Class 10th imp questions for maths 🤓🌟🙀

 🔢 Chapter-wise Important Questions for Class 10 Maths

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1. Real Numbers

Prove that √2 is an irrational number.

Find the HCF and LCM of two given numbers using Euclid’s Lemma.

Show that any positive odd integer is of the form 6q ± 1.

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2. Polynomials

Find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficients.

Divide a polynomial using the division algorithm.

If α and β are zeroes of a polynomial, form a quadratic polynomial using the given sum and product.

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3. Pair of Linear Equations in Two Variables

Solve a pair of linear equations graphically.

Solve by substitution, elimination, or cross-multiplication methods.

Word problems leading to simultaneous linear equations (e.g., ages, speed-distance, prices).

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4. Quadratic Equations

Solve quadratic equations using factorization, completing the square, and quadratic formula.

Word problems based on quadratic equations (e.g., geometry, time-speed-distance).

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5. Arithmetic Progressions (AP)

Find the nth term and sum of the first n terms.

Word problems using AP (e.g., savings, seats, patterns).

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6. Triangles

Prove Basic Proportionality Theorem (Thales' theorem).

Questions based on similarity criteria.

Pythagoras Theorem and its converse.

Area of similar triangles and ratio of their sides.

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7. Coordinate Geometry

Distance formula, Section formula (internal division), and Midpoint formula.

Prove points form a triangle or find type of triangle using coordinates.

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8. Introduction to Trigonometry

Find trigonometric ratios of standard angles.

Use trigonometric identities to simplify expressions.

Prove identities like:

\frac{1 - \cos^2 A}{\sin^2 A} = \cot^2 A

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9. Some Applications of Trigonometry

Height and distance problems involving angle of elevation/depression.

Use proper diagrams and values.

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10. Circles

Prove: The tangent at any point of a circle is perpendicular to the radius.

Prove: Tangents drawn from an external point are equal.

Find the length of tangents using the Pythagoras Theorem.

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11. Constructions

Divide a line segment in a given ratio.

Construct tangents to a circle from an external point.

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12. Areas Related to Circles

Find area of sector, segment, and shaded region.

Use of π = 22/7 or 3.14 based on requirement.

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13. Surface Areas and Volumes

Surface area and volume of cone, cylinder, sphere, hemisphere, and combinations.

Frustum problems.

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14. Statistics

Find mean, median, and mode of grouped data.

Use cumulative frequency table for median.

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15. Probability

Simple problems on finding theoretical probability.

Card, dice, and coin-based questions.

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✅ Tips:

Practice previous years' question papers.

Focus on NCERT Examples and Exercises.

Use formula charts and flashcards.

Practice word problems daily.

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