Vidaara.orgClass 10 · Mathematics
CodeVID-M10-04-CT
Quadratic Equations — 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.
Standard form of a quadratic is:
- A.$ax+b=0$
- B.$ax^2+bx+c=0\ (a\ne0)$
- C.$ax^3=0$
- D.$x+c=0$
2.
The roots of $x^2-5x+6=0$ are:
- A.$2,3$
- B.$1,6$
- C.$-2,-3$
- D.$5,1$
3.
The discriminant is:
- A.$b^2-4ac$
- B.$b^2+4ac$
- C.$4ac-b^2$
- D.$2a$
4.
The degree of a quadratic equation is:
- A.$1$
- B.$2$
- C.$3$
- D.$0$
5.
The roots of $x^2-9=0$ are:
- A.$3$
- B.$\pm3$
- C.$9$
- D.$\pm9$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Write $x(x+3)=0$ in standard form.
7.
Solve $x^2-7x+12=0$.
8.
Find $D$ for $x^2-5x+6=0$.
9.
Is $(x-2)^2=0$ a quadratic equation?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Check whether $(x+1)^2=2(x-3)$ is quadratic and write its standard form.
11.
Solve $6x^2-x-2=0$ by factorisation.
12.
Find $k$ for which $x^2-4x+k=0$ has equal roots.
13.
Represent "the product of two consecutive integers is $56$" as a quadratic equation.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
The sum of the squares of two consecutive natural numbers is $313$. Form the quadratic equation.
15.
Solve $x^2-4x-8=0$ by completing the square.
Answer Key
Section A — Multiple Choice Questions
- (B) $ax^2+bx+c=0\ (a\ne0)$
- (A) $2,3$
- (A) $b^2-4ac$
- (B) $2$
- (B) $\pm3$
Section B — Short Answer (2 marks)
- $x^2+3x=0$.
- $3,\ 4$.
- $1$.
- Yes.
Section C — Short Answer (3 marks)
- $x^2+7=0$ — quadratic.
- $\tfrac23,\ -\tfrac12$.
- $k=4$.
- $x^2+x-56=0$.
Section D — Long Answer (5 marks)
- $x^2+x-156=0$ (numbers $12,13$).
- $x=2\pm2\sqrt3$.
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