CLASS 7 MATHS Remedial MLL Worksheet TERM 2

 

            REMEDIAL Worksheet              

Class:- VII    Subject: Maths

Competencies 

•  Knowledge of Concepts

• Understanding the Concepts

• Ability to compute

• Problem Solving

Term 2  2024-2025

Chapters 

• Rational Numbers

• Perimeter and Area

• Algebraic Expressions

• Exponents and Powers

• Symmetry

• Visualising solid shapes

From Term 1

• Fractions and Decimals

• Simple Equations

• Fractions 

• Decimals

• Rational numbers

• Perimeter and area

• Algebraic expressions

• Integers

• Simple Equations

• Integers

• Lines and Angles

• Algebraic expressions

• Exponents & Powers

• Exponents & Powers

              Remedial class Worksheet               

Class: VII    Subject: Maths

NAME: _____________ FRACTIONS DATE: _____________

Competency : Understanding Fractions

1.Identify the Fractions & Write the fraction for each:

1. Three parts shaded out of five parts: 

2. Two shaded parts out of eight parts:  

3. One shaded part out of four parts:   

2. Write whether each of the following is a proper fraction, improper fraction, or mixed fraction.

1. 57 

2. 94 

3. 315 

3. Convert Improper Fractions to Mixed Fractions:

    a) Convert 113​ to a mixed fraction.

    b) Convert 154​ to a mixed fraction.

      c) Convert 206​ to a mixed fraction.

4. Reduce the Fractions to their Simplest Form:

1. 612

2. 824

3. 1421

5. Find three equivalent fractions for each by multiplying both numerator and denominator by 2,3,4.

1. 34

2. 27

3. 49

Competency : Ability to Compute

6. Add the Fractions with Same Denominator:

a) 38 + 28 b) 35 + 15

7. Add the Fractions with different  Denominator:

a) 512 + 42 b) 27 + 514

c) 12 + 14 d) 35 + 23

8. Subtract the Fractions with Same Denominator:

a) 710   210 b) 915  715

9. Subtract the Fractions with different  Denominator:

a) 512  410 b) 67  511

c) 12  14 d) 56  29

e) 56  13 f) 78  34

10. Multiply the following fractions: 

1. 23 x 34 b) 57 x 1415

11. Divide the following fractions: 

    a) 12 ÷  14 b) 35 ÷  23

Competency : Problem Solving

12. Solve the word problems: 

1. A pizza is cut into 8 equal slices. If you eat 3 slices, what fraction of the pizza did you eat?

2. A recipe calls for 1/2 cup of sugar and 1/4 cup of flour. How much more sugar than flour is needed?

3.  A car travels 3/4 of a mile in 1/2 minute. How many miles can it travel in one minute?

4. A piece of ribbon is 56​ m  long. If it is cut into 5 equal pieces, what is the length of each piece?

Remember:

• To add or subtract fractions, they must have a common denominator.

• To multiply fractions, multiply the numerators and denominators separately.

• To divide fractions, invert the second fraction and multiply.

Teacher's Signature

              Remedial class Worksheet  MLL             

Class: VII    Subject: Maths

NAME: _____________ DECIMALS DATE: _____________

Competency : Understanding Decimals

1.Write the place value of the digit '7' in each of the following numbers:

1. 3.47

2. 5.072

3. 0.837

2. Write each of the following in decimal form:

1. Three tenths

2. Seven hundredths

3. Fiftyfour thousandths

3. Convert the following fractions to decimal form:

1. 310

2. 7100

3. 51000

4. Write each of the following decimals as fractions in their simplest form:

1. 0.5

2. 0.25

3. 0.125

5. Use >, <, or = to compare the following pairs:

1. 0.6 ___ 0.56

2. 1.25 ___ 1.3

3. 2.05 ___ 2.5

6. Arrange the following decimals in ascending order:

 0.45, 0.5, 0.405, 0.54

7. Arrange in descending order: 

3.21, 3.1, 3.205, 3.12

Competency : Ability to Compute

8.Add the following decimals: 

a) 2.3 + 1.5

b) 12.34 + 5.67

c) 2.3 + 1.75

d) 4.56 + 3.7

e) 5.005 + 0.15

9. Subtract the following decimals: 

a) 5.6  2.3

b) 10.25  4.75

c) 6.5  2.75

d) 8.3  4.56

e) 10.25  0.5

10.Multiply the following decimals: 

