CBSE 2010, Maths, Sample Question Paper 20, Class IX

http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Sample Paper – 2010 Class – IX Subject – Maths SET – B Time : 3 hrs M. Marks 80 General Instructions: i. All questions are compulsory. ii. The question paper consists of 30 questions divided into four sections – A, B, C and D. Section A contains 10 questions of 1 mark each, Section B is of 5 questions of 2 marks each, Section C is of 10 questions of 3 marks each and section D is of 5 questions of 6 marks each. iii. There is no overall choice. However, an internal choice has been provided in two questions of three marks each and two questions of six marks each. SECTION A 1. Express 1/7 in decimal form. 2. Give example of two irrational numbers whose sum is a rational number. 3. If p(x) = x3 + 2x2 – x –1, find p(–3) 4. In which quadrant (–4,3) lie? 5. In (–2,5) abscissa is __________. 6. Give a solution for equation 2x – 5y = 8. 7. Every integer is rational number. True or False. 8. Simplify 23/10 . 21/5 9. Define angle. 10. The complement of 25° is _________. SECTION B 11. Calculate the value of x. 12. Evaluate (–2x – 5y + z)2 13. Rationalise 5√2 – 2√3 2√2 + √3 14. Check whither 4t3 + 4t2– t – 1 is a multiple of 2t + 1. 15. Find ∠DOC, if ∠AOC + ∠DOB = 75°. SECTION C 16. State and prove remainder theorem. or If the polynomials ax3 + 4x2 + 3x – 4 and x3 – 4x + a leave the same remainder when divided by x – 3, find the value of a. http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com 17. Calculate without actual calculation a. 92.5 × 107.5 b. (–7)3 + (12)3 – (5)3 OR Factorise (any 2) a. (x2 + x)2 + 4(x2 + x) – 12 b. 2√5a2 – 7 a – 3√5 c. 27y3 – 125z3 18. Express 1 with a rational denominator. √6 + √5 – √11 19. If a transversal intersects two parallel lines, prove that the bisectors of a pair of corresponding angles will be parallel. 20. In the given figure OR and OT bisects ∠POS and ∠SOQ respectively and ∠ROT=90°, prove that P, O and Q are collinear 21. Factorise x3 – 8x2 + 17x – 10 22. Find the area of the quadrilateral whose sides are 60cm, 11cm, 15cm and 52cm respectively and the angle between first two sides is right angle. Calculate its area. 23. Represent √21 on number line. 24. The volume of a box is given by 2x3 + 10x2 – 28x. Express the possible dimensions of the box as linear polynomials. 25. Find x, y, z SECTION D 26. A field is in the shape of a trapezium whose parallel sides are 25 cm and 10 cm and non–parallel sides are 14cm and 13cm. Find the area of the trapezium. OR Perimeter of a rhombus is 146cm and one of its diagonal is 55cm. Find the length of its other diagonal and its area. 27. In ∆ABC, the bisectors of ∠B and ∠C meet at O. If ∠A = 70°, find ∠BOC OR If x – 1 is a factor of x3 + ax2 – x + b and when the polynomial is divided by x – 2 leaves remainder 15. Find the values of a and b. 28. The taxi fare in a city is charged as: For the first two kilometers the fare is Rs.8 and for the subsequent distance is Rs.5 per km. Taking the distance covered as x km and total charges Rs.y. Write a linear for the information and draw its graph. Read from the graph charges for 12 km. http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com 29. “If a side of triangle is produced, then the exterior angle so formed is equal to sum of the two interior angles.” Prove. In the figure ∠ACD=120° and ∠APB = 100°, Find ∠PAC. 30. Simplify a. √6 + 3√2 – 4√3 . √2 + √3 √6 + √3 √6 + √2 b. 7√3 – 2√5 – 3√2 . c. √10 + √3 √6 + √5 √15 + 3√2 Paper Submitted by: Vikas bhatia Email : vikasbhatia_ls@yahoo.co.in Ph No. : 9837685866