Class 9 Mathematics -Guess paper 2025-26

                                               GUESS PAPER - Math -25-26

Short Questions (50):

1. Define a real number.
2. Write the formula for the difference of squares.
3. Solve: $(x+1)^2 = x^2 + 2x + 1$.
4. Define a polynomial with an example.
5. What is the degree of the polynomial $4x^3 + 2x + 7$?
6. Define a linear equation.
7. Solve: $3x + 5 = 11$.
8. Define a quadratic equation.
9. Write the quadratic formula.
10. Define the discriminant in quadratic equations.
11. Find the value of $a+b$ if $a=3$ and $b=4$.
12. Define arithmetic mean with its formula.
13. Solve: $x^2 - 4 = 0$.
14. Define a set with an example.
15. What is the union of two sets?
16. Define the intersection of two sets.
17. Write the formula for simple interest.
18. Solve for $x$: $2x = 16$.
19. What is a ratio?
20. Write the formula for the midpoint of a line segment.
21. Define slope.
22. Find the slope of a line passing through points (0, 0) and (2, 4).
23. State the Pythagorean theorem.
24. Write the formula for the distance between two points.
25. Define a parallelogram.
26. Find the area of a triangle using the formula $\text{Area} = \frac{1}{2} \text{Base} \times \text{Height}$.
27. Define a circle.
28. What is the radius of a circle?
29. Write the formula for the circumference of a circle.
30. Solve for $x$: $3x - 7 = 8$.
31. Write the general form of a linear equation in two variables.
32. Simplify: $\sqrt{16}$.
33. Write the formula for compound interest.
34. Define the mode of a dataset.
35. What is the range in statistics?
36. Write the formula for finding probability.
37. Solve: $(x-3)^2 = 9$.
38. Define an angle with an example.
39. What is a complementary angle?
40. Define supplementary angles.
41. What is the value of $\sin 90^\circ$?
42. Write the formula for $\tan \theta$.
43. Simplify: $\frac{1}{2} + \frac{3}{4}$.
44. Define a tangent to a circle.
45. Solve: $x^3 = 27$.
46. Write the formula for the surface area of a sphere.
47. Define probability.
48. Find the HCF of 12 and 15.
49. Define a factor of a number.
50. Simplify: $\frac{2}{5} \times \frac{3}{4}$.

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Long Questions (10):

1. Prove the Pythagorean Theorem with a diagram and example.
2. Solve a quadratic equation using the quadratic formula: $x^2 + 5x + 6 = 0$.
3. Derive the distance formula for two points in a coordinate plane.
4. Solve: $2x + 3y = 12$ and $4x - y = 8$ using simultaneous equations.
5. Prove that the sum of angles in a triangle is $180^\circ$.
6. Find the area of a parallelogram given the base and height.
7. Simplify $(x+2)^3$ using the binomial theorem.
8. Find the probability of drawing a red card from a deck of cards.
9. Derive the formula for the circumference of a circle and calculate it for a given radius.
10. Solve: $4x^2 - 25 = 0$ and explain the steps.

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This guess paper is based on commonly repeated and important topics for 9th class Mathematics. If you need detailed solutions or guidance for any question, let me know! 😊