EXPRESSIONS USING LETTER-NUMBERS

Easy (15)

1. Which of the following is an example of a letter-number?
   • 5
   • x (correct)
   • +
   • =

   Why: A letter-number is a symbol, usually a letter, used to represent an unknown quantity.

2. The expression for '5 added to y' is:
   • 5y
   • y - 5
   • y + 5 (correct)
   • 5 - y

   Why: Adding 5 to y means y + 5.

3. What is the coefficient of 'x' in the term '7x'?
   • x
   • 7 (correct)
   • 1
   • 7x

   Why: The coefficient is the numerical part multiplying the variable.

4. Which of the following is a like term to '3ab'?
   • 3a
   • 5b
   • 8ba (correct)
   • 3a²b

   Why: Like terms have the same letter-numbers with the same powers.

5. The perimeter of a square with side 's' is given by the expression:
   • s²
   • 2s
   • 4s (correct)
   • s + 4

   Why: A square has 4 equal sides, so its perimeter is 4 times the side length.

6. Which operation is usually omitted between a number and a letter-number?
   • Addition
   • Subtraction
   • Multiplication (correct)
   • Division

   Why: The multiplication symbol is often omitted for brevity.

7. If 'p' represents the number of pens, what does '3p' represent?
   • p + 3 pens
   • 3 more pens than p
   • 3 times the number of pens (correct)
   • p divided by 3 pens

   Why: When a number is written next to a variable, it implies multiplication.

8. Which of these is an algebraic expression?
   • 5 + 3 = 8
   • 2x - 7 (correct)
   • 10
   • x = 4

   Why: An algebraic expression contains variables, numbers, and operations, without an equality sign.

9. The terms '4x' and '4y' are like terms.

   Why: Like terms must have the exact same variables.

10. The expression 'a + 3' means '3 more than a'.

    Why: Adding 3 to 'a' means 'a' increased by 3, or '3 more than a'.

11. The distributive property states that a(b + c) = ab + ac.

    Why: The distributive property allows multiplication to be distributed over addition.

12. In the expression '5x + 2', the constant term is _________.

    Why: A constant term is a term without any variables.

13. The value of 'a + 3' if 'a = 10' is _________.

    Why: Substitute the value of 'a' into the expression and perform the addition.

14. The expression for 'x multiplied by 6' is _________.

    Why: Multiplication between a number and a variable is typically written by placing the number first.

15. Terms that have different letter-numbers are called _________ terms.

    Why: Terms with different variables are unlike terms.

Medium (15)

1. Which expression represents 'the sum of a and b, divided by 7'?
   • a + b / 7
   • (a + b) / 7 (correct)
   • 7 / (a + b)
   • 7a + 7b

   Why: Parentheses are needed to ensure the sum is divided by 7, not just 'b'.

2. Simplify the expression: 5x + 3y - 2x + y.
   • 3x + 4y (correct)
   • 7x + 4y
   • 3x + 2y
   • 7x + 2y

   Why: Combine like terms: (5x - 2x) and (3y + y).

3. If the cost of one apple is ₹a and one banana is ₹b, what is the cost of 3 apples and 2 bananas?
   • a + b + 5
   • 3a + 2b (correct)
   • 5ab
   • 3b + 2a

   Why: Cost of 3 apples is 3a, cost of 2 bananas is 2b. Add them for the total.

4. Apply the distributive property to simplify: 4(x + 5).
   • 4x + 5
   • x + 20
   • 4x + 20 (correct)
   • 20x

   Why: Multiply 4 by each term inside the parentheses.

5. The age of a father is 5 years more than three times the age of his son. If the son's age is 's' years, what is the father's age?
   • 3s - 5
   • s + 5
   • 3s + 5 (correct)
   • 5s + 3

   Why: Three times the son's age is 3s, and 5 years more than that is 3s + 5.

6. Match the algebraic expression with its verbal description.

   Why: Each expression translates directly to its verbal form.

7. Match the terms with their type.

   Why: Like terms have identical variable parts; unlike terms do not.

8. Match the expressions with their simplified forms.

   Why: Combine like terms by adding or subtracting their coefficients.

9. The perimeter of a regular pentagon with side length 'l' is _________.

   Why: A regular pentagon has 5 equal sides.

