Vidaara.orgClass 8 · Mathematics
CodeVID-M08-05-IDN-01
Standard Identities & Applications - Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$(a+b)^2=$
- A.$a^2+b^2$
- B.$a^2+2ab+b^2$
- C.$a^2-2ab+b^2$
- D.$2ab$
2.
$(a-b)^2=$
- A.$a^2-b^2$
- B.$a^2-2ab+b^2$
- C.$a^2+2ab+b^2$
- D.$a^2-ab$
3.
$(a+b)(a-b)=$
- A.$a^2+b^2$
- B.$a^2-b^2$
- C.$2ab$
- D.$a^2$
4.
$(x+3)^2=$
- A.$x^2+9$
- B.$x^2+6x+9$
- C.$x^2+3x+9$
- D.$x^2+9x$
5.
$102\times98=$ (use $a^2-b^2$)
- A.$9996$
- B.$10000$
- C.$9999$
- D.$9990$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Expand $(x+5)^2$.
7.
Expand $(x-4)^2$.
8.
Expand $(x+6)(x-6)$.
9.
Evaluate $51^2$ using an identity.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Expand $(2x+3)^2$.
11.
Expand $(3a-2)^2$.
12.
Evaluate $99^2$ using an identity.
13.
Evaluate $103\times97$ using an identity.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Using identities, evaluate $105^2$ and $95^2$.
15.
Simplify $(x+y)^2-(x-y)^2$ and find its value for $x=7,\ y=3$.
Answer Key
Section A — Multiple Choice Questions
- (B) $a^2+2ab+b^2$
- (B) $a^2-2ab+b^2$
- (B) $a^2-b^2$
- (B) $x^2+6x+9$
- (A) $9996$
Section B — Short Answer (2 marks)
- $x^2+10x+25$.
- $x^2-8x+16$.
- $x^2-36$.
- $2601$.
Section C — Short Answer (3 marks)
- $4x^2+12x+9$.
- $9a^2-12a+4$.
- $9801$.
- $9991$.
Section D — Long Answer (5 marks)
- $105^2=11025$; $95^2=9025$.
- $4xy=84$.
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