# Summative Assessment Paper-2

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### Summative Assessment Paper-2

• 1. Mathematics IX (Term - I) 1 SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice). 1. If mn = 32, where m and n are natural numbers, then nm equals : (a) 12 (b) 15 (c) 25 (d) 64 2. If p(x) = x2 – 2 2 x + 1, then p(2 2 ) is equal to : (a) 0 (b) 1 (c) 4 2 (d) 8 2 +1 3. The sides of a triangular flower bed are 5 m, 8 m and 11 m. The area of the flower bed is : (a) 2 4 21 m (b) 2 21 4 m (c) 2 330 m (d) 2 300 m 4. Area of the given traingle is : (a) 60 cm2 (b) 30 cm2 (c) 78 cm2 (d) 32.5 cm2 5. On factorising 4x2 + y2 + 1 + 4xy + 2y + 4x, we get : (a) (2x + y)2 (b) (2x + 2y + 1)2 (c) (x + y + 1)2 (d) (2x + y + 1)2 6. If x51 + 51 is divided by (x + 1), the remainder is : (a) 0 (b) 1 (c) 50 (d) 49 7. In the figure, l || m and t is a transversal. If ∠1 = (110° – x) and ∠5 = 4x, then the measures of ∠1 and ∠5 respectively are : (a) 55°, 55° (b) 22°, 88° (c) 55°, 88° (d) 88°, 88° 8. In the figure, ABC is a triangle, having sides BC and CA produced to D and E respectively. Which of the following is correct? (a) AB > BC (b) AB > AC (c) AC > BC (d) BC > AC MODEL TEST PAPER – 3 (UNSOLVED) Maximum Marks : 90 Maximum Time : 3 hours General Instructions : Same as in CBSE Sample Question Paper.
• 2. 2 Mathematics IX (Term - I) SECTION B (Question numbers 9 to 14 carry 2 marks each) 9. Express 1.27 in the form p q , where p and q are integers and q ≠ 0. 10. Verify whether m l is a zero of the polynomial p(x) = lx + m. 11. Using a suitable identity, expand (–2x + 3y + 2z)2 . 12. What is the perpendicular distance of the point A(7, – 4) from (i) x-axis (ii) y-axis? 13. In ∆ABC and ∆DEF, ∠A = ∠D, ∠B = ∠E and AB = EF. Will the two triangles be congurent? Justify your answer. OR In the figure, if OX = 1 2 XY, PX = 1 2 XZ and OX = PX, show that XY = XZ. 14. For what value of x + y (see the figure) will ABC be a line? Justify your answer. SECTION C (Question numbers 15 to 24 carry 3 marks each) 15. Simplify by rationalising the denominator : 4 4 4 5 4 5 4 5 + + + 16. Write the following in descending order of magnitude : 3 4 23 3 5 , , OR Simplify : 3 5 8 5 32 3 4 12 6 ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ 17. The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by (x + 1), leaves the remainder 19. Find the value of a. Also, find the remainder when p(x) is divided by (x + 2). 18. If x + y + z = 9 and xy + yz + zx = 26, find x2 + y2 + z2 . OR Factorise : 4x2 + 9y2 + 16z2 + 12xy – 24yz – 16zx 19. In the figure, find the area of the trapezium PQRS with height PQ. X Y PO Z
• 3. Mathematics IX (Term - I) 3 20. In the figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS. 21. Prove that the sum of the angles of a triangle is 180°. 22. In the figure, diagonal AC of a quadrilateral ABCD bisects the angles A and C. Prove that AB = AD and CB = CD. 23. AD and BC are equal perpendiculars to a line segment AB (see fig). Show that CD bisects AB. OR ABC and DBC are two isosceles triangles on the same base BC (see fig.) Show that ∠ABD = ∠ACD 24. In the figure, ∠Q > ∠R. If QS and RS are bisectors of ∠Q and ∠R respectively, then show that SR > SQ. SECTION D (Question numbers 25 to 34 carry 4 marks each) 25. Without actual division prove that (x – 2) is a factor of the polynomial 3x3 – 13x2 + 8x + 12. Also, factorise it completely. 26. If x2 + 2 1 x = 7, find the value of x3 + 3 1 x . 27. If two parallel lines are intersected by a transversal, then prove that the bisectors of the interior angles form a rectangle. OR In the given figure, AB || CD. Find the value of x
• 4. 4 Mathematics IX (Term - I) 28. In a ∆ABC, AD the angle bisector of ∠BAC intersects BC at D. Show that AB > BD. 29. In the figure, ABC is a triangle in which AB = AC and BE = CD. Prove that AD = AE. 30. Prove that if the line bisecting the vertical angle of a triangle is perpendicular to the base, the triangle is isosceles. 31. Factorise : 12(x2 + 7x)2 – 8(x2 + 7x) (2x – 1) – 15(2x – 1)2 . OR Factorise : 1 27 2 5 5 3 3 4 3 4 2 3 3 3 3 ( )x y y z z x+ + + ⎛ ⎝⎜ ⎞ ⎠⎟ + ⎛ ⎝⎜ ⎞ ⎠⎟ 32. On the coordinate axes, draw a triangle PQR whose vertices are P(1 ,– 6), Q(7, 4) and R (– 4, 4) 33. Represent 9 3. on the number line. 34. If x = 3 2 3 2 3 2 3 2 + = + and y , find the value of x2 + y2 . A B C D E