REMEDIAL Worksheet
Class:- VIII Subject: Maths
Competencies
Knowledge of Concepts
Understanding the Concepts
Ability to compute
Problem Solving
Term 2 2024-2025
Chapters
Algebraic Expressions and Identities
Mensuration
Exponents and Powers
Direct and Inverse Proportions
Factorisation
Introduction to Graphs
From Term 1
Linear equations in one variable
Squares and square roots.
Algebraic Expressions and Identities
Mensuration
Direct and Inverse Proportions
Factorisation
Introduction to Graphs
Linear equations in one variable
Squares and square roots.
Exponents and Powers
Remedial class Worksheet
Class: VIII Subject: Maths
NAME: _____________ Algebraic Expressions and Identities DATE: _____________
Competency : Understanding Terms, Factors, and Coefficients
1. Identify the terms, factors, and coefficients in each of the following expressions:
7x + 3
5xy - 4z
12a²b
9 - 4x + 3y
2. Classify the following as monomials, binomials, or polynomials:
8
3x + 4
5a² - 2a + 7
9y
3. Identify the type of algebraic expression:
4x² - 3x + 7
6y - 5
3a³
2x + 3y + 5z
4. Write examples of a monomial, binomial, and polynomial based on your understanding.
5. Add the following expressions:
(3x + 4) + (5x - 2)
(2a² + 3a) + (4a² - a)
(7x + 2y) + (3x - 5y)
6. Subtract the following expressions:
(8x - 3) - (5x + 2)
(6a² + 4a) - (2a² - 3a)
(9y - 4z) - (2y + z)
7. Multiply the following monomials:
(3x)(4x)
(5a)(-2a)
(-7y)(2y²)
8. Multiply the following binomials:
(x + 3)(x - 2)
(2a + 5)(a - 3)
(y + 4)(y + 1)
9. Multiply the following polynomial with a monomial:
(3x² + 5x - 2)(2x)
(4y - y² + 6)(3y)
10. Word Problems:
A rectangle’s length is represented by 2x + 3 and its width by x - 2 . Write an expression for the perimeter of the rectangle.
If a box contains pples and another box contains x - 3 apples, write an expression for the total number of apples.
The area of a square is represented by x². Write an expression for the area if each side of the square is increased by 3 units.
Riya has 2x pencils, and her friend has x + 4 pencils. Write an expression to show how many pencils they have together.
Remember:
Combine like terms to simplify algebraic expressions.
Use the distributive property to multiply algebraic expressions.
Follow the order of operations (BODMAS) when evaluating expressions.
Remedial class Worksheet MLL
Class: VIII Subject: Maths
NAME: _____________ MENSURATION DATE: _____________
Competency : Understanding MENSURATION
1. A rectangle has a length of 15 cm and a breadth of 10cm. Find its Perimeter & Area:
2. A square has a side length of 8cm. Calculate Perimeter & Area:
3. A circle has a radius of 7 cm. Find its Circumference & Area.
Fill in the blanks
1. Perimeter of a rectangle =
2. Area of a rectangle =
3. Perimeter of a square =
4. Area of a square =
5. Circumference of a circle =
6. Area of a circle =
7. Total Surface area of a cuboid =
8. Lateral Surface area of a cuboid =
9. Volume of a cuboid =
10. Total Surface area of a cube =
11. Lateral Surface area of a cube =
12. Volume of a cube =
13. Total Surface area of a cylinder =
14. Lateral Surface area of a cylinder =
15. Volume of a cylinder =
16. Area of Trapezium =
17. Area of Rhombus =
18. Area of Quadrilateral =
19. Area of Triangle =
20. Area of Parallelogram =
Solve word Problems
1. Find the area and perimeter of a rectangular garden that is 10 m long and 5 m wide.
2. A square park has a side length of 15 m. Calculate its perimeter and area.
3. The radius of a circular pond is 7 m. Find the area and circumference of the pond (use ╧А ≈ 3.14).
4. A cuboid water tank measures 8 m in length, 4 m in width, and 3 m in height. Find its surface area and volume.
5. A floor is to be tiled with square tiles, each having a side length of 0.5 m. If the floor has an area of 50 m², find how many tiles are needed.
