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CBSE Pre Board Class 9 2018 : Mathematics (Kendriya Vidyalaya (KV), Hyderabad)

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Shambhu Dutta
Convent of Jesus and Mary School (CJM), Ranaghat, Nadia

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KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 FOR HALF YEARLY EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR HALF YEARLY EXAM: CLASS IX VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Number System 1(1) 2(1) 6(2) 4(1) 13(5) Polynomials 1(1) 2(1) 3(1) 4(1) 10(4) Coordinate Geometry 1(1) -- 3(1) 4(1) 8(3) -- 2(1) 3(1) 4(1) 9(3) 1(1) -- 3(1) -- 4(2) 2(2) -- 3(1) 4(1) 9(3) Triangles -- 2(1) 3(1) 4(1) 9(3) Quadrilaterals -- 2(1) 3(1) 4(1) 9(3) -- 2(1) 3(1) 4(1) 9(3) 6(6) 12(6) 30(10) 32(8) 80(30) Chapter Linear Equation in two variables Introduction to Euclid s Geometry Lines and Angles Areas of Parallelograms and triangles Total MARKING SCHEME FOR HALF YEARLY EXAM VSA 1 NO. OF QUESTIONS 6 SA I 2 6 12 SA II 3 10 30 LA 4 8 32 SECTION MARKS GRAND TOTAL Prepared by: M. S. KumarSwamy, TGT(Maths) TOTAL 08 80 Page - 1 - KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 FOR HALF YEARLY EXAM (2017-18) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : IX DURATION : 3 HRS General Instructions: (i). All questions are compulsory. (ii). This question paper contains 30 questions divided into four Sections A, B, C and D. (iii). Section A comprises of 6 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises of 8 questions of 4 marks each. (iv). Use of Calculators is not permitted SECTION A 1. State PLAYFAIR axiom. 2. Rationalize the denominator of 3 2 3 2 . 3. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k. 4. One of the angles of a triangle is 50 and the other two angles are equal. Find the measure of each of the equal angles. 5. If x + 6 is a factor of p(x) = x3 + 3x2 + 4x + k, find the value of k. 6. Write the coordinates of the point lying on x-axis and with x-coordinate 4. SECTION B 7. Show that 1.272727 . can be expressed in the form of p , where p and q are integers and q q 0. 8. In the below figure, if AB || CD, APQ = 50 and PRD = 127 , find x and y. 9. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral. 10. ABCD is a parallelogram, AE DC and CF AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD. 11. ABC is right angled in which A = 90 and AB = AC. Find B and C. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2 - 12. Factorise: 27 x 3 1 9 1 x2 x 216 2 4 SECTION C 13. From the figure, find the coordinates of A, B, C, D, E and F. Which of the points are mirror image in (i) x axis (ii) y axis 14. If x = 3 2 1 , find x 2 2 x 3 2 15. If a and b are rational numbers and 7 4 3 a b 3 , find the values of a and b. 7 4 3 16. If a point C lies between two points A and B such that AC = BC, then prove that AC = 1 AB. 2 Explain by drawing the figure. 17. Show that the diagonals of a parallelogram divide it into four triangles of equal area. 18. In the below figure, ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that (i) APB CQD (ii) AP = CQ 19. The Autorikshaw fare in a city is charged Rs 10 for the first kilometer and @ Rs 4 per kilometer for subsequent distance covered. Write the linear equation to express the above statement. Draw the graph of the linear equation. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 3 - 20. Without actual division, prove that 2x4 5x3 + 2x2 x + 2 is divisible by x2 3x + 2. 21. Line l is the bisector of an angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of A (see the below figure). Show that: (i) APB AQB (ii) BP = BQ or B is equidistant from the arms of A. 22. In the above sided figure, if QT PR, TQR = 40 and SPR = 30 , find x and y. SECTION D 23. Simplify 4 5 4 5 by rationalizing the denominator. 4 5 4 5 24. If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, prove that the two triangles are congruent 25. Solve the equation 2x + 1 = x 3, and represent the solution(s) on (i) the number line, (ii) the Cartesian plane. 26. The polynomial f(x)= x4 2x3 +3x2 ax + b when divided by (x 1) and (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). 27. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 4 - 28. In the below figure, P is a point in the interior of a parallelogram ABCD. Show that 1 (i) ar (APB) + ar (PCD) = ar (ABCD) 2 (ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD) 29. Plot the following points on a graph paper: 1 2 x 5 8 y Join these points. What do you observe? 3 11 4 14 5 17 30. In the above sided figure, the sides AB and AC of a triangle ABC are produced to points E and D respectively. If bisectors BO and CO of CBE and BCD respectively meet at point O, then 1 prove that BOC = 900 BAC. 2 Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 5 -

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