ICSE Class 10 Quadratic Equations (in one variable) — Mock Test (2027)

Free online mock test for Quadratic Equations (in one variable) (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

Sample questions

1. 1.Solve the equation: $x + \frac{1}{x} = 3\frac{1}{3}, x \neq 0$. What is the solution set?
   • A.$\left\{-3, -\frac{1}{3}\right\}$
   • B.$\left\{3, \frac{1}{3}\right\}$
   • C.$\left\{3, -\frac{1}{3}\right\}$
   • D.$\left\{\frac{10}{3}, \frac{3}{10}\right\}$
2. 2.For the equation $x^{2} - (m + 2)x + (m + 5) = 0$, find the value of ‘m’ so that the equation has equal roots. What is the value of m?
   • A.-4
   • B.4
   • C.-2
   • D.2
3. 3.Without solving the quadratic equation $3x^{2} - 2x - 1 = 0$, determine whether $x = 1$ is a solution (root) of this equation or not.
   • A.$x = 1$ is a solution of the equation.
   • B.$x = 1$ is not a solution of the equation.
   • C.$x = 1$ makes the equation equal to 1, so it is not a root.
   • D.$x = 1$ is a solution only if the equation is linear.
4. 4.Discuss the nature of the roots of the equation $9x^{2} - 6x + 1 = 0$ without actually solving it.
   • A.Roots are real and equal.
   • B.Roots are real and distinct.
   • C.Roots are imaginary and distinct.
   • D.Roots are irrational and equal.
5. 5.A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, what is the value of x?
   • A.3 km/hr
   • B.4 km/hr
   • C.5 km/hr
   • D.6 km/hr