class 10 maths all important topics

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CLASS 10TH IMPORTANT QUESTION OF MATHS

Chapter 1: Real Numbers

1. Prove that the square root of 2 is irrational.
2. Find the HCF and LCM of two numbers using prime factorization.
3. Prove that the product of two irrational numbers is not always irrational.

Chapter 2: Polynomials

1. If a polynomial has (x – a) as a factor, prove that f(a) = 0.
2. Find the remainder when a polynomial is divided by a linear factor.
3. Factorize the quadratic polynomial $x^2 - 5x + 6$.

Chapter 3: Pair of Linear Equations in Two Variables

1. Solve the system of equations: $x + y = 7$ and $2x - y = 4$ using substitution or elimination.
2. Solve the pair of linear equations graphically.
3. Word problem on the application of linear equations.

Chapter 4: Quadratic Equations

1. Solve the quadratic equation $x^2 - 5x + 6 = 0$.
2. Use the quadratic formula to solve: $3x^2 + 7x - 6 = 0$.
3. Find the nature of the roots of the equation: $2x^2 + 3x + 1 = 0$.

Chapter 5: Arithmetic Progressions

1. Find the nth term of an AP where $a = 2$, $d = 3$, and $n = 10$.
2. The sum of the first 20 terms of an AP is 2100. Find the first term and common difference.
3. Find the sum of the first 30 terms of an AP.

Chapter 6: Triangles

1. Prove that the sum of the angles in a triangle is 180°.
2. Prove the Pythagorean theorem.
3. If two triangles are similar, prove that the corresponding sides are proportional.
4. Find the area of a triangle using Heron’s formula.

Chapter 7: Coordinate Geometry

1. Find the distance between the points (3, 4) and (7, 8).
2. Find the area of a triangle with vertices at (1, 2), (3, 4), and (5, 6).
3. Find the midpoint of the line segment joining (x1, y1) and (x2, y2).

Chapter 8: Introduction to Trigonometry

1. Define the six trigonometric ratios for an angle.
2. Use the Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$ to find unknown trigonometric values.
3. Solve for the value of $\sin\theta$, $\cos\theta$, and $\tan\theta$ when the angle is given.
4. Word problem based on trigonometric ratios.

Chapter 9: Some Applications of Trigonometry

1. Find the height of a tower using trigonometric ratios if the angle of elevation from a point on the ground to the top of the tower is known.
2. A ladder is leaning against a wall. Use trigonometry to find the height where the ladder touches the wall.
3. Calculate the distance between two buildings using trigonometric ratios.

Chapter 10: Circles

1. Prove that the angle subtended by a chord at the center of the circle is twice the angle subtended on the circumference.
2. Prove the tangent at any point of a circle is perpendicular to the radius at that point.
3. Find the length of a tangent drawn from a point outside the circle.

Chapter 11: Constructions

1. Construct a triangle given the three sides using the compass.
2. Construct a triangle with a given base, the sum of the other two sides, and the included angle.
3. Construct the locus of points that are equidistant from two given points.

Chapter 12: Areas of Parallelograms and Triangles

1. Prove that the area of a triangle is half the base multiplied by the height.
2. Find the area of a quadrilateral if the diagonals are given.
3. Find the area of a triangle using the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.

Chapter 13: Surface Areas and Volumes

1. Find the surface area of a sphere.
2. Find the volume of a cone with given radius and height.
3. Find the volume of a cylinder with given radius and height.
4. Word problems on surface area and volume of cones, cylinders, and spheres.

Chapter 14: Statistics

1. Find the mean, median, and mode for a given set of data.
2. Calculate the mode of a frequency distribution.
3. Calculate the range and standard deviation for a set of data.

Chapter 15: Probability

1. Calculate the probability of drawing a red card from a standard deck of cards.
2. Find the probability of getting an even number when rolling a dice.
3. Find the probability of getting a head when tossing a coin twice.

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