6. A cylindrical water tank has a diameter of 2 m and a height of 3 m. Calculate its volume (use ╧А ≈ 3.14).
7.If a cube has a volume of 64 cm³, find the length of one side.
8. A rectangular plot of land has a length of 12 m and width of 10 m. If it is to be fenced, calculate the cost of fencing at a rate of ₹50 per metre.
9. Convert 2500 cm² to m².
10. A tank holds 500 litres of water. If 1 litre = 1000 cm³, find the volume in cubic metres.
11. Convert 3.5 m² to cm².
12. A cuboid has dimensions l = 6cm, w = 4 cm, and h = 3cm. Calculate its Surface Area & Volume.
13. A cylinder has a radius r = 5cm and height h = 10cm. Find its Surface Area & Volume.
14. A cube has a side length of s = 4cm. Calculate its Surface Area & Volume.
15. A swimming pool is in the shape of a cuboid with dimensions 10 m, 5m, and 2 m.
Calculate Surface Area & Volume.
16. Calculate the area and circumference of a circle with a radius of 12cm.
17. Find the surface area and volume of a cylinder with a radius of 6cm and a height of 15cm.
Remedial class Worksheet MLL
Class: VIII Subject: Maths
NAME: _____________ Direct and Inverse Proportions DATE: _____________
Competency : Understanding Direct and Inverse Proportions
1.Fill in the blanks:
In direct proportion, when one quantity increases, the other quantity _______.
In inverse proportion, when one quantity increases, the other quantity _______.
The formula for direct proportion is y=kx, where k is the _______.
The formula for inverse proportion is xy=k, where k is the _______.
2. Identify the Proportion:
If 5 kg of rice costs ₹100, then 10 kg will cost ₹200. This is an example of (Direct/Inverse) proportion.
If 10 workers can complete a task in 15 days, then 5 workers will complete it in 30 days. This is an example of (Direct/Inverse) proportion.
3. Direct Proportion Problems:
If 7 notebooks cost ₹84, find the cost of 5 notebooks.
If a car travels 120 km in 2 hours, how far will it travel in 5 hours at the same speed?
A recipe calls for 4 cups of flour to bake 24 cookies. How many cups of flour are needed to bake 60 cookies?
4. Inverse Proportion Problems:
12 workers can finish a job in 8 days. How many days will it take 6 workers to finish the same job?
A pipe can fill a tank in 4 hours. If the rate of flow is halved, how long will it take to fill the tank?
A car covers a certain distance in 6 hours at a speed of 60 km/h. If the speed is increased to 90 km/h, how much time will it take to cover the same distance?
5. Mixed Questions:
A group of 15 students collected ₹450 for a charity. If there are 20 students in a group, how much will they collect, assuming the amount per student remains the same?
If 8 machines can produce 400 items in a day, how many items will 5 machines produce in the same time?
6. Solve Word Problems
A man earns ₹3000 for 5 days of work. How much will he earn in 8 days if his earnings are in direct proportion to the number of days worked?
If 16 bags of cement are required to build a wall 4 m high, how many bags will be needed to build a wall 6 m high, assuming direct proportion?
A car rental charges ₹1500 for a 100 km journey. How much would it charge for a 250 km journey?
A school team of 20 members can prepare for a competition in 15 days. If 5 more members join, how many days would it take to prepare, assuming work completion is inverse proportion to the number of members?
Remember:
In direct proportion, as one quantity increases, the other also increases proportionally.
In inverse proportion, as one quantity increases, the other decreases proportionally.
Use the unitary method to solve problems involving direct and inverse proportion.
