CBSE Class 9 Mathematics Question Paper

Chapters 1-7 (Number Systems to Triangles)

General Instructions:

• All questions are compulsory.
• The question paper consists of 30 questions divided into 4 sections: A, B, C, and D.
• Section A: 10 MCQs (1 mark each), Section B: 5 VSA (2 marks each), Section C: 10 SA (3 marks each), Section D: 5 LA (4 marks each).
• Total Marks: 80, Time: 3 hours.

Section A: Multiple Choice Questions (1 Mark Each)

1. (Number Systems) Which statement is NOT true? (Page 9)

\[ \text{a. Every rational number is a real number.} \]

\[ \text{b. Every integer is a rational number.} \]

\[ \text{c. Every real number is a rational number.} \]

\[ \text{d. Every whole number is an integer.} \]

a b c d

Correct Answer: Option c

2. (Number Systems) Which option shows a way to represent 7.356 on a number line? (Page 11)

a b c d

Correct Answer: Option a

3. (Polynomials) For what value of \( m \), will the expression \( x(m^{m-1}) + 3x\sqrt[3]{m} \) be a cubic polynomial? (Page 19)

\[ \text{a. -2} \]

\[ \text{b. 1} \]

\[ \text{c. 5} \]

\[ \text{d. 7} \]

a b c d

Correct Answer: Option a

4. (Coordinate Geometry) In which quadrant does the point (5, -7) lie? (Page 28)

\[ \text{a. First Quadrant} \]

\[ \text{b. Second Quadrant} \]

\[ \text{c. Third Quadrant} \]

\[ \text{d. Fourth Quadrant} \]

a b c d

Correct Answer: Option d

5. (Linear Equations) Which of these represents the graph of the equations: (Page 35)

\[ 2(x + 4y - 2) + 6(x - y) = 6 + 2y \]

\[ 3(x - 3) + 18(x + y) = 8(6y + 5) - 3x \]

a b c d

Correct Answer: Option c

6. (Euclid Geometry) For what value of \( x \) are the lines parallel? (Page 43)

\[ \text{a. Condition 1 alone is sufficient.} \]

\[ \text{b. Condition 2 alone is sufficient.} \]

\[ \text{c. Both conditions are necessary.} \]

\[ \text{d. Neither condition is sufficient.} \]

a b c d

Correct Answer: Option c

7. (Lines and Angles) Two lines are cut by a transversal. What is the measure of the angle? (Page 49)

a. 150° b. 30° c. 90° d. 120°

Correct Answer: Option b

8. (Triangles) What additional information is required to prove \( \triangle TOI \cong \triangle SOD \)? (Page 58)

\[ \text{a. } \angle M = \angle S \]

\[ \text{b. } \angle T = \angle D \]

\[ \text{c. } TO = SO \]

\[ \text{d. } TI = SD \]

a b c d

Correct Answer: Option a

9. (Triangles) Which of these pairs of triangles are not congruent? (Page 60)

a b c d

Correct Answer: Option c

10. (Triangles) In triangle \( \triangle LMN \), \( LN = MN \). If \( JK = 13 \, \text{cm} \), which could be the length of \( LK \)? (Page 61)

\[ \text{a. 9 cm} \]

\[ \text{b. 13 cm} \]

\[ \text{c. 17 cm} \]

\[ \text{d. 26 cm} \]

a b c d

Correct Answer: Option a

Section B: Very Short Answer Questions (2 Marks Each)

11. (Number Systems) Convert \( \frac{15}{x^2 + 2x} \) to an equivalent number whose denominator is a rational number. (Page 13)

Answer: ____________________

12. (Polynomials) Using the Remainder Theorem, find the remainder when \( p(x) = x^3 - 2x^2 + x - 1 \) is divided by \( x - 1 \). (Page 22)

Answer: ____________________

13. (Coordinate Geometry) Plot the point \( P(2, -3) \) on the Cartesian plane and state its quadrant. (Page 27)

Answer: ____________________

14. (Linear Equations) Solve the equation \( 2x + 3y = 32 \) for \( y \) when \( x = 4 \). (Page 38)

Answer: ____________________

15. (Euclid Geometry) State Euclid's fifth postulate. (Page 40)

Answer: ____________________

Section C: Short Answer Questions (3 Marks Each)

16. (Number Systems) Represent \( \sqrt{2} \) on a number line using successive magnification. Explain the steps. (Page 14)

Answer: ____________________

17. (Polynomials) Factorize the polynomial \( x^2 + 5x + 6 \) using the splitting middle-term method. (Page 21)

Answer: ____________________

18. (Coordinate Geometry) Find the distance between points \( A(m, 2n) \) and \( B(n+1, m) \) given \( m < 0, n > 0 \). (Page 26)

Answer: ____________________

19. (Linear Equations) A person invested some amount at 7% per annum simple interest and after 1 year, the interest was \( \frac{1}{10} \) of the principal. Form the linear equation and solve for the principal. (Page 36)

Answer: ____________________

20. (Euclid Geometry) Differentiate between axioms and postulates with one example each. (Page 41)

Answer: ____________________

21. (Lines and Angles) Two lines are cut by a transversal, and one angle is \( 150^\circ \). Find the measures of the corresponding and alternate interior angles. (Page 48)

Answer: ____________________

22. (Triangles) Prove that in \( \triangle LMN \), if \( LN = MN \), then the angles opposite these sides are equal. (Page 61)

Answer: ____________________

23. (Triangles) In \( \triangle ABC \), if \( \angle A = 50^\circ, \angle B = 60^\circ \), find \( \angle C \) using the angle sum property. (Page 56)

Answer: ____________________

24. (Lines and Angles) Prove that the sum of two adjacent angles formed by two intersecting lines is \( 180^\circ \). (Page 98)

Answer: ____________________

25. (Triangles) Explain the SAS congruence criterion with a diagram. (Page 62)

Answer: ____________________

Section D: Long Answer Questions (4 Marks Each)

26. (Number Systems) Prove that \( \sqrt{3} \) is an irrational number by contradiction. (Derived from Page 9)

Answer: ____________________

27. (Polynomials) Divide \( p(x) = x^4 - 3x^2 + 4x + 5 \) by \( x^2 + 1 - x \) and find the quotient and remainder. (Derived from Page 20)

Answer: ____________________

28. (Coordinate Geometry) Derive the section formula for a point dividing the line segment joining \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \). (Derived from Page 31)

Answer: ____________________

29. (Linear Equations) Solve the system of equations graphically: \( 2x + y = 6 \) and \( x - y = 2 \). Find the point of intersection. (Derived from Page 35)

Answer: ____________________

30. (Triangles) Prove the midpoint theorem of triangles using concepts of congruency. (Derived from Page 68)

Answer: ____________________