shaped water tank can hold 1728 m3 of water in it. Find the measurement of its sides. 2A
2
a.
Write the full form of L.C.M. 1K
b.
Find the L.C.M of 10 and 15. 1U
c.
Sunaulo Bihani aims to distribute 108 story books, 96 poem books, and 120 novels to the children of Bhimfedi Rural Municipality. Find the maximum number of children to receive the books in equal numbers. 2A
d.
Find how many story books, poem books, and novels each child will receive. 1A
3
a.
Simplify: \((+10) \div (-5) \times (-2)\). 1U
b.
The rule for a quiz competition was: (+5) for a correct answer, (−2) for an incorrect answer, 0 for no answer.
Who won the competition? 2HA
| Group | Right Answers | Wrong Answers | No Answer |
|---|---|---|---|
| A | 8 | 2 | 2 |
| B | 9 | 3 | 0 |
| C | 8 | 3 | 1 |
c.
If \(a = (-1),\ b = (+2),\ c = (-3)\), is \(b + ac\) greater than zero? Justify. 1HA
SET 2
Perfect Square & Cube · H.C.F / L.C.M · Integers
14 Marks
1
a.
There is a number between 61 and 70 which is both the square of a number and the cube of another number. Identify that number. 1K
b.
Find the cube root of 216. 1U
c.
There are 27 students in a class. Each student collected as much money as there are students in the class for a donation. How much total money was collected? 1A
d.
Sita said that if 65 is added to 7504, the resulting number will be a perfect square. Is she correct? Check by calculation. 2HA
2
a.
Write the full form of H.C.F. 1K
b.
Find the H.C.F of 108, 120, and 144 by the division method. 2U
c.
Three different bells ring at regular intervals: the first bell rings every 20 minutes, the second every 30 minutes, and the third every 45 minutes. If all three bells ring together at 10:00 AM, at exactly what time will they all ring together again? 2A
3
a.
Add \((+2) - (-1)\) by using a number line. 1U
b.
At 5:00 AM, the winter temperature in a mountainous region was recorded at −3°C. By 1:00 PM, the sun had caused the temperature to rise by 9°C. However, a cold wind moved in during the late afternoon, causing the temperature to drop by 11°C by 8:00 PM. What was the final temperature at 8:00 PM? 2A
c.
If \(a = (-1),\ b = (+2),\ c = (+3)\), is \(a^2 + b^2 - abc\) greater than 0? Justify. 1HA
SET 3
Perfect Square & Cube · G.C.F / L.C.M · Integers
14 Marks
1
Consider the following set of numbers: {64, 125, 400, 1024, 3375}.
a.
Identify the number which is both a perfect square and a perfect cube. 1K
b.
Find the square root of 1024 by the prime factorization method. 2U
c.
A square garden has an area of 400 m2. Find the length of its boundary (perimeter). 2A
2
a.
State the full form of G.C.F. 1K
b.
Find the L.C.M of 12, 15, and 20. 1U
c.
A school wants to distribute 60 apples, 84 bananas, and 108 oranges equally among students without leaving any fruit. Find the maximum number of students who can receive the fruits. 2A
d.
How many apples, bananas, and oranges will each student get? 1A
3
a.
Simplify using a number line: \((-3) + (+5)\). 1U
b.
In a test, (+4) marks are given for every correct answer and (−1) mark for every incorrect answer. Rohit tried all questions and scored 20 marks, though he got 8 correct answers. How many incorrect answers did he give? 2HA
c.
If \(x = (-2),\ y = (+4),\ z = (-1)\), find the value of \(x^2 - yz\). 1HA
SET 4
Perfect Cube · H.C.F / L.C.M · Integers
14 Marks
1
a.
Which is the smallest perfect square number of three digits? 1K
b.
Find the cube root of 3375. 1U
c.
A class of 35 students decided to collect funds for a picnic. Each student gave as many rupees as the number of students in the class. How much total money was collected? 1A
d.
Ram says that if we multiply 108 by 2, it becomes a perfect cube. Is he right? Justify. 2HA
2
a.
Write the full form of L.C.M. 1K
b.
Find the H.C.F of 72 and 90 by the prime factorization method. 2U
c.
Two electric lights are turned on at the same time. One blinks every 15 seconds and the other blinks every 24 seconds. After how many seconds will they blink together again? 2A
3
a.
Simplify: \((-15) \div (+3) + (-2)\). 1U
b.
A submarine is 800 feet below sea level. If it moves up 250 feet, what is its new position? Show this using an integer. 2A
c.
If \(p = (+2),\ q = (-3),\ r = (-4)\), is \(p \times q \times r\) a positive integer? Justify. 1HA
SET 5
Cube Root · H.C.F · Integers
14 Marks
1
Given the set of numbers: {27, 81, 225, 512, 4096}.
a.
Select the cube of 8 from the given set. 1K
b.
Find the square root of 225 by the division method. 2U
c.
A cube-shaped box has a volume of 512 cm3. Find the length of its side. 2A
2
a.
Is 1 considered a prime or composite number? 1K
b.
Find the H.C.F of 45 and 60. 1U
c.
In a library, there are 144 English books, 192 Science books, and 240 Math books. The librarian wants to arrange them in equal groups so that each group has books of the same subject. Find the maximum number of books in each group. 2A
d.
How many total groups of books will be formed? 1A
3
a.
Simplify using a number line: \((+4) - (+6)\). 1U
b.
A lift goes down into a tunnel at a rate of 6 meters per minute. If it starts from 10 meters above the ground, how long will it take to reach −350 meters? 2HA
c.
