Worksheet Solutions: Framing Algebraic Expressions | Mathematics Class 6 ICSE PDF Download

A. Multiple-Choice Questions 

Q1. Which expression means “three times a number p increased by 5”?
(a) 3p − 5
(b) 3 + 5p
(c) 5p + 3
(d) 3p + 5

Ans: (d) 3p + 5

Sol: “Three times p” is 3p. 
“Increased by 5” means add 5 
→ 3p + 5.

Q2. The perimeter of a rectangle with length l and breadth b is:
(a) l + b
(b) 2lb
(c) 2(l + b)
(d) l² + b²

Ans: (c) 2(l + b)

Sol: A rectangle has two lengths and two breadths: l + b + l + b = 2(l + b).

Q3. Evaluate xy/m when x = 4, y = 15, m = 5.

(a) 8
(b) 10
(c) 12
(d) 20
Ans: (c) 12
Sol: xy/m = (4 × 15) ÷ 5 = 60 ÷ 5 = 12.

Q4. Which formula gives the surface area of a cube of edge a?

(a) 4a
(b) a²
(c) 6a
(d) 6a²
Ans: (d) 6a²
Sol: A cube has 6 square faces, each area a² 
→ total = a² + a² + a² + a² + a² + a² = 6a².

Q5. Use F = (9/5)C + 32. What is F when C = 30?

(a) 54°F

(b) 62°F

(c) 86°F

(d) 90°F

Ans: (c) 86°F

Sol: (9/5) × 30 
= 54; 
54 + 32 = 86°F.

B) Short Answer Questions 

Q6. Write an expression for “twice the sum of x and 7”.

Ans: 2(x + 7)

Sol: “Sum of x and 7” is (x + 7). 
“Twice” means multiply by 2 
→ 2(x + 7).

Q7. A rectangle has l = 12 cm and b = 7 cm. Find its perimeter.

Ans: 38 cm

Sol: P = 2(l + b) 
= 2(12 + 7) 
= 2 × 19 
= 38 cm.

Q8. Evaluate 3x²y when x = 2 and y = 5.

Ans: 60

Sol: x² = 2² = 4. 
Then 3 × 4 × 5 
= 60.

Q9. Let m = −3. 
Find (i) 2m + 21, 
(ii) m² + 9m.

Ans: 

(i) 2m + 21 = 2(−3) + 21 
= −6 + 21 
= 15.

(ii) m² + 9m = (−3)² + 9(−3) 
= 9 − 27 
= −18.

Q10. A worker’s base pay is B for t hours. Overtime rate is R per hour. If total hours are T, write W and then find W when B = 1200, t = 30, R = 50, T = 36.

Ans: W = B + R(T − t); value = 1500

Sol:

Formula: W = B + R(T − t).

Here T − t = 36 − 30 = 6 extra hours.

Overtime = 50 × 6 = 300.

Total W = 1200 + 300 = 1500.

C. Long Answer Questions 

Q11. A rectangle has length (x + 4) cm and breadth (x − 1) cm.

(a) Write Perimeter in terms of x.

(b) Write Area in terms of x.

(c) Find Perimeter and Area when x = 6.

Ans:

(a) Perimeter = 2(l + b) 
= 2[(x + 4) + (x − 1)] 
= 2(2x + 3).

(b) Area = l × b 
= (x + 4)(x − 1).

(c) For x = 6: l = 6 + 4 = 10 cm; b = 6 − 1 = 5 cm.

P = 2(10 + 5) = 2 × 15 = 30 cm.

A = 10 × 5 = 50 cm².

Q12. Let a = −3, b = 4, m = 2.

(a) Find S = a + b − m.

(b) Find Q = (a × b) ÷ m.

(c) Find B = 2a² − b².

Ans:

(a) S = (−3) + 4 − 2 = 1 − 2 = −1.

(b) Q = (−3 × 4) ÷ 2 = (−12) ÷ 2 = −6.

(c) a² = (−3)² = 9; b² = 16.

B = 2 × 9 − 16 = 18 − 16 = 2.

Note: Square before multiplying; keep track of signs carefully.

Q13. A person’s weekly base pay is B = 1500 for t = 35 hours. Overtime rate is R = 60 per hour. In one week they work T = 42 hours.

(a) Write a formula for total wages W and find its value.

(b) The same day, the outdoor temperature is C = 28°C. Convert this to Fahrenheit using F = (9/5)C + 32.

Ans:

(a) W = B + R(T − t)

Extra hours = T − t = 42 − 35 = 7.

Overtime pay = 60 × 7 = 420.

Total wages = 1500 + 420 = 1920.

(b) F = (9/5) × 28 + 32

(9/5) × 28 = 9 × 5.6 = 50.4

F = 50.4 + 32 = 82.4°F.