SAMPLE QUESTION - 2009

Class - IX

Subject - Mathematics

Time: 3hrs Max.Marks:80

General Instructions

1. All questions compulsory

2. The question paper consist of thirty questions divided in to 4 sections A,B,C and D. Section

A comprises of ten questions of 1 marks each ,Section B comprises of five questions of 2

marks each, Section C comprises of ten questions of 3 marks each and section D comprises

of five questions of 6 marks each

SECTION-A

1) The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.2) Find the remainder obtained on dividing 3x4 – 4x3 – 3x –1 by x – 1.3) Evaluate (104)3 using suitable identity.4) 5 people were asked about the time in a week they spend in doing social work in their community. They said 10, 7, 13, 20 and 15 hours, respectively.

Find the mean (or average) time in a week devoted by them for social work.5) If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.6) If A, B and C are three points on a line, and B lies between A and C (See Fig. 5.7), then prove that AB + BC = AC.7) Lines PQ and RS intersect each other at point O. If ∠POR: ROQ = 5: 7, find all the angles.8) ABCD is a parallelogram, AE _|_DC and CF AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.9) E and F are respectively the mid-points of equal sides AB and AC of Triangle ABC Show that BF = CE.10) Two coins are tossed simultaneously 500 times, and we get

Two heads: 105 timesOne head: 275 timesFind the probability of occurrence of each of these events.

SECTION-B

1) Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.2) If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.3) The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. (Use = 3.14)4) Show that the diagonals of a rhombus are perpendicular to each other.5) Show that a median of a triangle divides it into two triangles of equal areas.

SECTION-C

1) Construct a triangle ABC in which BC = 7cm, ∠B = 75° and AB + AC = 13 cm.2) A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base28 cm, find the height of the parallelogram.3) If circles are drawn taking two sides of a triangle as diameters, prove that the point ofintersection of these circles lie on the third side.

4) The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of metal sheet would be needed to make it?5) Thirty children were asked about the number of hours they watched TV programmes

in the previous week. The results were found as follows:1 6 2 3 5 12 5 8 4 810 3 4 12 2 8 15 1 17 63 2 8 5 9 6 8 7 14 12(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.(ii) How many children watched television for 15 or more hours a week?

6) Triangle ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that BCD is a right angle.7) Plot the following ordered pairs of number (x, y) as points in the Cartesian plane. Use the scale 1cm = 1 unit on the axes.

x – 3 0 – 1 4 2y 7 –3.5 – 3 4 – 3

Factorize x3 – 23x2 + 142x – 120.ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA.AC is a diagonal. Show that: PQRS is a parallelogram. And SR =1/2AC.10) The sides AB and AC of 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° –1/ 2∠ /_ BAC.

SECTION-D 1) D, E and F are respectively the mid-points of the sides BC, CA and AB of a Triangle ABC.Show that (i) BDEF is a parallelogram. (ii) ar (DEF) =1/4ar (ABC)(iii) ar (BDEF) =1/2ar (ABC).

2) Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at point on the minor arc and also at a point on the major arc.

3) Prove that two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. You are given that PA = PB and QA = QB and you are to show that PQ _|_AB and PQ bisects AB. Let PQ intersect AB at C.

4) Prove that Parallelograms on the same base and between the same parallels are equal in area. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).

5) The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find(i) Height of the cone (ii) slant height of the cone(iii) Curved surface area of the cone.