Teacher's Signature
Remedial class Worksheet MLL
Class: VIII Subject: Maths
NAME: _____________ Factorisation DATE: _____________
Competency : Understanding Factorisation
Fill in the blanks
1. Factorising an algebraic expression means expressing it as the ________ of its factors.
2. The factors of an expression ) are ________ and ________.
3. The common factor of ) and ) is ___________.
4. The factorised form of ) is _________.
5. Factor out the common term:
5x+10 =
3x² + 6x =
6. Factorise using the distributive property:
)
)
7. Factorise the expressions by grouping:
)
)
8. Factorise using the difference of squares:
)
)
9. Factorise using perfect square identities:
)
)
10. Factorise using the middle term splitting method:
)
)
11. Factorise and simplify the expression:
)
12. If the area of a rectangle is given by ), find its possible dimensions by factorising the expression.
13. Factorise ) by identifying it as a quadratic expression.
Remedial class Worksheet MLL
Class: VIII Subject: Maths
NAME: _____________ Introduction to Graphs DATE: _____________
Competency : Understanding Introduction to Graphs
1. Fill in the blanks
A _______ graph uses rectangular bars to represent data.
A _______ graph shows the relationship between two variables using points connected by line segments.
The _______ chart is a circular chart divided into sectors to show proportions.
The _______ plane is a two-dimensional plane formed by the intersection of the x-axis and y-axis.
2. Identify the type of graph used in each situation:
A company wants to show the percentage of sales from different products.
A school records temperature changes every hour throughout the day.
A survey records the number of students who prefer different types of sports.
3. Answer True or False:
A bar graph can display both positive and negative values.
A line graph is typically used to represent continuous data.
Pie charts are useful for showing trends over time.
4.Plot the following points on a graph paper and label them:
A(2,3)A(2, 3)A(2,3)
B(−4,1)B(-4, 1)B(−4,1)
C(0,−2)C(0, -2)C(0,−2)
D(3,−3)D(3, -3)D(3,−3)
Identify the quadrant where each point lies.
Fill in the blanks:
The point (0, 0) is called the _______.
Points with positive x and y coordinates lie in the _______ quadrant.
Points with a positive x-coordinate and a negative y-coordinate lie in the _______ quadrant.
5. Bar Graph Interpretation:
A bar graph shows the number of books read by four students in a month:
John: 5 books
Sarah: 8 books
Riya: 6 books
Aman: 7 books
Questions:
Who read the most books?
How many books did Sarah and Aman read together?
How many more books did Sarah read than John?
Line Graph Interpretation:
A line graph shows the temperature changes throughout the day at a certain location:
6 AM: 15°C
9 AM: 18°C
12 PM: 25°C
3 PM: 28°C
6 PM: 22°C
Questions:
What was the highest temperature recorded?
Between which two times was the greatest increase in temperature observed?
What was the temperature drop from 3 PM to 6 PM?
Pie Chart Interpretation:
A pie chart shows the distribution of time spent on various activities in a day:
Sleeping: 8 hours
Studying: 6 hours
Playing: 2 hours
Eating: 2 hours
Other Activities: 6 hours
Questions:
What fraction of the day is spent studying?
What percentage of the day is spent sleeping?
How much more time is spent on studying than playing?
6. A school principal wants to track the performance of students over different subjects. Which type of graph would be most appropriate to show each student's scores in multiple subjects?
7. A company wants to track its monthly revenue throughout the year. Which type of graph would best represent the data to show trends over time?
8. A teacher wants to compare the number of students participating in different school clubs. Which type of graph would best suit this purpose?
