# KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

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1 KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 FOR HALF YEARLY EXAM (017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR HALF YEARLY EXAM: CLASS IX Chapter VSA (1 mark) SA I ( marks) SA II (3 marks) LA (4 marks) Total Number System 1(1) (1) 6() 4(1) 13(5) Polynomials 1(1) (1) 3(1) 4(1) 10(4) Coordinate Geometry 1(1) -- 3(1) 4(1) 8(3) Linear Equation in two variables Introduction to Euclid s Geometry -- (1) 3(1) 4(1) 9(3) 1(1) -- 3(1) -- 4() Lines and Angles () -- 3(1) 4(1) 9(3) Triangles -- (1) 3(1) 4(1) 9(3) Quadrilaterals -- (1) 3(1) 4(1) 9(3) Areas of Parallelograms and triangles -- (1) 3(1) 4(1) 9(3) Total 6(6) 1(6) 30(10) 3(8) 80(30) MARKING SCHEME FOR HALF YEARLY EXAM SECTION MARKS NO. OF QUESTIONS TOTAL VSA SA I 6 1 SA II LA GRAND TOTAL 80 Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -

2 KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 FOR HALF YEARLY EXAM (017-18) 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 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.. Rationalize the denominator of. 3. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k. 4. One of the angles of a triangle is 50º 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) = x 3 + 3x + 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 can be expressed in the form of p q, where p and q are integers and q In the below figure, if AB CD, APQ = 50 and PRD = 17, 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. ΔABC is right angled in which A = 90 and AB = AC. Find B and C. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - -

3 1. Factorise: x x x 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 =, find x 1 x 15. If a and b are rational numbers and a b 3, find the values of a and b If a point C lies between two points A and B such that AC = BC, then prove that AC = 1 AB. 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 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 -

4 0. Without actual division, prove that x 4 5x 3 + x x + is divisible by x 3x 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.. In the above sided figure, if QT PR, TQR = 40 and SPR = 30, find x and y. SECTION D 3. Simplify by rationalizing the denominator. 4. 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 5. Solve the equation x + 1 = x 3, and represent the solution(s) on (i) the number line, (ii) the Cartesian plane. 6. The polynomial f(x)= x 4 x 3 +3x 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). 7. 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 -

5 8. In the below figure, P is a point in the interior of a parallelogram ABCD. Show that (i) ar (APB) + ar (PCD) = 1 ar (ABCD) (ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD) 9. Plot the following points on a graph paper: x y Join these points. What do you observe? 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 prove that BOC = 90 BAC. 0 1 Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 5 -

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