Half Yearly Class 9 Mathematics Set 2 | Mathematics (Maths) Class 9 PDF Download

Time: 3 Hours
Maximum Marks: 80
General Instructions:
(i) The question paper comprises four sections: A, B, C, and D. 
(ii) All questions are compulsory. However, internal choices are provided in some questions. 
(iii) Section A has 10 Questions carrying 1 mark each.
(iv) Section B has 5 Questions carrying 2 marks each.
(v) Section C has 10 Questions carrying 3 marks each.
(vi) Section D has 5 Questions carrying 6 marks each.
(vii) Use of calculators is not permitted.

Section A

Q1. Is 2/7 a terminating decimal?   (1 Mark) 

Q2. How many zeroes does the polynomial x² − 4 have?   (1 Mark) 

Q3. What is the x-coordinate of a point on the y-axis?   (1 Mark) 

Q4. If 2x − 3y = 6 is a linear equation, what is its slope?   (1 Mark) 

Q5. State Euclid’s third postulate.   (1 Mark) 

Q6. If two angles of a triangle are complementary, what is the third angle?   (1 Mark) 

Q7. Simplify: √12.   (1 Mark) 

Q8. If p(2) = 0 for p(x) = x² − kx + 4, find k.   (1 Mark) 

Q9. In which quadrant does (−4, −2) lie?   (1 Mark) 

Q10. If two lines are parallel, what is the measure of their corresponding angles?   (1 Mark) 

Section B

Q1. Express 5/11 as a decimal.   (2 Marks)

Q2. Find the sum of the zeroes of 2x² − 8x + 6.   (2 Marks)

Q3. Find the coordinates of the point dividing A(3, 2) and B(−1, −4) in the ratio 1:1.   (2 Marks)

Q4. Solve 5x − 2y = 10 for x when y = 5.   (2 Marks)

Q5. If ∠A = 40°  and ∠B = 50° in ΔABC, Find ∠C.   (2 Marks)

Section C

Q1. Prove that √7 is irrational.   (3 Marks)

Q2. Find the zeroes of x² − 5x + 6.   (3 Marks) 

Q3. Find the coordinates of the point dividing A(2, −3) and B(−4, 5) in the ratio 2:3.   (3 Marks) 

Q4. Solve: 3x + 2y = 12 and x − y = 1 using elimination method.   (3 Marks) 

Q5. Using Euclid’s axioms, explain why a point has no dimension.   (3 Marks) 

Q6. If AB ∥ C D and a transversal intersects them, find the alternate interior angles if one angle is 70°.   (3 Marks) 

Q7. Find k such that 3x²  + kx + 12 has equal roots.   (3 Marks) 

Q8. Express as a fraction.   (3 Marks) 

Q9. Simplify:    (3 Marks) 

Q10. Solve: 2x + 3y = 9 and 4x − y = 5 using elimination method.   (3 Marks) 

Section D

Q1. Find the quotient and remainder when x³ − 5x² + 6x − 2 is divided by x − 2.   (6 Marks) 

Q2. For points A(1, 1), B(5, 1), C (3, 4), find the distance AC and check if △ABC is equilateral.   (6 Marks) 

Q3. Prove that alternate interior angles are equal for parallel lines cut by a transversal.   (6 Marks) 

Q4. Solve graphically: 2x + y = 8 and x − 2y = 1. Find the area of the triangle formed by these lines and the x-axis.   (6 Marks) 

Q5.Solve: 3x − y = 7 and 2x + 3y = 1 using elimination method.  Verify the solution.   (6 Marks) 

You can access the solutions to this Half Yearly here.