Class 8 Maths – Chapter 9

Algebraic Expressions & Identities

STEP 10: Model Question Paper (Solved)

📋 General Instructions

• All questions are compulsory.
• Show all necessary steps.
• Use algebraic identities wherever required.

🟦 Section A: Very Short Answer (1 × 5 = 5)

1. Write the identity for (a − b)².
   Answer: (a − b)² = a² − 2ab + b²
2. How many terms are there in 3x² + 2x − 5?
   Answer: 3 terms
3. Find the coefficient of y in 7y − 4.
   Answer: 7
4. Is (x + y)(x − y) an identity?
   Answer: Yes
5. Write one monomial.
   Answer: 5x

🟩 Section B: Short Answer (2 × 4 = 8)

1. Expand: (x + 3)²
   Solution:
   (x + 3)² = x² + 2(x)(3) + 3²
   = x² + 6x + 9
2. Find the value of (a + b)² when a = 2, b = 5.
   Solution:
   (2 + 5)² = 7² = 49
3. Write the identity for (a + b)(a − b).
   Answer: a² − b²
4. Identify the constant term in 6x² − 9.
   Answer: −9

🟧 Section C: Long Answer (4 × 3 = 12)

1. Expand and simplify: (2x + 5)²
   Solution:
   (2x + 5)² = (2x)² + 2(2x)(5) + 5²
   = 4x² + 20x + 25
2. Verify: (a + b)² = a² + 2ab + b²
   Solution:
   LHS = (a + b)² = a² + 2ab + b²
   RHS = a² + 2ab + b²
   LHS = RHS ✔ Verified
3. If a + b = 6 and ab = 8, find a² + b².
   Solution:
   a² + b² = (a + b)² − 2ab
   = 6² − 2(8)
   = 36 − 16
   = 20

👨‍🏫 Examiner Tip

• Identity written = marks secured
• Step-by-step working = full credit
• Neat presentation = positive impression