Algebra - Worksheets

 CBSE Worksheet 01

Ch-11 Algebra

---

1. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder. She has 10 dots in a row. How many dots will her Rangoli have for r rows?
   1. 10 + r 
   2. 10r
   3. 10 – r
   4. r
2. Which of the following is expression with one variable?
   1. x + y + z
   2. y + 1
   3. 1
   4. x + y – 5
3. The length of a rectangular hall is 4 meters less than 3 times the breadth of the hall. What is the length, if the breadth is b meters?
   1. 12b
   2. 3b – 4
   3. None of these
   4. 3b + 4
4. The _______ of the variable in an equation which satisfies the equation is called a solution to the equation.
   1. value
   2. factor
   3. term
   4. None of these
5. The teacher distributes 4 pencils per student. Can you tell how many pencils are needed for given number of students? (Use s for the number of students.)
   1. 4 – s
   2. 4+s
   3. s
   4. 4s

6. Match the following:

   Column A	Column B
   (a) 3 times y added to 13	(p) 5y - 8
   (b) 8 subtracted from 5 times y	(q) 3x - 5
   (c) 5 reduced from 3 times x	(r) 2x + 5
   (d) 5 added to double of x	(s) 3y + 13

7. Fill in the blanks:

   1. The value of 2x - 12 is zero, when x = ________.
   2. The product of 2 and x is being added to the product of 3 and y is expressed as ________.
   3. The numerical coefficient of the terms 12xy2$\frac{1}{2}x{y}^2$ is _________.
   4. The no. of terms in the expression 3x2y−4x2y2+12xy2−5x$3x^{2}y-4x^2{y}^2+\frac{1}{2}x{y}^2-5x$ is ______.

8. State whether the following statements are true or false:

   1. The parts of an algebraic exponent which are connected by + or – sign are called its terms.
   2. 5 times x subtracted from 8 times y is 5x-8y.
   3. A number having fixed value is called variable.
   4. The numerical coefficient of -2x2y is -2.

9. Write which letters give us the same rule as that given by L.

10. Rearrange the terms of the following expressions in ascending order of powers of x:
    5x2, 2x, 4x4, 3x3, 7x5

11. Give expressions for the following

    1. 7 added to
    2. 7 subtracted from
    3. p multiplied by
    4. p divided by
    5. 7 subtracted
    6. - p multiplied by
    7. - p divided by
    8. p multiplied by - 5.

12. The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students ? (Use s for number of students.)

13. Form expressions using y, 2 and 7. Every expression must have y in it. use only two number operations. These should be different.

14. Find the value of the expression 2x - 3y + 4z, if x = 10, y = -12 and z = 11.

15. Deepak’s present age is one-third his mother’s present age. If the mother’s age was five times his age 6 years ago, what are their present ages?

CBSE Worksheet 01
Ch-11 Algebra

---

Answer

1. 2. 10r, Explanation: Let the total number of rows be 'r'.
      As, No. Of dots in a row =10.
      So, the dots needed for 10 rows = r x 10= 10r.
2. 2. y + 1, Explanation: The equation has one variable as "y" whose value is not known. therefore, the equation is in one variable.
3. 2. 3b – 4, Explanation: breadth of a rectangular hall = b meters
      let length of a rectangular hall be 'l' meter
      according to the question, l = 3 times the breadth - 4 = 3b - 4
4. 1. value, Explanation: It is correct because the value of the variable must satisfy the equation.
5. 4. (d) 4s, Explanation: Let the number of pencils be 's'.
      As, the number of pemcils distributed to each student= 4
      Thus, No. of pencils for 's' students = 4 x s= 4s.
6. 1. →$\to$ (s)
   2. →$\to$ (p)
   3. →$\to$ (q)
   4. →$\to$ (r)
7. 1. 6;
   2. 2x + 3y;
   3. 12$\frac{1}{2}$;
   4. 4
8. 1. True
   2. False
   3. False
   4. True

9. The other letters which give us the same rule as L are T, V and X because the number of matchsticks required to make each of them is 2.

10. If the given terms are arranged in the ascending order of powers of x, we get,

    2x, 5x2, 3x3, 4x4, 7x5.

11. 1. p + 7
    2. p – 7
    3. 7p
    4. p7$\frac{p}{7}$
    5. - m - 7
    6. -5p
    7. −p5$-\frac{p}{5}$
    8. - 5p.

12. Number of pencils to be distributed to each student= 5

    And, let the number of students in class be 's'.

    As per the logic, Number of pencils needed =(Number of students in the class) x. (Number of pencils to be distributed to one student )

    So, Number of pencils needed= 5 x s =5s.

13. The different expressions that can formed are: 2y + 7, 2y – 7, 7y + 2, 7y-2, (y/2) - 7, (y/7)-2, y - (7/2), y + (7/2)

14. Given expression = 2x - 3y + 4z
    If x = 10, y = -12 and z = 11,
    The expression becomes, (2×10)−(3×−12)+(4×11)$(2\times 10)-(3\times -12)+(4\times 11)$
    = 20 - (-36) + 44
    = 20 + 36 + 44
    = 100.

15. Let present age of mother = x years
    Deepak's present age =x3years$=\frac{x}{3}years$
    6 years ago, mother's age = (x - 6) years
    Deepak's age =(x3−6)$=\left(\frac{x}{3}-6\right)$ years
    According to the problem, 6 years ago, mother's age is 5 times Deepak age.
    i.e., (x - 6) =5×(x3−6)$=5\times \left(\frac{x}{3}-6\right)$
    x−5x3=−30+6$x-\frac{5x}{3}=-30+6$
    3x−5x3=−24$\frac{3x-5x}{3}=-24$
    −2x3=−24$\frac{-2x}{3}=-24$
    2x=24×3$2x=24\times 3$
    x=722=36$x=\frac{72}{2}=36$
    Therefore, present age of mother = 36 years and
    Present age of Deepak =x3=363=12$=\frac{x}{3}=\frac{36}{3}=12$years.