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Sample Paper (Based on CBSE CCE SA - 1) (IX) MATHEMATICS [Time allowed: 3 hours] [Maximum marks: 80] General Instructions: 1. All questions are compulsory. 2. The question paper consists of 34 questions divided into 4 sections, section A, B, C, and D. 3. Section A contains 10 multiple choice type questions each carry 1 mark. Section B contains 8 questions of 2 marks each, section C contains 10 questions of 3 marks each and section D contains 6 questions of 4 marks each. 4. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. Attempt only one of the alternatives in all such questions. 5. Use of calculators is not permitted. SECTION - A 1. Which of the following represents a rational number (a) 2 − 5 (b) 2 + 9 5 7 (c) 3 3 (d) 4 2. The degree of the polynomial (x2 + 3) (3 – x3) is (a) 3 (b) 6 (c) 2 (d) 5 3. The value of k for which, (2k – 30) and (4k) form a supplementary pair is o o (a) 40° (b) 35° (c) 20° (d) 90° 4. In a quadrilateral ABCD, AB = AD and AC bisects ∠A, which congruence criterion will make ∆ABC ≅ ∆ADC (a) ASA (b) SAS (c) AAS (d) SSS 5. Which of the following is not a criterion for the congruence of triangles (a) SAS (b) ASA (c) SSA (d) SSS 6. In geometry, there are ___________ undefined terms (a) 4 (b) 3 (c) 2 (d) 1 AVTE/IX/M/10-11/Sept./SA-1 1 7. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is (a) an isosceles (b) an obtuse (c) a right (d) an equilateral 8. An angle which differ from its complement angle by 20o is (a) 55o (b) 45o (c) 25o (d) 10o 9. 4 16 − 8 3 8 + 4 5 243 is equal to (a) –2 (b) 2 (c) 4 (d) –3 10. In ∆ABC, AD is a median, then (a) AB + AD > 2AC (b) AB + AC > 2AD (c) A D + AC > 2AB (d) AB +AC < 2AD SECTION - B A 11. If a + b + c = 8, ab + bc + ca = 19, find a2 + b2 + c2 . O 12. In fig. 1, OA ⊥ OD, OC ⊥ OB, OD = OA and OC = OB. D C Prove that AB = CD. Fig. 1 B −1 3 1 2 13. Simplify: 64 64 − 64 3 3 14. Solve the equation : x – 15 = 20 and state which axiom do you use here. 15. Factorise: x3 + x2 – 4x – 4. 16. Two adjacent angles are equal. Is it necessary that each of these angles will be right angle? Justify your answer. 17. Which of the following points do not lie in any quadrants? E A (i) (8, 5) (ii) (0, 5) C 2y 2y D O (iii) (6, 3) (iv) (–3, 0) 5y B F 18. In fig. 2, AB, CD and EF are three concurrent lines at O. Fig. 2 Find the value of y. l m n y x OR a b In fig. 3, x = y and a = b. Prove that l || n. Fig. 3 AVTE/IX/M/10-11/Sept./SA-1 2 SECTION - C 19. Find a and b; 3 + 7 = a + b 7 . 3−4 7 P T 20. Factorise : x – y . 8 8 21. In fig. 4, side QR of ∆PQR has been produced to S. Q R S If ∠P : ∠Q : ∠R = 3 : 2 : 1 and RT ⊥ PR, find ∠TRS. Fig. 4 22. Locate 17 on the number line. 23. Without actually calculating cubes, find the value of 483 – 303 – 183. 24. True or False? Justify your answer. (i) If area of rectangle equals the area of square and the area of square equals area of triangle, then area of rectangle also equals the area of the triangle. (ii) The statement that are proved called as axioms. P 25. In fig. 5, QP ⊥ PR, BA ⊥ AC such that PQ = BA and QC = BR. R B Q C Prove that ∆PQR ≅ ∆ABC. Fig. 5 A OR A D In fig. 6, ∠A = ∠D and ∠ACB = ∠CBD. Prove that AC = DB. B C Fig. 6 26. In a quadrilateral PQRS, prove that PQ + QR + RS + PS > 2PR. 27. Plot the points P(1,4), Q(1, –1), R(7, –1) and S(7, 4). Name the figure and also find its area. OR Find some ordered pairs (x, y) such that x + 2y = 5 and plot them. How many such ordered pairs can be found and plotted? 28. Find the area of an isosceles triangle, the measure of one its equal sides being b and the third side is a. OR A triangle and a parallelogram have the same base and same area. If the sides of the triangle are 90 cm, 84 cm and 78 cm and the parallelogram stands on the base 90 cm, find the height of the parallelogram. AVTE/IX/M/10-11/Sept./SA-1 3 SECTION - D 29. Factorise : (a2 - 2a)2 - 23(a2 - 2a) + 120. −7 30. (i) Represent on the number line. 5 p (ii) Express 0.004646..... in the form of . q 31. Find the values of a and b so that polynomials x3 + 10x2 + ax + b is exactly divisible by (x – 1) as well as (x + 2). OR A If x + y + z = 9 and x2 + y2 + z2 = 35, find the value of x3 + y3 + z3 - 3xyz. 32. In fig. 7, the bisectors of ∠ABC and ∠BCA intersect each other at the point O. O 1 Prove that, ∠BOC = 900 + ∠A. 2 B Fig. 7 C 33. If D is the mid-point of the hypotenuse AC of right angled triangle ABC. 1 Prove that BD = AC . 2 T S R Q 34. (i) ABC is an isosceles triangle with AB = AC, side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle. (ii) In the given fig. 8, PS = PR, ∠TPS = ∠QPR. Prove that PT = PQ. Fig. 8 P OR In Fig. 9, the side QR of D PQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS 1 meet at point T, then prove that ∠QTR = ∠QPR . 2 Fig. 9 For answers log on www.avteschool.org or send a mail to avte37@yahoo.co.in AVTE/IX/M/10-11/Sept./SA-1 4

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