If you are searching CBSE Class 9 Maths Half Yearly Question Paper 2022- 23 then you will at a right place. Here you will get Subject Question Paper of CBSE Class 9.
DAV PUBLIC SCHOOL
Term - 1 Examination 2022 - 23
Class - IX Time : 3Hrs
Subject - Mathematics M. M : 80
General Instructions :
i)The question paper comprises of four sections A, B, C and D. You are to attempt all the sections.
ii) All questions are compulsory.
iii) Internal choice are given in section B, C and D.
Section - A
1. Choose and write the correct option in each of the following questions. (10x1= 10)
i) The sum of any two irrational numbers
a) is always a rational number
b) is never a rational number
c) is always a irrational number
d) can be a rational number
ii) What is the decimal representation of an irrational number?
a) Always terminating
b) Always non- terminating
c) Neither terminating nor repeating
d) Repeating
iii) If x+y = -4 and xy = 2 , then the value of x²+y² is
a) 16
b) 12
c) 18
d) None of these
iv) The polynomial px²+ qx+ rx⁴+5 is of type
a) Linear
b) Quadratic
c) Cubic
d) Biquadratic
v) The perpendicular distance of the point P(5, 7) from y- axis is
a) 5
b) 12
c) 2
d) 7
vi) The graph of the linear equation 2x+ 3y = 6 is a line which meets the x- axis at the points
a) (0, 2)
b) (2, 0)
c) (0, 3)
d) (3, 0)
vii) If the supplement of an angle is four times of its complement, then angle is
a) 60°
b) 50°
c) 80°
d) 100°
viii) If the coordinates of two points are P(-2, 3) and Q(-3, 5) , then the value of (abscissa of P) - (abscissa of Q) is
a) 1
b) -5
c) -2
d) 8
ix) Which of the following is not a criterion for congruence of triangles?
a) SAS
b) ASA
c) SSA
d) SSS
x) If PQRS is a parallelogram, then <P - <R is
a) 45°
b) 90 °
c) 60°
d) 0°
2. Answer the following questions : (5x1= 5)
i)Write a rational number between √ 2 ans √3
ii)The two angles measuring (30°-a) and (125°+2a) are supplementary to each other. Find the value of a.
iii) Is triangle ABC possible, if <A=40° , <B= 130° and <C = 40°
iv) Write the coefficient of x² in the expansion of (X - 2)³.
v) Three angles of a quadrilateral are 75,90 and 75. What is it's fourth angle?
3. Fill in the blanks. ( 5x1= 5)
i) If (x+1) is a factor of 2x²+ kx then the value of k is ______________
ii) Equation of x-axis is ____________
iii) A point in ______________ quadrant has positive abscissa and negative ordinate.
iv) Diagonals of a rectangle bisect each other and are ______________.
v) Lines which are parallel to a given line are ______________ to each other.
Section - B
Question numbers 4 to 9 are of 2 marks each.
4. Express 18.4888888.... in the form of p/q, where p and q are integers and q≠0.
5. Plot the points A(3, 0) B (3, 3)and C (0,3) in the Cartesian plane. Join OA, AB, BC ans CO. Name the figure so formed.
6. Factorise 4x² - 1- 6y - 9y²
Or
Find the factors of (1-x³)
7. Without finding the cubes, factorise ( x-2y) ³+ ( 2y- 3z)³+ ( 3z- x) ³
8. In ∆ PQR < Q = 40° and <R = 72° , then find the shortest and the longest sides of a triangle.
Or
Prove that opposite to equal sides of a triangle are equal.
9. The angles of a quadrilateral are in the ratio 3:5:9:13 . Find all the angles of the quadrilateral.
Section - C
Question numbers 10 to 17 are of 3 matks each.
10. Represent √5 on number line.
Or
Visualise 5.378 on the number line.
11. If the polynomial kx³ + 3x² - 8 a d 3x³ -5x + k leave the same remainder when divided by x +2, then find the value of k.
12. Yamini and Fatima together contributed Rs. 100 towards Prime Minister's Relief Fund to help the earthquake victims. Write a linear equation with this data. Draw the graph of the same.
Or
The cost of a toy is same as that of cost of three balls. Express this statement as a linear equation in two varible. Also draw its graph.
13.The taxi fare in a city is as follows : for the 1st kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs 5 per kilometer. Taking the distance covered as x km and the total fare as Rs y, write a linear equation for this information and draw it's graph.
14. In the figure, if l||m and < 1 = ( 2x+y) ° and < 3 = (3y+20) ° , find <4 and <5
15. In the adjoining figure if AB = AC, <B= 50° snd AD is median, then find < BAD.
16. Show that the line segment joining the mid points of the opposite sides of a quadrilateral bisect each other.
17. In figure, ABC and DBC are two isosceles triangle on the same base BC. Show that <AND = < ACD.
Section - D
Question numbers 18 to 23 are of 4 marks each.
18. Find four irrational numbers between 1/7 and 2/7.
19. If x = 3+2√2 , the find the value of x³ - ¹/x³.
Or
Factorise x⁴-y⁴
20. Students in a school are preparing flags as shown in figure for a rally to make people aware for saving water. In the diagram ∆ ABC is shown with AC extended through point D. If <BCD = 6x+ 2 , < BAC = 3x+5 and < ABC = 2x-1 , what is the value of x?
State the property to solve this problem.
21. Prove that the sum of angles of a triangle is 180°.
Or
If the bisector of angles <B and <C of a triangle ABC meet at a point of O, then prove that < BOC = 90° +½<A
22. Prove that the line segment joining the mid points of two sides of a triangle is parallel to the third side and is half of it.
23 ∆ ABC is an isosceles triangle un which AB = AC. Side BA is produced to D such that AD = AB . Show that <BCD is a right angle.
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