Hint: Describe algebraic expressions in order to distinguish them from arithmetic expressions.

Question.1. Sakshi wrote an algebraic expression. Which of these could she have written?

(a) 15 + 20 − 18
(b) (5 × 3) + 10
(c) \left(\frac{18}{2}\times 6\right)
(d) 8m+2

Question.2. Which option correctly describes why (7u-7) is an algebraic expression?

(a) Because both the terms have the same numbers.
(b) Because it involves a variable under an operation.
(c) Because it involves multiplication and subtraction operation.
(d) Because it involves a variable under multiplication and subtraction operation.

Ans.1. (d) 8m+2
Ans.2. (b) Because it involves a variable under an operation.

Hint: Examine patterns in order to identify relationship in patterns.

Question.3. What is the general rule for the given pattern?

(a) m
(b) m+1
(c) m+2
(d) m+3

Question.4. Consider the pattern of shapes made using matchsticks.Another matchstick is added to the first shape of the pattern to get:If similarly, matchsticks are added to each shape, how will the relationship in the pattern change?

(a) It will decrease by n matchsticks
(b) It will increase by n matchsticks
(c) It will decrease by n+1 matchsticks
(d) It will increase by n+1 matchsticks

Ans.3. (b) m+1
Ans.4. (b) It will increase by n matchsticks

Hint: Introduce a variable in order to form a rule for the given pattern.

Question.5. The number of matchsticks required to form a pattern are given in the table.How many matchsticks will be required to form nL’s?

(a) n
(b) \frac{n}{4}
(c) 4n
(d) n+4

Question.6. Abhinav makes a pattern by using matchsticks as shown:What is the general rule for the given pattern?

(a) 12n
(b) 16n
(c) 7n+5
(d) 5n+7

Ans.5. (c) 4n
Ans.6. (c) 7n+5

Hint: Use variable with different operations in order to generalise a given situation.

Question.7. Kartik is packing juice packs in cartons such that each carton has 40 juice packs. After packing j cartons, he is left with 25 juice packs. Which of these expressions represents the total number of juice packs?

(a) 40j+25
(b) 40j-25
(c) 25j+40
(d) 25j-40

Question.8. The cost of a closet is Rs. 19 less than 4 times the cost of a table. The cost of a sofa is Rs. 5 more than 2 times the cost of a table. If the cost of the sofa is s, which expression gives the cost of the closet?

(a) 2s+29
(b) 8s+1
(c) 2s-29
(d) 8s-1

Ans.7. (a) 40j+25
Ans.8. (c) 2s-29

Hint: Use variable(s) in order to express some mathematical rules and formulae.

Question.9. The side length of an equilateral triangle is x metres. Which of the following option represents the perimeter of the triangle?

(a) 3+x metres
(b) 3x metres
(c) 3-x metres
(d) \frac{3}{x} metres

Question.10. There are 7 jars with 43 marbles in each jar. Which of these properties can be used to calculate the total number of marbles in the jars?

(a) u\times (v+w)=u\times v+w, distributive property of addition over multiplication.
(b) u+v=v+u, commutative property of addition.
(c) u\times (v+w)=u+v+w, commutative property of addition.
(d) u\times (v+w)=u\times v+u\times w, distributive property of addition over multiplication.

Ans.9. (b) 3x metres
Ans.10. (d) u\times (v+w)=u\times v+u\times w, distributive property of addition over multiplication

Hint: Use variable with different operations in order to form an algebraic expression.

Question.11. Anjali thinks of a number z. She multiplies the number by –9 and subtracts it from 14. Which of these algebraic expressions she could have formed?

(a) 14-9z
(b) -9z-14
(c) 14+9z
(d) -9z+14

Question.12. The digit at hundreds place of a three-digit number is five more than the digit at its ones place and digit at tens place is three less than the digit at its ones place. If the digit at ones place is u, which of the following expressions represents the three-digit number?

(a) 100(5+u)+10(u-3)+u
(b) 100(5+u)+10(3-u)+u
(c) (5+u)+(u-3)+u
(d) (5+u)+(3-u)+u

Ans.11. (c) 14+9z
Ans.12. (a) 100(5+u)+10(u-3)+u

Hint: Change the given algebraic expression in statements in order to describe the situation in ordinary language.

Question.13. Consider the following. The cost of a crayon pack is Rs. (2c-5), where c is the cost of a paint brush. Which of these describes the situation?

(a) The cost of a crayon pack is Rs. 5 less than twice the cost of a paint brush.
(b) The cost of a crayon pack is Rs. 2 less than five times the cost of a paint brush.
(c) The cost of a crayon pack is Rs. 2 less than five more than the cost of a paint brush.
(d) The cost of a crayon pack is Rs. 5 less than two more than the cost of a paint brush.

Question.14. Ria’s age is x years. Jai’s age is \frac{x}{2}+5. If Jai is elder than Amit, which of these could be the possible relation between Amit’s and Ria’s age?

(a) Amit’s age is 5 years more than half of Ria’s age
(b) Amit’s age is 5 years more than twice of Ria’s age.
(c) Amit’s age is 5 years more than thrice of Ria’s age.
(d) Amit’s age is 5 years more than one-third of Ria’s age.

Ans.13. (a) The cost of a crayon pack is Rs. 5 less than twice the cost of a paint brush.
Ans.14. (d) Amit’s age is 5 years more than one-third of Ria’s age.

Hint: Explain the meaning of an equation in order to identify equations from the given options.

Question.15. Which of the following is an equation?

(a) \frac{2}{3}-5x
(b) 3y-25>9
(c) \frac{1}{5}z+23=38
(d) 9w<72

Question.16. Rishabh identified that there is an error in a book. The error is in the following statement.
7p-27 is an example of an equation”
Which of these is a way to fix the error?

(a) replace 27 with 7
(b) replace 27 with 1
(c) replace minus sign with plus sign
(d) replace minus sign with equal sign

Ans.15. (c) \frac{1}{5}z+23=38
Ans.16. (d) replace minus sign with equal sign

Hint: Use trial and error in order to find the solution of the given equation.

Question.17. Which of the following option shows the solution of the equation 4-3s=-2?

(a) (b) (c) (d)

Question.18. Observe the table below.Which of these is the solution to the equation \frac{v}{2}-7=-9\frac{1}{2}?

(a) -4
(b) -5
(c) -6
(d) -7

Ans.17. (a) Ans.18. (b) -5

Hint: Evaluate for the given values of variable in order to identify the solution of the equation.

Question.19. Which of the following is the solution of the equation r-6=-2?

(a) 8
(b) 4
(c) –4
(d) –8

Question.20. A bookcase has 9 shelves and each shelf has m books in it. Harsh arranges 4 books in the bookcase and takes out 9 books. If 58 books are left in the bookcase, how many books are in each shelf?

(a) 5
(b) 7
(c) 36
(d) 54

Ans.19. (b) 4
Ans.20. (b) 7