Vidaara.orgClass 9 · Mathematics
CodeVID-M9-02-CT
Polynomials — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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 polynomial allows $x$ raised to:
- A.negative powers
- B.non-negative integer powers
- C.fractional powers
- D.any
2.
$(x+2)+(x+3)=$
- A.$2x+5$
- B.$x+5$
- C.$2x+6$
- D.$x^2+5$
3.
The remainder of $p(x)\div(x-a)$ is:
- A.$p(0)$
- B.$p(a)$
- C.$0$
- D.$a$
4.
$a^2-b^2=$
- A.$(a+b)(a-b)$
- B.$(a-b)^2$
- C.$(a+b)^2$
- D.$a^2+b^2$
5.
The degree of $3x^2+2x+1$ is:
- A.$1$
- B.$2$
- C.$3$
- D.$0$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the degree of $4x^3-2x+7$.
7.
Add $(x^2+2x)$ and $(3x^2-x)$.
8.
Find the remainder of $x^2-5x+6$ by $(x-2)$.
9.
Factorise $x^2-9$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
State the degree and number of terms of $7x^4-3x^2+x$.
11.
Multiply $(x+2)(x^2-2x+4)$.
12.
Find the remainder when $x^3-3x^2+4x-4$ is divided by $(x-2)$.
13.
Factorise $4x^2-25$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
For $p(x)=2x^3-3x^2+x-5$, find $p(0),\ p(1)$ and $p(-1)$.
15.
If $p(x)=x^2+2x+1$ and $q(x)=x-1$, find $p(x)\cdot q(x)$.
Answer Key
Section A — Multiple Choice Questions
- (B) non-negative integer powers
- (A) $2x+5$
- (B) $p(a)$
- (A) $(a+b)(a-b)$
- (B) $2$
Section B — Short Answer (2 marks)
- $3$.
- $4x^2+x$.
- $0$.
- $(x+3)(x-3)$.
Section C — Short Answer (3 marks)
- Degree $4$; $3$ terms.
- $x^3+8$.
- $0$.
- $(2x+5)(2x-5)$.
Section D — Long Answer (5 marks)
- $-5,\ -5,\ -11$.
- $x^3+x^2-x-1$.
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