a) 2.5 × 3.2

b) 1.23 × 4.5

c) 0.6 × 0.5

d) 3.25 × 2

e) 1.5 × 0.2

11. Divide the following decimals: 

a) 12.5 ÷ 2.5

b) 25.6 ÷ 0.8

c) 6.4 ÷ 2

d) 3.6 ÷ 1.2

e) 4.8 ÷ 0.8

Competency : Problem Solving

12. Solve the word problems:

1. A book costs ₹125.75. How much will 5 books cost?

2. A person walks 2.5 km in the morning and 3.75 km in the evening. How much distance did he walk in total?

3. A piece of cloth is 10.5 metres long. If 3.5 metres is cut off, how much cloth is left?

4. Rina bought 3.25 metres of cloth and used 1.5 metres to make a dress. How much cloth is left?

5. A car travels 56.4 kilometres in one hour. How much distance will it cover in 2.5 hours?

6. Rahul has 5.5 litres of milk. He gives 2.25 litres to his friend. How much milk does he have left?

Remember:

• Always align the decimal points while adding or subtracting decimals.

• Count the decimal places in the factors to determine the decimal place in the product.

• When dividing by a decimal, shift the decimal point in the divisor and dividend to make the divisor a whole number.

Teacher's Signature

              Remedial class Worksheet  MLL             

Class: VII    Subject: Maths

NAME: _____________ RATIONAL NUMBERS DATE: _____________

Understanding Rational Numbers

1.Write whether each of the following numbers is a rational number:

1. 34                  b) 0                c)  57     d) 80  

(Is this a rational number? Why or why not?)

2. Simplify the following fractions to write them in standard form:

1. 612                  b) 2040                 c)  1525     ​

3.Find two equivalent rational numbers for each:

1. 35                  b) 27                   

4. Use >, <, or = to compare the following pairs:

1. 35    25                  b) 37   57         c)  712   56

5. Arrange the following rational numbers in ascending order:

 38 , 12 , 34 

6. Plot the following rational numbers on a number line:

   

7.  State whether the following rational numbers are to the left or right of zero on the number line:

a)    b)     c)    

Competency : Ability to Compute

8.Add the following rational numbers:

 a) 12 + 14 b)   23 + 16

c)  d) 

9.Subtract the following rational numbers: 

a) 34  12 b)  25  310

 

c)  d)                      e) 

10.Multiply the following rational numbers: 

a) 23 x 34 b)  12 x 45 c)  d)

e)

11.Divide the following rational numbers: 

a) 12 ÷  14 b) 35 ÷ 215

c)  d)

e)

Competency : Problem Solving

12.Solve the word Problems:

1. A piece of cloth is 58 metres long. If 14 metre is cut off, how much cloth is left?

2. A car travels 34 of a kilometre in 12  minute. How many kilometres can it travel in one minute?

3. A tank is 13  full of water. If  16 more water is added, what fraction of the tank is full?

4. Riya owes her friend 56 ​ of a chocolate bar. She decides to repay 13 ​ of the chocolate. How much does she still owe?

5. A tank is 34​ full. If 12​ of its capacity is used, how much water is left in the tank?

6. A recipe calls for 23 cup of sugar, but Ramesh accidentally adds 34 cup. By how much did he exceed the required amount?

Remember:

• To add or subtract rational numbers, they must have a common denominator.

• To multiply rational numbers, multiply the numerators and denominators separately.

• To divide rational numbers, invert the second rational number and multiply.

Teacher's Signature

              Remedial class Worksheet  MLL             

Class: VII    Subject: Maths

NAME: _____________ PERIMETER AND AREA DATE: _____________

Understanding PERIMETER AND AREA

1. Find the perimeter and area of the following shapes:

1. A rectangle with length and width .

2. A square with side length .

3. A circle with radius .

Competency : Ability to Compute

2. Find missing dimensions:

1.  A rectangle has a perimeter of and length . Find its width.

2. A square has a perimeter of . Find the length of each side.

3. Calculate the perimeter of a square with side 5 cm.

4. Find the area of a rectangle with length 8 cm and breadth 4 cm.

5. A square has a perimeter of 20 cm. Find its side length.

6. A rectangle has an area of 36 sq cm. If its length is 9 cm, find its breadth.

Competency : Problem Solving

Solve the word Problems:

3. A garden is in the shape of a rectangle with a length of and a width of . Calculate the area of the garden.

4. A square park has an area of . What is the length of each side?

5. A circular pond has a radius of . Find the circumference and the area of the pond (Use ).

6. Find the area of a shape that consists of a rectangle and a semicircle:

    The rectangle has a length of and a width of .

