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 quadratic equation $p^{2}x^{2} + (p^{2} - q^{2})x - q^{2} = 0$ for $x$ and select the correct pair of roots.
   • A.$x = \frac{q}{p}, -\frac{q}{p}$
   • B.$x = \frac{p}{q}, -\frac{p}{q}$
   • C.$x = p + q, p - q$
   • D.$x = q^2, -p^2$
2. 2.Solve the equation $2x^2 - 7x = 39$ by factorisation. Which of the following is the solution set?
   • A.$\left\{-3, \frac{13}{2}\right\}$
   • B.$\left\{3, -\frac{13}{2}\right\}$
   • C.$\left\{6, -\frac{13}{4}\right\}$
   • D.$\left\{\frac{7}{2}, -3\right\}$
3. 3.Find the value(s) of m for which the quadratic equation (1 + 3m)x² - 2(1 + m)x + m = 0 has equal roots. What are the possible values of m?
   • A.m = 1 and m = -1
   • B.m = 1 and m = -1/2
   • C.m = 0 and m = -1/3
   • D.m = 2 and m = -1/2
4. 4.Solve the quadratic equation: $\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = 3\frac{1}{3}$
5. 5.Determine which of the following statements is true about the values $x = \frac{-1}{3}$ and $x = \frac{2}{3}$ in relation to the equation $9x^2 - 3x - 2 = 0$.
   • A.$x = \frac{-1}{3}$ and $x = \frac{2}{3}$ are both solutions of the equation.
   • B.$x = \frac{-1}{3}$ is a solution, but $x = \frac{2}{3}$ is not.
   • C.$x = \frac{2}{3}$ is a solution, but $x = \frac{-1}{3}$ is not.
   • D.Neither $x = \frac{-1}{3}$ nor $x = \frac{2}{3}$ is a solution of the equation.