Given \(m = (-1)\) and \(n = (-2)\), calculate \(m^3 + n^2\). Is the result positive or negative? 1HA
SET 6
Perfect Square · L.C.M · Integer Temperature
14 Marks
1
a.
Write the cube of 5. 1K
b.
Find the square root of 576 by prime factorization. 1U
c.
400 plants are to be planted in a garden so that each row has as many plants as the total number of rows. Find the number of rows and the number of plants in each row. 1A
d.
A student multiplied 432 by a number to make it a perfect square. What is the smallest positive number he could have used? Justify your answer. 2HA
2
a.
What is the H.C.F of two co-prime numbers? 1K
b.
Find the L.C.M of 24, 36, and 40 by the division method. 2U
c.
Traffic lights at three different road crossings change after every 48 seconds, 72 seconds, and 108 seconds. If they all change at the same time at 8:00 AM, at what time will they change together again? 2A
3
a.
Simplify: \((+8) \times (-3) \div (-4)\). 1U
b.
The temperature at 12 noon was 10°C above zero. If it goes down by 2°C every hour until midnight, at what time would the temperature be −8°C? 2A
c.
If \(a = (+3),\ b = (-4),\ c = (-1)\), prove that \(a(b + c) = ab + ac\). 1HA
SET 7
Cube Root · H.C.F / L.C.M · Integers
14 Marks
1
Given numbers: {100, 343, 625, 1000}.
a.
Which of these numbers is a perfect cube but not a perfect square? 1K
b.
Find the cube root of 1000. 2U
c.
The area of a square playground is 625 m2. Find the cost of fencing it at Rs. 20 per metre. 2A
2
a.
Define Least Common Multiple (L.C.M). 1K
b.
Find the H.C.F of 84 and 105. 1U
c.
Three measuring rods are 64 cm, 80 cm, and 96 cm long. Find the shortest length of cloth that can be measured exactly using any of the rods. 2A
d.
Convert that shortest length of cloth into metres. 1A
3
a.
Show the subtraction of \((-4)\) from \((-2)\) on a number line. 1U
b.
A shopkeeper makes a profit of Rs. 5 on every pen sold and a loss of Rs. 2 on every pencil sold. If he sells 40 pens and 60 pencils, what is his total profit or loss? 2HA
c.
If \(x = (-5)\) and \(y = (-2)\), is \((x - y)^2\) equal to \(x^2 - y^2\)? Justify. 1HA
SET 8
Square/Cube Root · L.C.M · Integers
14 Marks
1
a.
What is the square of 12? 1K
b.
Find the square root of 900 by the division method. 1U
c.
A cube-shaped room has a volume of 729 m3. Find the height of the room. 1A
d.
Is 250 a perfect cube? If not, what is the smallest natural number you must divide it by to get a perfect cube? Justify. 2HA
2
a.
Write the H.C.F of 15 and 16. 1K
b.
Find the L.C.M of 30, 45, and 60 by the division method. 2U
c.
A shopkeeper sells candles in packets of 12 and candle stands in packets of 8. If you want to buy an equal number of candles and stands, what is the minimum number of packets of each you need to buy? 2A
3
a.
Simplify: \((-12) \div (-4) - (+2)\). 1U
b.
A plane is flying at a height of 5000 metres above sea level. Right below it, a submarine is floating 1200 metres below sea level. What is the vertical distance between them? 2A
c.
If \(a = (-2),\ b = (+5),\ c = (-3)\), check if \(a + (b + c) = (a + b) + c\). 1HA
SET 9
Cube Pattern · L.C.M · Integers
14 Marks
1
Look at the pattern: {1, 8, 27, 64, 125, …}.
a.
What is the next number in this pattern? 1K
b.
Find the cube root of 64. 2U
c.
The volume of a cube-shaped block of wood is 125 cm3. Find the area of one of its faces. 2A
2
a.
Are the numbers 8 and 9 co-prime? 1K
b.
Find the L.C.M of 14 and 21. 1U
c.
Three boys start walking together from the same spot. Their steps measure 63 cm, 70 cm, and 77 cm. What is the minimum distance each should cover so that all can cover the distance in complete steps? 2A
d.
How many steps will the boy with the 70 cm step take to cover that distance? 1A
3
a.
Add using a number line: \((-5) + (+8)\). 1U
b.
In an exam, 3 marks are given for every correct answer and 1 mark is taken away for every incorrect answer. If Sita scored 30 marks and got 14 correct answers, how many incorrect answers did she give? 2HA
c.
If \(x = (+4)\) and \(y = (-3)\), find the value of \(x^2 - 2xy + y^2\). 1HA
SET 10
Square Root · H.C.F · Integer Profit/Loss
14 Marks
1
a.
Find the square of 15. 1K
b.
Find the square root of 1296 by the division method. 1U
c.
A group of students decided to plant trees. The number of rows of trees was equal to the number of trees in each row. If they planted 1024 trees in total, find the number of rows. 1A
d.
Hari says that 8000 is a perfect cube but not a perfect square. Check if he is right by calculation. 2HA
2
a.
State the full form of H.C.F. 1K
b.
Find the H.C.F of 108, 144, and 180 by prime factorization. 2U
c.
Three bells ring at intervals of 12, 15, and 20 minutes. If they start ringing together at 7:00 AM, at what time will they ring together again? 2A
3
a.
Simplify: \((-20) \div (+5) \times (-3)\). 1U
b.
Over three days, a shopkeeper made a profit of Rs. 400 on the first day, a loss of Rs. 150 on the second day, and a profit of Rs. 200 on the third day. What was his total profit or loss over these three days? 2A
c.
If \(a = (-1)\) and \(b = (-2)\), is \(a^3 + b^3\) greater than \((a + b)^3\)? Justify your answer. 1HA