ICSE Class 10 Trigonometric Identities — Mock Test (2027)

Free online mock test for Trigonometric Identities (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.(iii) Using tables find the value of: $\tan 31^\circ 27'$
   • A.0.6084
   • B.0.6104
   • C.0.6116
   • D.0.6146
2. 2.If $\sin A = \frac{1}{2}$, then the value of $\cot A$ is
   • a.$\sqrt{3}$
   • b.$\frac{1}{\sqrt{3}}$
   • c.$\frac{\sqrt{3}}{2}$
   • d.1
3. 3.Given A is an acute angle and $13 \sin A = 5$, evaluate without using tables: $\frac{(5 \sin A - 2 \cos A)}{\tan A}$.
4. 4.Which of the following correctly proves the identity $\frac{\tan \theta + \sin \theta}{\tan \theta - \sin \theta} = \frac{\sec \theta + 1}{\sec \theta - 1}$?
   • A.Express $\tan \theta$ as $\frac{\sin \theta}{\cos \theta}$, factor out $\sin \theta$ from numerator and denominator, then simplify to match the R.H.S.
   • B.Multiply numerator and denominator by $\cos \theta$ directly without expressing $\tan \theta$ in terms of $\sin \theta$ and $\cos \theta$.
   • C.Replace $\tan \theta$ with $\sin \theta$ and $\sec \theta$ with $\cos \theta$, then cross-multiply to verify the identity.
   • D.Square both sides of the equation and use the Pythagorean identity to show equality.
5. 5.Eliminate θ from the following equations: $x = h + a \cos \theta$, $y = k + b \sin \theta$. Which of the following relations is obtained?
   • A.$\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$
   • B.$\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$
   • C.$\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1$
   • D.$(x - h)^2 + (y - k)^2 = a^2 + b^2$