    The semicircle has a diameter equal to the width of the rectangle.

7. Calculate the perimeter of a shape that combines a square and a semicircle:

    The square has a side length of .

    The semicircle has a diameter equal to the side length of the square.

8. A rectangular garden is 10 m long and 8 m wide. Find its perimeter and area.

9. A square park has a side of 25 m. Find the cost of fencing it at ₹20 per metre.

10. A rectangular room is 5 m long and 4 m wide. How many tiles of size 25 cm × 25 cm are needed to cover the floor?

Remember:

• Rectangle: Perimeter =2(l+b)=2(l+b), Area =l×b

• Square: Perimeter =4×s, Area =s²

• Circle: Perimeter (Circumference) =2πr, Area =πr²

• Triangle (for given base and height): Area =12×b×h

• The perimeter is the distance around a shape.

• The area is the amount of surface enclosed by a shape.

Teacher's Signature

              Remedial class Worksheet  MLL             

Class: VII    Subject: Maths

NAME: _____________ ALGEBRAIC EXPRESSIONS DATE: _____________

Understanding ALGEBRAIC EXPRESSIONS

1. Identify the terms, coefficients, and variables in the following expressions:

   a)

  b) 

   c)

2. State whether each of the following is a term, coefficient, or constant:

1. -

2. b)    

3. c) 

3. Write an algebraic expression for each of the following statements:

•    The sum of times and .

•      subtracted from times .

•    Twice the square of plus .

•      more than the product of and .

4. Translate the following into algebraic expressions:

•      increased by .

•     times minus .

•    The square of plus times .

5.  Evaluate each expression for the given values:

 a)  for and

b) for

c)    for and

d)  for

e)     for

6. Simplify the following expressions by combining like terms:

   a)

b)

c)   

7. Simplify the following by expanding and combining like terms:

1.  

2. b) 

Competency : Ability to Compute

8. Add the following algebraic expressions: 

a) 2x + 3y and 4x - 2y

b) 5a² + 3ab and 2a² - ab

 c)  and

d) and

9. Subtract the following algebraic expressions: 

a) 5x - 2y from 8x + 3y

b) 3a² - 2b² from 5a² + 4b²

c)  from

d)  from

10. Multiply the following algebraic expressions: 

a) 2x(3x + 4)

b) (x + 2)(x - 3)

Competency : Problem Solving

Solve the word Problems:

1. The length of a rectangle is 2x + 3 and its breadth is x - 1. Find its perimeter.

2. The cost of a pen is ₹x and the cost of a notebook is ₹y. What is the total cost of 5 pens and 3 notebooks?

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.

Teacher's Signature

              Remedial class Worksheet  MLL             

Class: VII    Subject: Maths

NAME: _____________ INTEGERS DATE: _____________

Understanding INTEGERS

1. Identify the following numbers as positive or negative integers:

     ( -15 )     ( 23 )     ( -7 )     ( 0 ) (Is zero positive or negative?)

2. Represent the following integers on a number line:

    ( -6, -2, 0, 3, 7 )

3. Write the opposite of each integer:

   a) ( -12 ) b)  ( 8 ) c) ( -5 ) d) ( 0 )

4. Compare the following pairs of integers using >, <, or =:

1.    ( -4 )__ ( -7 ) b) ( 3 ) _____( -3 ) c)    ( -6 ) _____ ( -6 )

5. Arrange the following integers in ascending order:

    ( -3, 4, -1, 0, 2 )

 

Competency : Ability to Compute

6. Add the following integers: 

a) 5 + (-3) b) (-2) + (-4)   c) ( 5 + (-3) d) ( -8 + (-4) e) ( -6 + 7 )

7. Subtract the following integers: 

a) 7 - (-2) b) (-5) - 3   c) ( 7 - (-2) )   d) ( -5 - 3 ) e)  ( -10 - (-5) )

8. Multiply the following integers: 

a) 3 × (-4) b) (-2) × (-5) c) ( -4 x 6 ) d)     ( -3 x -5 ) e)  ( 7 x (-2) 

9. Divide the following integers: 

a) 12 ÷ (-3)

b) (-15) ÷ (-5)

c) ( -20÷ 4 )

d) ( -15 ÷ (-3)    

e)( 9 ÷(-3) )

Competency : Problem Solving

10. Solve the word Problems:

1. The temperature on Monday was 25°C. On Tuesday, it dropped by 5°C. What was the temperature on Tuesday?

2. A submarine was 200 metres below sea level. It ascended 50 metres. What is its new position?

3. A shopkeeper gains ₹10 on each pen sold and loses ₹5 on each pencil sold. If he sells 5 pens and 3 pencils, what is his net profit or loss?

