Worksheet Solutions: Algebra

Q.1. Find the rule which gives the number of lines required to make the following pattern. Use a variable to write the rule.

(i) Letter

 __________ 

(ii) Letter 

__________ 

(iii) Letter 

__________ 

(iv) Letter 

__________

Ans.
(i) For each of the n copies, the letter uses 2 straight lines. Therefore the total number of lines = 2n.
(ii) Each copy of this letter uses 3 straight lines. Therefore the total number of lines = 3n.
(iii) Each copy of this letter uses 4 straight lines. Therefore the total number of lines = 4n.
(iv) Each copy of this letter uses 2 straight lines. Therefore the total number of lines = 2n.

Q.2. Children stand 10 in a row to perform a drill. How many children can there be in a drill? Give the rule to calculate this. (Use n for the number of rows) 

Ans.
Let n be the number of rows.
Each row has 10 children.
Total number of children = number of rows × children per row = n × 10 = 10n.

Q.3. Form an algebraic expression using the statements given below :
(i) 17 subtracted from '-y' __________
(ii) '-m' multiplied by 10 __________
(iii) x divided by '-2' __________
(iv) 4 added to 6 times y __________ 

Ans.
(i) Seventeen subtracted from -y is written as -y - 17.
(ii) -m multiplied by 10 is written as -10m.
(iii)

(This denotes x divided by -2, which is written as -x/2.)
(iv) Four added to six times y is written as 6y + 4.

Q.4. If y is Meena's age now in years how old will she be after 7 years? __________ 

Ans.
Present age of Meena = y years.
After 7 years her age will be y + 7 years.

Q.5. If the side of a square is m units, then what is it's perimeter? __________ 

Ans.
A square has four equal sides.
If one side is m units, perimeter = 4 × side = 4m units.

Q.6. Is 2 p-3> 7 an algebraic equation? __________ 

Ans.
No, 2p - 3 > 7 is not an algebraic equation.
Explanation: An algebraic equation must contain an equal sign (=). The given statement uses the greater‐than sign (>) and so it is an inequality, not an equation.

Q.7. A teacher distributes 6 books per student. How many books are needed if s is the number of students?

Ans.
Let the number of students be s.
Books per student = 6.
Total books required = 6 × s = 6s.

Q.8. Pick out the correct solution from the values given in the bracket next to each equation:

r - 8 = 0 (8, - 8, 0, 1) r = __________

Ans.
r - 8 = 0
Add 8 to both sides: r = 0 + 8 = 8.

Q.9. Match the following :

Sol:
(i) Solve for x in 5x = 20:
5x = 20
Divide both sides by 5: x = 20 ÷ 5 = 4.
(ii) Solve for x in 8 = x + 3:
x + 3 = 8
Subtract 3 from both sides: x = 8 - 3 = 5.
(iii) Solve for x in 12 ÷ x = 4:
12/x = 4
Multiply both sides by x: 12 = 4x
Divide both sides by 4: x = 12 ÷ 4 = 3.
(iv) Solve for x in 8 - x = 2:
8 - x = 2
Subtract 8 from both sides: -x = 2 - 8 = -6
Multiply both sides by -1: x = 6.
Ans.
1. ↔ (b)
2. ↔ (c)
3. ↔ (d)
4. ↔ (a)

Q.10. Give a mathematical expression for the statement: m multiplied by 5 and 6 subtracted from the product.

Ans:
m multiplied by 5 gives the product 5m.
6 subtracted from this product gives 5m - 6.