Unit Test Solution: Expression Using Letter-Numbers | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers  9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: Riya is 5 years older than her brother Samir. If Samir’s age is 12 years, what is Riya’s age?  (1 Mark)

a) 15 years
b) 17 years
c) 10 years
d) 7 years

Solution:
Riya’s age = Samir’s age + 5 = 12 + 5 = 17 years
Answer: b) 17 years

Q2: A shop sells apples at ₹25 each and oranges at ₹15 each. What is the total cost of buying 3 apples and 2 oranges?  (1 Mark)

a) ₹90
b) ₹105
c) ₹75
d) ₹85

Solution:
Cost of 3 apples = 3 × ₹25 = ₹75
Cost of 2 oranges = 2 × ₹15 = ₹30
Total cost = ₹75 + ₹30 = ₹105
Answer: b) ₹105

Q3: The perimeter of a square is given by the formula 4s, where s is the side length. What is the perimeter if the side length is 6 cm?  (1 Mark)

a) 18 cm
b) 24 cm
c) 12 cm
d) 30 cm

Solution:
Perimeter = 4 × s = 4 × 6 = 24 cm
Answer: b) 24 cm

Q4: A bus travels 10 km every hour. How far does it travel in 3 hours?  (1 Mark)

a) 20 km
b) 25 km
c) 30 km
d) 35 km

Solution:
Distance = Speed × Time = 10 × 3 = 30 km
Answer: c) 30 km

Q5: If x represents a number, which expression represents 7 more than twice the number?  (1 Mark)

a) 2x + 7
b) 7x + 2
c) 2x - 7
d) x + 14

Solution:
Twice the number = 2x
7 more than twice the number = 2x + 7
Answer: a) 2x + 7

Q6: A garden hose is 15 meters long. An additional hose of length m meters is attached to it. Write an expression for the total length of the hose. If m = 8 meters, find the total length. (2 Marks)

Solution:
Expression for total length = 15 + m
If m = 8 meters:
Total length = 15 + 8 = 23 meters

Q7: A bakery sells cupcakes at ₹20 each and cookies at ₹10 each. Write an expression for the total cost of buying c cupcakes and k cookies. Find the cost if 5 cupcakes and 3 cookies. (2 Marks)

Solution:
Expression for total cost = 20c + 10k
For c = 5 and k = 3:
Total cost = (20 × 5) + (10 × 3) = 100 + 30 = ₹130

Q8: Simplify the expression: 5x + 2y - 3x + 4y - 7. (2 Marks)

Solution:
Combine like terms:
(5x - 3x) + (2y + 4y) - 7 = 2x + 6y - 7
Simplified expression: 2x + 6y - 7

Q9: A student scores 4p points for each correct answer and loses 2q points for each incorrect answer in a quiz. In three rounds, their scores are 4p - 2q, 3p - q, and 5p - 3q. Write and simplify an expression for the total score. If p = 5 and q = 1, find the total score. (3 Marks)

Solution:
Total score = (4p - 2q) + (3p - q) + (5p - 3q)
= (4p + 3p + 5p) + (-2q - q - 3q)
= 12p - 6q
If p = 5 and q = 1:
Total score = (12 × 5) - (6 × 1) = 60 - 6 = 54

Q10: Subtract the expression 4x - 2y + 5 from 7x + 3y - 8. If x = 2 and y = 1, evaluate the resulting expression. (3 Marks)

Solution:
Subtract: (7x + 3y - 8) - (4x - 2y + 5)
= (7x - 4x) + (3y - (-2y)) + (-8 - 5)
= 3x + 5y - 13
If x = 2 and y = 1:
Result = (3 × 2) + (5 × 1) - 13 = 6 + 5 - 13 = -2

Q11: A pattern of triangles is made with matchsticks. Each triangle requires 3 matchsticks, but adjacent triangles share one matchstick. Find the number of matchsticks needed for 5 triangles and write an expression for n triangles. (3 Marks)

Solution:
For 1 triangle: 3 matchsticks
For 2 triangles: 3 + 2 = 5 matchsticks (1 shared)
For 3 triangles: 5 + 2 = 7 matchsticks
Pattern: 3 + 2(n - 1) = 2n + 1
For 5 triangles: 2 × 5 + 1 = 10 + 1 = 11 matchsticks
Expression for n triangles: 2n + 1

Q12: In a number grid with 4 columns, numbers are arranged as follows: (5 Marks)
Row 1: 1, 2, 3, 4
Row 2: 5, 6, 7, 8
Row 3: 9, 10, 11, 12
and so on.
(a) Write the general expression for the number in row r and column c.
(b) Find the row and column for the number 150.
(c) Find the row and column for the number 200.

Solution:
(a) General expression: Number in row r and column c = 4(r - 1) + c
(b) For 150:
150 ÷ 4 = 37 remainder 2 → Column 2, Row 38
(c) For 200:
200 ÷ 4 = 50 remainder 0 → Column 4, Row 50

Q13: A traffic signal changes colors in the sequence: Red, Yellow, Green, Yellow, Red, and so on. (5 Marks)
(a) Write expressions for the positions of each color in the sequence.
(b) Find the colors at positions 100, 150, and 200.
(c) If the cycle continues, what is the color at position 500?

Solution:
(a) Red: 4n - 3 (positions 1, 5, 9, ...)
Yellow: 2n (positions 2, 4, 6, 8, ...)
Green: 4n - 1 (positions 3, 7, 11, ...)
(b) Position 100: 100 is even, so 2n → Yellow
Position 150: 150 is even, so 2n → Yellow
Position 200: 200 is even, so 2n → Yellow
(c) Position 500: 500 is even, so 2n → Yellow