4. The temperature in the city was ( -5° )C in the morning. By noon, it increased by ( 7° )C. What is the temperature at noon?

5.  A submarine is at ( -250 ) metres below sea level. It ascends ( 100 ) metres. What is its new position?

6. Riya owes her friend ( 15 ) dollars. She repays ( 5 ) dollars. How much does she still owe?

Remember:

• To add integers with the same sign, add their absolute values and keep the common sign.

• To add integers with different signs, subtract their absolute values and keep the sign of the larger number.

• To subtract an integer, add its opposite.

• The product of two integers with the same sign is positive, and the product of two integers with different signs is negative.

• The quotient of two integers with the same sign is positive, and the quotient of two integers with different signs is negative.

Teacher's Signature

              Remedial class Worksheet  MLL             

Class: VII    Subject: Maths

NAME: _____________ SIMPLE EQUATIONS DATE: _____________

Understanding SIMPLE EQUATIONS

1. Identify the variables and constants in the following expressions:

1. 5x + 3 b) 4y - 7 

     c) 9 - z d) 2a + 6b 

2. Write an algebraic expression for each of the following statements:

•    Three more than twice a number.

•    Five less than a number y .

•    Seven times a number z .

•    The sum of x  and four.

3. Form an equation for each of the following situations:

•    The sum of a number x  and 5  is 12 .

•    A number y  subtracted from 10  gives 4 .

•    Twice a number z  is equal to 18 .

•    The product of x  and 3  is equal to 21 .

    Competency : Ability to Compute

4. Solve the following equations: 

a) x + 5 = 10 b) 2y - 3 = 7 c) 4z/3 = 8 

d)  x + 7 = 15 e)  y - 4 = 9 f)  3z = 21 

 g) 2x + 3 = 13 h) 5x - 7 = 18 i)    4x = 28 

 

 j) x - 9 = 0 

5. Find the value of the unknown variable in each equation: 

a) 3x + 5 = 14 b) 7y - 2 = 19 c) 5z/2 - 3 = 7

Competency : Problem Solving

6. Solve the word Problems:

1. If you add 7 to a number, you get 15. What is the number?

2. If you subtract 5 from a number and divide the result by 2, you get 4. Find the number.

3. The sum of two consecutive numbers is 25. Find the numbers.

4. Riya’s age is 4  years more than twice her sister’s age. If her sister’s age is 8  years, form an equation and find Riya’s age.

5. The length of a rectangle is 3  times its width. If the width is 5  cm, form an equation and find the length.

6. A number added to 7  gives 20 . Form an equation and find the number.

7. The cost of 5  pencils is 25  rupees. Form an equation and find the cost of one pencil.

Remember:

• To solve an equation, we need to find the value of the unknown variable that makes the equation true.

• Use inverse operations (addition/subtraction, multiplication/division) to isolate the variable.

• Check your solution by substituting it back into the original equation.

[Teacher's Signature]

              Remedial class Worksheet               

Class: VII    Subject: Maths

NAME: _____________ INTEGERS DATE: _____________

Fill up the blanks 

1) Integers which are neither positive nor negative are ……………….. 

2) Predecessor of (–99) is ……………….. 

3) Successor of (–100) is ……………….. 

4) Largest 3 digit negative integer is ……………….. 

5) A negative integer is always …………………… than zero. [greater/smaller] 

6) 1 more than a given number gives its ………………… [successor/predecessor] 

7) 1 less than a given number gives its ………………… [successor/predecessor] 

8) There is no least ………………. integer. 

9) The ………………… negative integer is (–1). 

10) The smallest positive integer is ……………….. 

11) Zero is ……………….. than every positive integer. 

12) Every positive integer is …………………. than every negative integer. 

13) Farther a number from zero on the right, ……………….. is its value. 

14) If ………………. is represented by ‘+’ sign, then loss is represented by ‘-‘ sign. 

15) If ‘going up’ is represented by the ‘+ve’ sign, then …………………. is represented  by the ‘–ve’ sign. 

16) 38 ÷ 0 = ……………… 

17) 0 ÷ 11 = …………….. 

18) 13 ÷ 1 =……………..  

