Section A: Multiple-Choice Questions (MCQs)
Q1: One plate of dosa costs ₹50, and one plate of idlis costs ₹30. If x plates of dosa and y plates of idli are ordered, which expression represents the total amount earned in rupees?
a) 50x – 30y
b) 50x + 30y
c) (50 + 30) x (x + y)
d) 30x + 50y
Ans: b) 50x + 30y
Explanation: The total amount is the cost of x dosas (50 × x) plus the cost of y idlis (30 × y). Thus, the expression is 50x + 30y.
Option b is correct.
Q2: A flour mill takes 12 seconds to start and 6 seconds per kg of grain to grind. Which expression describes the time to grind z kg of grain, starting from off?
a) 12 + 6 + z
b) 12 x 6 x z
c) 12 + 6 x z
d) (12 + 6) x z
Ans: c) 12 + 6 x z
Explanation: The total time includes 12 seconds to start plus 6 seconds per kg for z kg (6 x z).
Thus, the expression is 12 + 6 x z.
Option c is correct.
Q3: For a matchstick pattern, the number of matchsticks in step y is given by 4y + 1. How many matchsticks are needed for step 5?
a) 22
b) 21
c) 18
d) 28
Ans: b) 21
Explanation: Substitute y = 5 into the expression 4y + 1:
4 x 5 + 1 = 20 + 1 = 21
Option b is correct.
Q4: A shop rents out chairs and tables. The net cost for x chairs and y tables is 25x + 60y. What is the cost for 3 chairs and 2 tables?
a) 195
b) 206
c) 155
d) 135
Ans: a) ₹195
Explanation: Substitute x = 3 and y = 2 into 25x + 60y:
25 x 3 + 60 x 2 = 75 + 120 = 195
Option a is correct.
Q5: In a quiz, Meera’s score in one round is 5p – 2q, where p is the points for a correct answer and q is the penalty. If p = 6 and q = 1, what is her score?
a) 29
b) 24
c) 28
d) 32
Ans: c) 28
Explanation: Substitute p = 6 and q = 1 into 5p – 2q:
5 x 6 – 2 x 1 = 30 – 2 = 28
Option c is correct.
Section B: True or False
a) The terms 5xy and −2yx are like terms.
Ans: True
Like terms have the same variables raised to the same powers. Since yx is the same as xy (commutative property), these terms can be combined.
b) If n = 4, then the value of 5n−3 is 17.
Ans: True
Substituting n = 4:
5(4)−3=20−3=175(4)−3=20−3=17.
The calculation is correct.
c) The expression 2y+7 has three terms:
2, y, and 7.
Ans: False
The expression 2y+7 has two terms: 2y (a single term with coefficient and variable) and 7 (a constant term). Terms are separated by addition or subtraction operators.
d) 3 (x + 2) = 3x + 6.
Ans: True
Applying the distributive property correctly: 3 multiplies both x and 2 inside the parentheses, resulting in 3x+6. This is an example of proper algebraic expansion.
Section C: Patterns Based QuestionQ1: Matchsticks form squares: 1 square = 4 matchsticks, 2 squares = 7 matchsticks, 3 squares = 10 matchsticks. Find the rule for n squares. How many matchsticks are needed for 12 squares?
a) Rule for n squares: Observe the pattern:
1 square → 4 matchsticks
2 squares → 7 matchsticks (4 + 3)
3 squares → 10 matchsticks (7 + 3)
Pattern: Each new square adds 3 matchsticks (because one side is shared between squares).
General formula: Matchsticks = 4 + 3 (n−1) = 3n + 1b) Matchsticks for 12 squares:
Substitute n=12 into the formula:
3(12)+1 = 36 + 1 = 37 matchsticks.
Section D: Word Problems
Q1: Arjun is 6 years older than Bhavna. If Bhavna’s age is b years, write an expression for Arjun’s age and find Arjun’s age when Bhavna is 14 years old.
Ans: Expression: a = b + 6; Arjun’s age = 20 years
Explanation: Arjun’s age is 6 years more than Bhavna’s, so the expression is a = b + 6. Substitute b = 14:
a = 14 + 6 = 20
Arjun is 20 years old.
Q2: Maya makes matchstick patterns with W’s, each requiring 5 matchsticks. Write an expression for the number of matchsticks needed for n W’s and calculate the number needed for 10 W’s.
Ans: Expression: 5n; 50 matchsticks
Explanation: Each W needs 5 matchsticks, so the expression is 5n. For n = 10:
5 x 10 = 50
50 matchsticks are needed.
Q3: Rakesh buys oranges at ₹25 each and 1 kg of flour at ₹45. Write an expression for the total cost of o oranges and f kg of flour, and find the cost for 4 oranges and 3 kg of flour.
Ans: Expression: 25o + 45f; Cost = ₹235
Explanation: The total cost is 25o + 45f. Substitute o = 4 and f = 3:
25 x 4 + 45 x 3 = 100 + 135 = 235
The cost is ₹235.
Q4: The perimeter of a regular pentagon is 5 times the side length. Write an expression for the perimeter if the side length is q cm, and find the perimeter when q = 6 cm.
Ans: Expression: 5q; Perimeter = 30 cm
Explanation: The perimeter is 5q. Substitute q = 6:
5 x 6 = 30
The perimeter is 30 cm.
Q5: In a quiz, Vikram’s scores in three rounds are 4p – 3q, 5p – 2q, and 3p – q, where p is points for a correct answer and q is the penalty. Find his total score expression and calculate it if p = 7 and q = 2.
Ans: Expression: 12p – 6q; Score = 78
Explanation: Add the scores:
(4p – 3q) + (5p – 2q) + (3p – q) = (4p + 5p + 3p) + (-3q – 2q – q) = 12p – 6q
Substitute p = 7 and q = 2:
12 x 7 – 6 x 2 = 84 – 12 = 78
Vikram’s total score is 78.