Half Yearly Class 9 Mathematics Set 1 | 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. Express as a fraction.  (1 Mark) 

Q2.  Find the degree of the polynomial 3x⁴ − 5x² + 2.  (1 Mark) 

Q3. Write the coordinates of the point where the x-axis and y-axis intersect.  (1 Mark) 

Q4.  In ax + by + c = 0, what is b if the line is parallel to the x-axis?  (1 Mark) 

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

Q6. If one angle of a triangle is 80and the other two are equal, find each equal angle.  (1 Mark) 

Q7. Simplify: √18.  (1 Mark) 

Q8.  If (x − 3) is a factor of x² − 5x + k, find k.  (1 Mark) 
Q9. In which quadrant does the point (2, −5) lie?  (1 Mark) 

Q10.  If two lines intersect, what is the measure of a pair of vertically opposite angles?  (1 Mark) 

Section B

Q1. Rationalize the denominator:   (2 Marks) 

Q2. Find the remainder when p(x) = x³ − 4x² + 6x − 1 is divided by x − 2.  (2 Marks)

Q3. Find the distance between points P (1, 4) and Q(−3, −2).  (2 Marks)

Q4.  Solve 3x + 2y = 10 for y when x = 2.  (2 Marks)

Q5. If two angles on a straight line are (2x + 10)^o and (x − 10)^o, find x.  (2 Marks)

Section C

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

Q2.  Using factor theorem, show that (x + 1) is a factor of x³ + x² − 2x − 2.  (3 Marks) 

Q3.  Find the coordinates of the midpoint of the line segment joining A(−2, 3) and B(4, −1).  (3 Marks) 

Q4. Solve: x + y = 5 and 2x − y = 4 using substitution method.  (3 Marks) 

Q5. Using Euclid’s postulates, prove that a line segment can be drawn joining any two points.  (3 Marks) 

Q6. In △PQR, ∠P = 50°, ∠Q = 70°. Find ∠R. If ST ∥ QR, find ∠P ST.  (3 Marks) 
Q7. Find k such that x²  + kx + 4 has equal roots.  (3 Marks) 

Q8. Express as a fraction.  (3 Marks)  

Q9. Simplify:   (3 Marks) 

Q10. Solve: 4x − y = 8 and 2x + y = 7 using substitution method.  (3 Marks) 

Section D

Q1. Factorize x³  − 7x  + 14x − 8 completely.  (6 Marks) 

Q2. In the coordinate plane, find the area of △ABC  with vertices A(0, 0), B(3, 0), C (1, 4). Is it a right-angled triangle?  (6 Marks) 

Q3. Prove that vertically opposite angles are equal when two lines intersect. Use this to show that the sum of angles in a triangle is 180° .  (6 Marks) 

Q4. Solve graphically: x + y = 6 and 2x − y = 3. Find the area of the triangle formed by these lines and the y-axis.  (6 Marks) 

Q5. Solve: 2x + 3y = 11 and x − 2y = −2 using elimination method. Verify the solution.  (6 Marks) 

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