← Back to topic
Vidaara.orgClass 10 · Mathematics
CodeVID-M10-04-STD-01
Standard Form of a Quadratic — Assignment
Chapter: Quadratic Equations
Topic: Standard Form of a Quadratic Equation
Maximum Marks: 35
Time: 75 minutes
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.
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 degree of a quadratic equation is:
  • A.$1$
  • B.$2$
  • C.$3$
  • D.$0$
3.
A quadratic has at most how many roots?
  • A.$1$
  • B.$2$
  • C.$3$
  • D.$0$
4.
Is $2x^2-3x+1=0$ a quadratic?
  • A.No
  • B.Yes
  • C.only if $x>0$
  • D.cannot say
5.
In $ax^2+bx+c=0$, $a$ must be:
  • A.$0$
  • B.$\ne0$
  • C.$1$
  • D.negative
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write $x(x+3)=0$ in standard form.
7.
Is $(x-2)^2=0$ a quadratic equation?
8.
Convert $2x^2=5x-3$ to standard form.
9.
Identify $a,b,c$ in $3x^2-2x+1=0$.
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.
Represent "the product of two consecutive integers is $56$" as a quadratic equation.
12.
Write the standard form of $(x-2)(x+1)=0$.
13.
Is $x+\tfrac1x=3$ 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.
A train travels $360$ km at uniform speed. With $5$ km/h more it would take $1$ hour less. Form the quadratic equation in speed $x$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $ax^2+bx+c=0\ (a\ne0)$
  2. (B) $2$
  3. (B) $2$
  4. (B) Yes
  5. (B) $\ne0$
Section B — Short Answer (2 marks)
  1. $x^2+3x=0$.
  2. Yes.
  3. $2x^2-5x+3=0$.
  4. $a=3,\ b=-2,\ c=1$.
Section C — Short Answer (3 marks)
  1. $x^2+7=0$ — quadratic.
  2. $x^2+x-56=0$.
  3. $x^2-x-2=0$.
  4. Yes — $x^2-3x+1=0$.
Section D — Long Answer (5 marks)
  1. $x^2+x-156=0$ (numbers $12,13$).
  2. $x^2+5x-1800=0$.
Generated by Vidaara.org · Assignment VID-M10-04-STD-01 · vidaara.org