CBSE Sample Paper-4 (solved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX Time allowed: 3 hours Maximum Marks: 9 General Instructions: a) All questions are compulsory. b) The question paper consists of 31 questions divided into five sections A, B, C, D and E. c) Section A contains 4 questions of 1 mark each which are multiple choice questions, Section B contains 6 questions of 2 marks each, Section C contains 8 questions of 3 marks each, Section D contains 1 questions of 4 marks each and Section E contains three OTBA questions of 3 mark, 3 mark and 4 mark. d) Use of calculator is not permitted. Section A 1. How many linear equation in x and y can be satisfied by x =1 and y =2? (a) Only one (b) Two (c) Infinitely many (d) Three 2. If AB = 16 cm, BC = 12 cm and AB is perpendicular to BC, then the radius of the circle passing through A,B and C are (a) 6 cm (b) 8 cm (c) 1 cm (d) 12 cm 3. If two parallelograms PQRS and AQRB are on the same base QR and between the same parallels QR and PB, what will be the ar (PQRS) if ar (AQRB) = 25cm? (a) 5 cm 2 (b) 6 cm 2 (c) 25 cm 2 (d) 35 cm 2 4. What is the longest pole that can be put in a room of dimensions length = 2 cm, breadth = 2 cm and height = 1 cm? (a) 15 cm (b) 25 cm (c) 2 cm (d) 3 cm Section B 5. Find the value of k, if x = -1 and y = 2 is a solution of kx + 3y = 7.
6. In the figure, D is the midpoint of AB and DE BC. Find x and y. 7. In the figure, ABC is a triangle with AD as median. If the area of Δ ABD is 15 cm 2, then find the area of Δ ABC. 8. In the figure, if O is the centre of the circle, then show that XOZ = 2( XZY + YXZ ). If points A, B and C are such that AB BC and AB = 12 cm, BC = 16 cm. Find the radius of the circle passing through the points A, B and C.
9. If the radius of a sphere is doubled, then what percent of its volume is increased? 1. A coin is tossed 15 times and found that head comes 115 times and tell 35 times. If a coin tossed at random, what is the probability of getting a) a head and b) a tail? Section C 11. Find the measure of each angle of a parallelogram, if one of its angles is 15 less than twice the smallest angle. In the figure, the area of ΔBCE is 21cm 2. If CD = 6 cm, then find the length of AF. 12. The bus fare in a town is 1 for the first km and 6 per km for the subsequent distance. Assume the distance as x km and total fare as y km, write a linear equation for the information, what will be the total fare for 15 km? 13. In the figure, if B = 68, then find A, C and D. 14. In the figure, if O is the centre if the circle, then find the value of x. 15. If the circumference of the base of a right circular cylinder is 11 cm, then find its base area.
16. If a coin is tossed for a certain number of times. How many times the coin was tossed, if the probability of getting a head is.4 and it appeared up for 24 times? 17. Find the length of a chord which is at a distance of 4 cm from the centre of a circle of radius 5 cm. 18. Find the area of trapezium whose parallel sides are 9 cm and 5 cm respectively and the distance between these sides is 8 cm. = 2 + 36 = 56 cm 2 Section D 19. Draw the graph of each of the following equations and in each case check whether. a. x = 2, y = 5 b. x = -1, y =3 are the solutions i. 2x + 5y = 13 ii. 5x + 3y = 4 2. Ram used to save a part of his pocket money. He wishes to buy paint for a communitycentre from his savings. He buys paint in a certain container which is sufficient to paint an area equal to 9.375 m 2? a. How many brocks of dimensions 22.5 cm x 1 cm x 7.5 cm can be painted out of this counter? b. Which mathematical concept is used in the above problem? c. By using the pocket money saving to buy paints for community centre which values are depicted by Ram? 21. The sum of a 2-digit number is 7. When the digits are reversed the number increases by 27. Find the original number. 22. A plastic box 1.5 cm long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine: i) The area of the sheet required for making the box. ii) The cost of the sheet for it, if a sheet measuring 1m 2 cost Rs. 2. 23. l and mare two parallel lines intersected by another pair of parallel lines p and q. Show that triangle ABC = Triangle CDA. 24. ABCD is a cyclic quadrilateral with AD BC. Prove that AB = DC.
In the below figure ABCD is a cyclic quadrilateral whose diagonals intersect at P. if DBC = 7 and BAC = 3. Find BCD 25. If an angle of a parallelogram is 4 of its adjacent angle, then find the measures of all the 5 angle of the parallelogram. 26. Construct the angles of the following a. 3 1 b. 22 2 c. 15 27. A conical tent of radius 7 m and height 24 m and height 24 m is to be made. Find the cost of the 5 m wide cloth required at the rate of Rs. 5 per metre. 28. Three coins are tossed simultaneously 2 times with the following frequencies of different outcomes. Outcomes 3 Heads 2 Heads 1 Head No Head Frequency 23 72 71 28 If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up. Section E 29. OTBA Question for 3 marks from Statistics. Material will be supplied later. 3. OTBA Question for 3 marks from Statistics. Material will be supplied later. 31. OTBA Question for 4 marks from Statistics. Material will be supplied later.