Certainly, I can help you with important questions for CBSE Class 10 Maths. However, please note that I don’t have access to specific updates or changes in the curriculum beyond my last update in September 2021. Therefore, I can provide you with general topics and types of questions that are often important in Class 10 Maths. You should consult your current textbooks and teachers for the most accurate and up-to-date information.
Here are some important topics and sample questions for Class 10 Maths:
1. Real Numbers: a) Prove that √2 is an irrational number. b) Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3k or 3k+1.
2. Polynomials: a) Factorize: x^2 – 5x + 6 b) Find the value of k for which the polynomial 2x^3 – kx^2 + 8x – 5 has (x – 1) as a factor.
3. Pair of Linear Equations in Two Variables: a) Solve the pair of equations: 3x + 4y = 10 and 2x – 3y = 1. b) Represent the following situation algebraically: “The sum of two numbers is 12. If one number is twice the other, find the numbers.”
4. Quadratic Equations: a) Find the roots of the quadratic equation: 2x^2 – 5x – 3 = 0 b) If one root of the quadratic equation x^2 – px + 16 = 0 is 4, find the value of p.
5. Triangles: a) In triangle ABC, if AD is the median, prove that AB + AC > 2AD. b) Prove that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
6. Coordinate Geometry: a) Find the coordinates of the midpoint of the line segment joining A(-2, 3) and B(4, -5). b) Find the distance between points P(3, -2) and Q(1, 4).
7. Trigonometry: a) Prove that sin^2θ + cos^2θ = 1. b) If tanθ = 4/3, find sinθ and cosθ.
8. Circles: a) Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. b) Find the length of the tangent drawn from a point 8 cm away from the center of a circle of radius 5 cm.
9. Constructions: a) Construct a triangle XYZ with XY = 6 cm, YZ = 7 cm, and angle XYZ = 60°. b) Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4 cm, CD = 7 cm, AD = 5 cm, and AC = 8 cm.
10. Areas Related to Circles: a) Find the area of a sector of a circle with radius 10 cm and angle of sector 60°. b) In a circle of radius 7 cm, an arc subtends an angle of 120° at the center. Find the length of the arc.
Remember, practicing a variety of questions from each topic will help you gain a better understanding of the concepts and improve your problem-solving skills. Make sure to refer to your current textbook and any guidelines provided by your teachers for the most accurate information.