19) 55 + ………….= 0  

20) (–31) +………….. = 0 

21) (–55) +………….. = (–89) 

22) (–33) +……………. = 79  

23) 1000 +…………. = (–1000) 

24) 251 ÷ ……………..= 1 

25) (–70) ÷………………….. = 5

              Remedial class Worksheet               

Class: VII    Subject: Maths

LINES AND ANGLES 

Fill in the blanks: 

(a) Two ______________ are said to form a linear pair of the angles if their non   common arms are two opposite rays. 

(b) If a ray stands on a line, then the sum of the adjacent angles so formed is ________. 

(c) The sum of all angles around a point is _________________. 

(d) An angle which is equal to its complement is _____________. 

(e) Two angles are called a pair of _____________________ if their arms form two pairs of opposite rays. 

(f) If two lines intersect then the Vertically opposite angles are _____________ 

(g) A line which intersects two or more lines at distinct points is called a--------------- 

(h) Vertically opposite angles are always……………… 

(i) If two lines are intersected by a transversal such that any pair of  corresponding angles are equal then the lines are _________________ 

(j) Sum of two complementary angles is ……………. and sum of two supplementary angles are………………… 

(k) Sum of interior angles on the same side of a transversal is_______. 

(l) Two lines in a plane which do not meet at a point anywhere, are called________lines. 

(m) Two angles forming a________pair are supplementary. 

(n) The supplement of a right angle is always a _______angle. 

(o) The angles in a linear pair are--------------- 

(p) If ∠ AOB = 600, then reflex ∠ AOB is equal to--------------- 

              Remedial class Worksheet               

Class: VII    Subject: Maths

ALGEBRAIC EXPRESSIONS 

1. Add:  (i) 3x2y, 5x2y, x2y  

(ii) a + b – 3, b + 2a – 1 

2. Subtract (i) 3x2– x from 5x – x2  

(ii) 24xy – 10y – 18x from 30xy + 12y – 14x. 

3. Simplify by combining the like terms: (i) a – (a – b) – b – (b – a)  

(ii) x2– 3x + y2– x – 2y2 

4. Subtract 3x2– 5y – 2 from 5y – 3x2 + xy and find the value of the result  if x = 2, y = –1. 

5. From the sum of 2x2 + 3xy – 5 and 7 + 2xy – x2 subtract 3xy + x2– 2. 

6. An algebraic expression containing three terms is called a ----------------- 

7. Number of terms in the expression 3x2y – 2y2z –z2x+ 5 is ----------------------

8. The terms of expression 4x2–3xy are --------------- and ----------------- 

9. Factors of 5x2y2z are ---------------------------- 

10. Coefficient of x in –9xyz is --------------------- 

11. The sum of x4– xy+2y2and – x4 + xy – 2y2is ------------------- 

12. The subtraction of 5 times of y from x is ---------------------------- 

13. The value of 3x2– 5x + 3, when x =1 is -------------- 

14. Terms with the same algebraic factors are called ____________ terms. 

15. A ________________ can take any value and ________________ has a fixed value.

              Remedial class Worksheet               

Class: VII    Subject: Maths

EXPONENTS AND POWERS 

1. Express the following in usual form. 

(a) 8.01 x 107 

(b) 1.75 x 10-3 

2. Express the following in standard form: 

(i) 8,19,00,000 

(ii) 5,94,00,00,00,000 

(iii) 6892.25 

3. Express the following in exponential form. 

(a)3 x 3 x 3 x a x a x a x a 

(b ) a x a x b x b x b x c x c x c x c  

(c) s x s x t x t x s x s x t 

4. Simplify and express each of the following in exponential form. 

5. Find the value of 

(a) 30 ÷ 40 

(b) (80– 20) × (80 + 20) 

(c) (20 + 30 + 40) – (40– 30– 20) 

6. Simplify: 

              Remedial class Worksheet               

Class: VII    Subject: Maths

EXPONENTS AND POWERS 

FILL UP THE BLANKS 

9) a6x a5x a° = a—- 

10) 1 lakh = 10—- 

11) 1 million = 10—- 

12) 432 = 24x 3—- 

13) 53700000 = ___ x 107 

14) 88880000000 = ___ x 1010. 

15) 27500000 = 2.75 x 10—- 

16) 340900000 = 3.409 x 10—- 

17) 50x 250x 1250= ------------------ 

18) In standard form, the number 72105.4 is written as 7.21054 x 10n,  where n = ------------ 

19) In standard form, the number 829030000 is written as K x 108,  where K is equal to------ 

20) If 2x =128, then the value of x = --------------------