SAMPLE PAPER-SA II MATHEMATICS Class IX Time allowed : 3 hours Maximum Marks : 90

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1 SAMPLE PAPER-SA II MATHEMATICS Class IX Time allowed : hours Maximum Marks : 90 General Instructions : (i) All questions are compulsory. (ii) (iii) (iv) The question paper consists of 1 questions divided into five sections A, B, C, D and E. Section-A comprises of questions of 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 8 questions of marks each and Section-D comprises of 10 questions of marks each. Section E comprises of two questions of marks each and 1 question of marks from Open Text theme. There is no overall choice. Use of calculator is not permitted. Question numbers 1 to carry one mark each. SECTION-A 1 In the figure, OAB is an equilateral triangle. If O is the centre of the circle, find the measure of ACB. 1 The volume of two hemisphere are in the ratio 7:15. Find the ratio of their radii. 1 If the mean of the observations : x, x, x 5, x 7, x 10 is 9, find the last observation. 1 Find the range of first 5 composite numbers. 1 SECTION-B Question numbers 5 to 10 carry two marks each. 5 In the adjoining figure, SQR 60 and QSR 0. Find the measures of RPQ and SPR. Also, prove that SQ is a diameter of the circle passing through the points P, Q, R and S. Page 1 of 6

2 6 Construct an angle of measure 75, using compass and ruler. 7 In the figure, ABCD and ABPQ are parallelograms. Show that PQDC is also a parallelogram. 8 The slant height and curved surface area of one cone is twice that of the other cone. Find the ratio of their radii? 9 Following table shows the birth months of the 80 students of Class XII. Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Find the probability that a student selected at random was born a month in which the Independence day or Republic day are celebrated. 10 The marks obtained out of 100 by the students of a class are given in the following table : Marks Number of students If a student is selected at random, find the probability that he/she is a student who scored less than 50%. SECTION-C Question numbers 11 to 18 carry three marks each. 11 The mean of 1 numbers is 15. If each number is multiplied by, what will be the new mean and hence state the relation between the new mean and the old mean. 1 The following table shows the marks scored by students of a class in a chemistry examination (max. marks 5) MARKS No. OF STUDENS Represent the data using a histogram. 1 PQRS is a trapezium with PQ SR. A line drawn parallel to PR meets PQ at A and QR at B. Show that ar ( PAS) ar ( PBR). Page of 6

3 1 In the given figure, O is the centre of the circle. If BAC x and OBC y, prove that x y 90. A 15 Construct a triangle whose angles are in the ratio 1 : : 5 and length of side included by first two angles is 6 cm. 16 In the figure, PQRS is a trapezium in which PQ SR, QS is a diagonal and X is the mid-point of PS. A line through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid-point of side QR. 17 In the figure, X is the mid-point of the side RS of a parallelogram PQRS. A line through R parallel to PX intersects PQ at Y and SP produced at Z. Show that PS PZ and RY YZ. 18 Radius and slant height of a solid right circular cone are in the ratio : 5. If the curved surface area is 60 cm then find its volume. Page of 6

4 SECTION-D Question numbers 19 to 8 carry four marks each. 19 Read the given frequency polygon and the prepare a grouped frequency distribution table. Also another the following questions : (a) What does the graph indicate? (b) At what time is the temperature lowest? (c) At what time is the temperature highest? (d) At 1.00 hrs, what will be the temperature of the patient? 0 PQ is parallel to side YZ of XYZ. RY XZ and SZ XY meet extended PQ in R and S respectively. Show that ar(xry) ar(xzs). 1 In ABC, if A 60 and bisectors of B and C meet AC and AB at P and Q respectively and intersect each other at I, prove that APIQ is a cyclic quadrilateral. Construct a triangle in which base is of length 6. cm, base angle is 105 and sum of the other two sides of a triangle is 10.1 cm. Page of 6

5 In the figure, ABC is an isosceles triangle in which AB AC. P, Q and R are the mid points of sides BC, AC and AB respectively. Show that AP RQ and AP is bisected by RQ. A resident building was on the fire. A fire fighting truck is coming for their rescue containing water in cylindrical shaped tank. How much water does it contain, if the whole water is used to extinguish all the fire which is spread in 90 m area and 10 L water is needed to extinguish 1 m area. A fire fighter risked his life to rescue 17 children and adults and save them. (a) If water is full to the brim in the tank and its radius is 1 m, find its height. (1 m 1000 l) (b) Which value is depicted by fire fighter? 5 The length and breadth of a hall are in the ratio : and its height is 550 cm. The cost of decorating its walls on diwali (including doors and windows) at Rs 6.60 per square metres is ` 508. Find the length and breadth of the room. 6 A hemispherical dome is constructed from 1 cm thick metallic sheet. If the inner radius of dome is 99 cm, then find the volume of the used metal sheet ( p5 ). Also find its outer 7 surface area. 7 If in a cylinder, radius is doubled and height is halved, then what is the percentage change in following : (a) curved surface area. (b) volume. 8 A manufacturing company kept a record of the numbers of Ketchup bottles/pouch of different sizes packed in a week : Pouch Bottle 500 gram 00 gram 500 gram 1000 gram What is the probability that randomly sold Ketchup is : (i) a bottle of 1/ kg (ii) atteast 00 gm bottle (iii) a bottle of 1 kg at most 500 gm Page 5 of 6

6 SECTION-E (Open Text) (* Please ensure that open text of the given theme is supplied with this question paper.) Theme : Childhood Obesity in India 9 Taking the height as 10 cm, form a linear equation in two variables taking BMI as x and weight as y kg. Draw its graph also. 0 Megha eats cheese burgers, each of them contributes 0 calories. By jumping rope (skipping) for 15 minutes she can burn 110 calories. Then for how many minutes she should do skipping to burn all the calories obtained from burger. 1 Form a linear relationship between the calories taken by eating one cheese burger and the calories burnt by swimming. Draw the graph for the same. -o0o0o0o- Page 6 of 6