10. If a box contains 'b' books, then 4 such boxes contain _________ books.

    Why: Multiply the number of boxes by the number of books per box.

11. Arrange the steps to simplify the expression 3(x + 2) + 5x in the correct order.

    Why: First distribute, then group like terms, then combine them.

12. Arrange the following phrases to form an algebraic expression for '5 less than twice a number x'.

    Why: First, represent 'twice a number x', then apply '5 less than'.

13. Observe the pattern of matchsticks and choose the correct expression for the number of matchsticks required to make 'n' such figures.
    • n + 1
    • 2n (correct)
    • 2n + 1
    • 3n - 1

    Why: Each 'L' shape requires 2 matchsticks. For 'n' figures, it's 2n.

14. Look at the pattern of squares formed by matchsticks. Which expression represents the number of matchsticks required for 'n' squares?
    • 4n
    • 3n + 1 (correct)
    • n + 3
    • 4n - 1

    Why: The first square needs 4, subsequent squares add 3 matchsticks.

15. The given table shows the relationship between Aftab's age ('a') and Shabnam's age ('s'). Which expression correctly represents Shabnam's age?
    • s = a - 3
    • s = 3a
    • s = a + 3 (correct)
    • s = a / 3

    Why: From the table, Shabnam's age is always 3 more than Aftab's age.

Hard (10)

1. Simplify the expression: 7(2x - 3) - 5x + 10. What is the coefficient of x in the simplified expression?

   Why: First distribute, then combine like terms to find the coefficient of x.

2. If the perimeter of an equilateral triangle is 'P' and its side length is 's', then P = 3s. If the perimeter is 45 units, what is the side length 's'?

   Why: Substitute P=45 into P=3s and solve for s.

3. A rectangular garden has a length that is 4 meters more than its width. If the width is 'w' meters, and the perimeter of the garden is 32 meters, what is the width 'w'?

   Why: Form an expression for the perimeter in terms of 'w', then solve the equation.

4. Evaluate the expression 2a² - 3b + 5 when a = 3 and b = 4.

   Why: Substitute the values of 'a' and 'b' into the expression and follow the order of operations.

5. Assertion (A): The expression 5x + 7y - 2x can be simplified to 3x + 7y. Reason (R): Only like terms can be added or subtracted.

   Why: The assertion is true because 5x and -2x are like terms and can be combined, which is explained by the reason.

6. Assertion (A): The perimeter of a regular hexagon with side 's' is 6s. Reason (R): A regular hexagon has six equal sides.

   Why: The perimeter of a regular hexagon is indeed 6s, and this is because it has six equal sides.

7. A shopkeeper sells 'x' number of notebooks at ₹15 each and 'y' number of pens at ₹8 each. He also gives a discount of ₹10 on the total purchase if the total amount exceeds ₹100. If a customer buys 7 notebooks and 5 pens, and the total amount is more than ₹100, what is the final amount the customer has to pay?
   • ₹145
   • ₹135 (correct)
   • ₹155
   • ₹125

   Why: Calculate the cost of notebooks and pens, sum them, then apply the discount if applicable.

8. A bus travels at a speed of 'v' km/h. It travels for 3 hours and then stops for 1 hour. After the stop, it travels for another 2 hours at the same speed. What is the total distance covered by the bus?
   • 3v + 1
   • 5v (correct)
   • 6v
   • v + 6

   Why: Distance = speed × time. Sum the distances for each travel segment.

9. A rectangular park has length 'L' and width 'W'. A jogging track of uniform width 'x' is built inside the park along its boundary. Which expression represents the area of the jogging track?
   • LW - (L-x)(W-x)
   • LW - (L-2x)(W-2x) (correct)
   • (L+x)(W+x) - LW
   • 2x(L+W-2x)

   Why: Area of track = Area of outer rectangle - Area of inner rectangle.

10. The diagram shows a composite shape made of a rectangle and a triangle. If the rectangle has length 'l' and width 'w', and the triangle has base 'l' and height 'h', what is the total area of the composite shape?
    • lw + lh
    • lw + (1/2)lh (correct)
    • l + w + h
    • 2(l+w) + (1/2)lh

    Why: Sum the area of the rectangle (lw) and the area of the triangle ((1/2)bh).