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|| CBSE Class 9 Term 1 Maths Question Paper 2022 23 ||


If you are searching Class 9 Maths Term 1 Question Paper, then you will at a right place. Here you will get all subject question paper and all subject solutions of DAV, NCERT . 
      
                    HALF YEARLY EXAM

STD : IX                                           F. M : 80
 
SUB : MATHS                                 TIME : 3HRS.

INSTRUCTIONS :

• All questions are compulsory. 
• This question paper contains 33 Questions divided into Section A, B, C and D. 
• Section A comprises of 10 questions 1 mark each. Section B comprises 6 questions of 2 marks each. Section C comprises 10 questions 3 marks each. Section D comprises 7 questions 4 marks each. 


                               Section A

1. What is origin in Cartesian system? 
2. Write the standard form of a linear equation in two variables. 
3. Euclid began his exposition by listing how many definitions in Book 1 of the ' Elements' ? 
4. What is xam plane? 
5. State 'PLAYFAIR' axiom. 
6. One of the angles of a triangke is 50° and the other two angles are equal. Find the measure of each of the equal angles. 
7. State true or false. 
i Every integer is a whole number. 
ii) Every real number is irrational. 
8. If AC = BD then prove that AB= CD
9.Define transversal lines . 
10. Find two solutions of equation  5x–2y= 13.

                            Section B

11. Factorise 2x²+ + y² + 8z²-2√2 xy +4√2 yz - 8zx.
12. Without actually calculating the cubes, find the values of (x - 2y³) +(2y - 3z) ³ + (3z- x) ³.
13.Construct 22½° and justify the construction 
14.Prove that angles opposite to equal sides of an isosceles triangle are equal. 
15. Three vertices of a rectangle are (-1, 1), (5, 1) , and (5, 3). Plot these points and find the co - ordinates of the fourth vertex. 
16. The angles of a quadrilateral are in the ratio of  3:5:9:13. Find all the angles of a quadrilateral. 

                             Section C

17. Show that the sum of any two sides of a triangle is greater than the third side. 
18. D is the point on side BC of triangle ABC such that AD= AC. Show that AB>AD.
19. Factorise : x³- 23x²+142x-120.
20. If x= 1+√2 , find the value of (x -¹/x) ³ . 
21. Visualise 3.456 on the number line using successive magnification. 
22. Write Euclid's fifth postulate. Does Euclid's fifth postulate imply the existence of parallel lines? Explain. 
23. Construct a ∆ ABC in which BC= 7cm, B= 75° and AB+AC= 13 cm
24. Without actual division prove that 2x⁴ – 5x³ + 2x² –x + 2 divisible by x²– 3x + 2.
25.  Locate √3 on number line. 
26.  An isosceles triangle has perimeter 40 cm and each of the equal side is 12 cm. Find the area of a triangle. 
          
                                 Section D
                
27 . Give the geometric representation oy y+ 3 = 0 as an equation in :
a) one variable
b) two variables
28. If in two right triangles,  hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangles, prove that the two triangles are congruent . 
29. ABCD is a rectangle and P, Q, R ans S are mid- points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus. 
30. The polynomial f(x) = x⁴ –2x³ + 3x² -ax + b when divided by ( x –1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f(x) is divided by (x–3). 
31. State and prove remainder theorem. 
32. In  below figure, P is a point in the interior of parallelogram ABCD. Show that
(i) ar(APB )+ ar ( CD) = ½ ar(ABCD) 
ii) ar (APD) + ar (PBC) =ar(APB) + ar(PCD) 
33.  Find the area if a quadrilateral in which AB= 4cm, BC= 5cm , CD= 3cm, DA= 6cm , AC= 8cm.


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