Q1: Deepak’s present age is onethird his mother’s present age. If the mother’s age was five times his age 6 years ago, what are their present ages?
Ans:
Q2: Form expressions using y, 2 and 7. Every expression must have y in it. use only two number operations. These should be different.
Ans: The different expressions that can formed are: 2y + 7, 2y – 7, 7y + 2, 7y2, (y/2) – 7, (y/7)2, y – (7/2), y + (7/2).
Q3: Give expressions for the following
(a) 7 added to
(b) 7 subtracted from
(c) p multiplied by
(d) p divided by
(e) 7 subtracted
(f) – p multiplied by
(g) – p divided by
(h) p multiplied by – 5.
Ans: (a) p + 7
(b) p – 7
(c) 7p
(d) p/7
(e) – m – 7
(f) 5p
(g)
(h) – 5p.
Q4: Write which letters give us the same rule as that given by L.
Ans: 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.
Q5: Fill in the blanks:
(a) The value of 2x – 12 is zero, when x = ________.
(b) The product of 2 and x is being added to the product of 3 and y is expressed as ________.
(c) The numerical coefficient of the terms is _________.
(d) The no. of terms in the expression is ______.
Ans: (a) 6;
(b) 2x + 3y;
(c) 1/2;
(d) 4
Q6: 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.)
Ans: Let the number of pencils be ‘s’.
As, the number of pencils distributed to each student = 4
Thus, No. of pencils for ‘s’ students = 4 x s = 4s.
Q7: 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?
Ans: 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.
Q8: 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?
Ans: 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.
Q9: Find the value of the expression 2x – 3y + 4z, if x = 10, y = 12 and z = 11.
Ans: Given expression = 2x – 3y + 4z
If x = 10, y = 12 and z = 11,
The expression becomes, (2 × 10) – (3 × –12) + (4 × 11)
= 20 – (36) + 44
= 20 + 36 + 44
= 100.
Q10: 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.)
Ans: 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.
Q11: Rearrange the terms of the following expressions in ascending order of powers of x:
5x^{2}, 2x, 4x^{4}, 3x^{3}, 7x^{5}
Ans: If the given terms are arranged in the ascending order of powers of x, we get, 2x, 5x^{2}, 3x^{3}, 4x^{4}, 7x^{5}.
Q12: State whether the following statements are true or false:
(a) The parts of an algebraic exponent which are connected by + or – sign are called its terms.
(b) 5 times x subtracted from 8 times y is 5x  8y.
(c) A number having fixed value is called variable.
(d) The numerical coefficient of 2x^{2}y is 2.
Ans: (a) True
(b) False
(c) False
(d) True
Q13: Match the following:
Ans:
Q14: The _______ of the variable in an equation which satisfies the equation is called a solution to the equation.
Ans: value, It is correct because the value of the variable must satisfy the equation.
Q15: Which of the following is expression with one variable?
x + y + z, y + 1, 1, x + y – 5
Ans: y + 1, The equation has one variable as “y” whose value is not known. therefore, the equation is in one variable.
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