Remedial class Worksheet MLL
Class: VIII Subject: Maths
NAME: _____________ Linear equations in one variable DATE: _____________
Competency : Understanding Linear equations in one variable
Fill in the blanks
1. A linear equation in one variable has the general form _______ where is the variable.
2. The solution to a linear equation is the value of the _______ that makes the equation true.
3. In the equation , the coefficient of is _______.
4. In a linear equation, the highest power of the variable is _______.
5. Solve for :
6. Solve the following equations:
7. Solving Word Problems Using Linear Equations
i. A car rental company charges a fixed amount of ₹100 plus ₹10 per kilometre travelled. If a person paid ₹250 for a ride, how many kilometres did they travel? (Form and solve a linear equation)
ii. The sum of three consecutive numbers is 72. Find the numbers.
iii. A piece of rope is 50 metres long. It is cut into two pieces such that one piece is 10 metres longer than the other. Find the lengths of the two pieces.
iv. The perimeter of a rectangle is 36 cm. The length is 4 cm more than the width. Find the dimensions of the rectangle.
v. A number increased by 7 equals 15.
vi. Twice a number is equal to 24.
vii. A number divided by 5 gives 9.
viii . The difference between a number and 6 is 13.
ix .The sum of a number and 12 is equal to 20. Find the number.
x. Raju's age is 5 years less than twice his sister's age. If his sister’s age is , write an equation for Raju's age.
xi.A pen costs ₹5 more than a pencil. If the pencil costs rupees, write an equation for the cost of the pen.
Remedial class Worksheet
Class: VIII Subject: Maths
NAME: _____________ Squares and Square Roots DATE: _____________
Competency : Understanding Squares and Square Roots
I Fill in the blanks
1. The square of 6 is _______.
2. The square of 12 is _______.
3. The square root of 49 is _______.
4. A number multiplied by itself gives the _______ of the number.
5. The square of an odd number is always _______ (odd/even).
II. Identifying Perfect Squares (True or False)
1. 64 is a perfect square.
2. 50 is a perfect square.
3. The square of 9 is 81.
4. The square root of 25 is 6.
5. Every positive number has two square roots.
III. Calculate the squares:
IV. Find the square roots (by prime factorization or direct calculation):
V. Estimate the square roots of the following numbers (find the nearest whole number):
VI . Fill in the blanks:
The square root of a number between 64 and 81 is between _______ and _______.
The square root of a number between 100 and 121 is between _______ and _______.
VII. Applying Squares and Square Roots in Word Problems
1. A square-shaped garden has an area of 144 square metres. Find the length of one side of the garden.
2. The area of a square is 196 square metres. Calculate the length of one side of the square.
3. A student’s desk has a square top with an area of 81 square centimetres. What is the length of one side of the desk?
4. If the square of a number is 169, what is the number?
5. The area of a square park is 225 square metres. Find the perimeter of the park.
Remedial class Worksheet
Class: VIII Subject: Maths
NAME: _____________ Exponents and Powers DATE: _____________
Competency : Understanding Exponents and Powers
I. Fill in the Blanks
1. In the expression, the base is _______ and the exponent is _______.
2. is equal to _______.
3. A negative exponent can be written as _______.
4. The value of is _______.
5. The expression is equal to _______.
6. What is the base and the exponent in the expression 2³?
7. What is the value of 10^0?
II. Laws of Exponents (True or False)
1.
2.
3.
4.
5. is a valid law of exponents.
6. Simplify the following:
a) 2^3 × 2^4
b) 3^5 ÷ 3^2
c) (2³)²
7.Write the following in exponential form:
a) 2 × 2 × 2 × 2 × 2
b) 3 × 3 × 3 × 5 × 5
III. Simplify the following:
IV. Simplify using negative exponents:
V. Write the following in scientific notation:
50,000
0.005
123,000,000
0.00042
VI. Convert the following from scientific notation to standard form:
VII. Application Problems
A cell phone battery has a capacity of mAh. Write this capacity in standard form.
The mass of a dust particle is approximately grams. Write this mass in standard form.
The speed of light is approximately metres per second. How would you express this speed in standard form?
If a bacterium measures about metres in length, what is its length in standard form?
If a bacteria doubles every hour, how many bacteria will there be after 5 hours if there were 2 bacteria initially?
A computer can perform a calculation in 10^-6 seconds. How many calculations can it perform in 1 second?
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