Extra Curriculum Support

Sec A

1. Which of the following is an example of binomial?

A. 3x , B. -x + 1 , C. 2x2 + x + 1 , D. x4 + x - 1

2. For what value of k, we have 7x2 - 5x + k = -4, given that x = -2.

A. 22 , B. -42 , C. -22 , D. 42

3. A ? takes on different numerical values; its value is not fixed.

A. Constant , B. Variable , C. Alphabets , D. None of above

Sec B

1. Solve the following equations by trial and error method: (i) 5p + 2 = 17 (ii) 3m – 14 = 4

2. Solve the following equations (i) 2q – 6 = 0 (ii) 2q + 6 = 0

3. Simplify: 3(a + b) - 2(2a - b) + 4a - 7.

4. Add the following expressions: 6m - 7n - 5p, -4m - 9n + 6p, -4m - 9n + 6p.

Sec C

1. If 12 of −34 of a number is 6, then what is the number?

2. Solve the following: The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

Sec D

1. Find the amount to be paid at the end of 3 years in each case.

(a) Principal = Rs 1,200 at 12% p.a.

(b) Principal = Rs 7,500 at 5% p.a.

2. Find a number, such that one-fourth of the number is 3 more than 7.

Problem 1

Ramesh is saving money to buy a book. He saves x rupees every day. After 10 days, he donates 2x rupees to a charity and uses the rest to buy the book. Write an algebraic expression for the amount of money he has left after the donation and explain the value of sharing with others even when saving for oneself.

Problem 2

Priya and her friends decide to plant trees in their neighborhood. They plant 3x trees on the first day and 4x−5 trees on the second day. Create an algebraic expression for the total number of trees planted and discuss the importance of teamwork in achieving environmental goals.

Problem 3

A school organizes a fundraiser where each student contributes x rupees. If 5 students contribute 2x rupees each, write an algebraic expression for the total amount collected and reflect on how collective efforts can lead to significant contributions for a cause.

Q1

If the product of two algebraic expressions is 15x2y and one of the expressions is 3xy, what is the other expression? Explain how you would determine it.

Q2

How would you form an algebraic expression using the smallest possible number of terms to represent the scenario: "Twice the sum of a number and its square, reduced by three times the number"?

Q3

Given the expression 4x−3(x+5), can it be simplified to a form with fewer terms? If so, what is the simplified form, and what does this tell us about the nature of like terms?

Q4

Create an algebraic expression that represents the area of a rectangle if its length is 3x+2 and its width is 2x−1. How would you determine the conditions under which the area is a perfect square?

Questions

1. The factors of the term –xy2 are

(a) x × y × y (b) – 1 × y × y (c) – 1 × x × y (d) – 1 × x × y × y

2. An algebraic expression having one or more terms with non-negative integral exponents of the variables is called ---.

3. Every polynomial is a monomial.

4. Twice the sum of length x and breadth y of a rectangle is the perimeter of a rectangle. Write the expression for perimeter.

5. Subtract the sum of – 3x3y2 + 2x2y3 and – 3x2y3 – 5y4 from x4 + x3 y2 + x2y3 + y4.

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

(a) monomial (b) binomial (c) trinomial (d) All of these

7. The subtraction of 5 times of y from x is.

(a) 5x – y (b) y – 5x (c) x – 5y (d) 5y – x

8. The expression for the number of diagonals that we can make from one vertex of a n sided polygon is.

(a) 2n + 1 (b) n – 2 (c) 5n + 2 (d) n – 3

9. The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?

(a) 2x + 16 (b) 6x + 9 (c) 8x + 3 (d) 8x + 12

10. A binomial has more than two terms.

11. A trinomial has exactly three terms.

12. Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.

13. (a) What should be subtracted from 2x3 – 3x2y + 2xy2 + 3y3 to get x3 – 2x2y + 3xy2 + 4y3?

(b) What should be subtracted from –7mn + 2m2 + 3n2 to get m2 + 2mn + n2 ?

14. Subtract 9a2 – 15a + 3 from unity.

15. Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.

16. Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.

17. Challenge Write an expression for the sum of 1 and twice a number n. If you let n be any odd number, will the result always be an odd number?

18. Critical Thinking Will the value of 11x for x = –5 be greater than 11 or less than 11? Explain.

19. Express the following properties with variables x, y and z.

(i) Commutative property of addition

(ii) Commutative property of multiplication

(iii) Associative property of addition

(iv) Associative property of multiplication

(v) Distributive property of multiplication over addition

Q1

Shopping Spree

Scenario: Riya goes to a bookstore to buy x novels and y textbooks. Each novel costs ₹200 and each textbook costs ₹300. She has a discount coupon that gives her a total discount of ₹(50x + 30y).

Question:

1.Write the algebraic expression for the total cost before applying the discount.

2. Express the total cost after applying the discount and simplify it. If Riya spent ₹1,000 after applying the discount, find the possible values of x and y.

Sol 1

1. Total Cost Before Discount:

Total Cost = 200x + 300y

2. Total Cost After Discount:

Total Cost After Discount=(200x+300y) − (50x+30y) = 200x+300y−50x−30y = 150x+270y

Given that Riya spent ₹1,000 after the discount: 150x+270y = 1000

To find integer solutions, we can simplify this equation: 15x+27y = 100

Possible integer values for y (from 0 to 3) give:

• If y = 0 : x = 10015 ≈ 6.67

• If y = 1 : x = 100−2715 ≈ 4.87

• If y = 2 : x = 100−5415 ≈ 3.07

• If y = 3 : x = 100−8115 ≈ 1.27

Since none of the values yield integers, adjust the total budget or discount terms.

Q2

Garden Planning

Scenario: A school organizes a supply drive. They collect x boxes of pencils and y boxes of crayons. Each box of pencils costs ₹30, and each box of crayons costs ₹50. The school received a donation of ₹(10x + 5y) to help cover the costs.

Question:

1. Write the algebraic expression for the total cost of the supplies.

2. After applying the donation, express the total amount spent. If the total amount spent is ₹300, find the possible values of x and y.

Sol 2

1. Total Cost of Supplies:

Total Cost = 30x + 50y

2. Total Amount Spent After Donation:

Total Amount Spent = (30x+50y) − (10x+5y) = 30x+50y−10x−5y = 20x+45y Given that the total amount spent is ₹300: 20x+45y=300

Simplifying: 4x+9y=60

To find integer values for y (from 0 to 6):

• If y = 0 : x = 604 ≈ 15

• If y = 1 : x = 60−94 ≈ 12.75

• If y = 2 : x = 60−184 ≈ 10.5

• If y = 3 : x = 60−274 ≈ 8.25

• If y = 4 : x = 60−364 ≈ 6

• If y = 5 : x = 60−454 ≈ 3.75

• If y = 6 : x = 60−544 ≈ 1.5

Possible integer solutions are (15,0) and (6,4).