Published on March 5, 2014
MATHEMATICS-IX (Term-II) Model Test Paper-1 (Unsolved) [For S.A.-II (Term - II)] Time : 3 hours M.M. : 90 General Instructions : Same as in Sample Question Paper. SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. In the given figure, PQRS is a rectangle. If ∠RPQ = 30°, then the value of (x + y) is : (a) 90° (b) 120° (c) 150° (d) 180° 2. In the figure, if area of parallelogram ABCD is 30 cm2, then ar (ADE) + ar (BCE) is equal to : (a) 20 cm2 (b) 30 cm2 (c) 15 cm2 (d) 25 cm2 3. In the figure, chord AB is greater than chord CD. OL and OM are the perpendiculars from the centre O on these two chords as shown in the figure. The correct relation between OL and OM is : (a) OL = OM (b) OL < OM (c) OL > OM (d) none of these 4. Ratio of the volume of a cone and a cylinder of same radius of base and same height is : (a) 1 : 1 (b) 1 : 2 (c) 1 : 3 (d) 1 : 4 5. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are written in ascending order. If median of data is 63, then x is : (a) 62 (b) 63 (c) 124 (d) 126 6. In the given figure, ABCD is a rhombus. If ∠OAB = 35°, then the value of x is : (a) 25° (c) 55° (b) 35° (d) 70° 1
7. If the slant height of a cone is 13 cm and the base radius is 5 cm, then the height of cone is : (a) 12 cm (b) 8 cm (c) 10 cm (d) 18 cm 8. If P(E) denotes the probability of an event E, then : (a) P(E) < 0 (b) P(E) >1 (c) 0 < P(E) < 1 (d) –1 < P(E) < 1 SECTION B (Question numbers 9 to 14 carry 2 marks each.) 9. The cost of 6 eggs is the same as the cost of one bread. Express this statement as a linear equation in two variables. (Take the cost of one egg to be Rs x and that of a bread to be Rs y). 10. In the figure, ABCD is a quadrilateral and BD is one of its diagonals. Show that ABCD is a parallelogram and find its area. 11. In the figure, ABCD is a rectangle. P and Q are the mid-points of AD and DC respectively. Find the length of PQ. 12. AOB is a diameter of a circle and C is a point on the circle. Check whether AC2 + BC2 = AB2 is true or not. OR For what value of x in the figure, points A, B, C and D are concyclic? 13. If the edge of a cube is doubled, what is the ratio of the volume of the first cube to that of the second cube? 14. A die is thrown 225 times and the results were as follows : Outcomes 1 2 3 Frequencies 34 50 16 Find the probability of getting a prime number. 2 4 5 6 71 24 30
SECTION C (Question numbers 15 to 24 carry 3 marks each.) 15. Draw the graph of the equation 2y – x = 7 and determine from the graph whether x = 3, y = 2 is its solution or not. 16. Determine the point on the graph of the linear equation 2x + 5y = 19 whose ordinate 1 times its abscissa. 2 17. The angles between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram. is 1 OR ABCD is a trapezium with parallel sides AB = a cm and DC = b cm. E and F are the mid-points of the non-parallel sides. Show that the ratio of ar(ABFE) and ar(EFCD) is (3a + b) : (a + 3b). 18. Construct a triangle whose sides are 4.2 cm, 3.9 cm and 6.1 cm. Bisect its greatest angle and measure each part. 19. If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ≅ arc PYB. 20. The total surface area of a solid cylinder is 462 cm2 and its curved surface area is one third of its total surface area. Find the radius of the cylinder. 21. A hemispherical vessel full of water is emptied in a cone. The radii of the vessel and the cone are 12 cm and 8 cm respectively. Find the height of the water in the cone. OR A shopkeeper has one spherical ladoo of the radius 5 cm. With the same amount of material, how many ladoos of radius 2.5 cm can be made? 22. Prepare a continuous grouped frequency distribution from the following data : Mid-point Frequency 5 4 15 8 25 13 35 12 45 6 Also find the size of class intervals. 3
23. Show that if diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. 24. Find the mean of the following data : x 4 6 8 10 12 f 4 8 14 11 3 OR A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 and that of boys is 71. Find the mean score of the whole class. SECTION D (Question numbers 25 to 34 carry 4 marks each.) 25. Draw the graph of the linear equation 2x + 3y = 12. At what points, the graph of the equation cuts the x-axis and the y-axis? 26. E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram. 27. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium. 28. 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. 29. A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 cm. (i) How many students can sit in the tent if a student on an average, occupies 5 2 m 7 on the ground? (ii) Find the volume of the cone. OR The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone. 30. Draw a histogram for the following data : Class-interval : Frequency : 25-29 30-34 35-39 40-44 45-49 50-54 8 15 23 20 10 9 4
31. Show that the diagonals of a rhombus are perpendicular to each other. OR Show that a diagonal of a parallelogram divides it into two congruent triangles and hence prove that the opposite sides of a parallelogram are equal. 32. The parking charges of a car in a parking lot is Rs 30 for the first two hours and Rs 10 for subsequent hours. Taking total parking time to be x hours and total charges as Rs y, write a linear equation in two variables to express the above statement. Draw a graph for the linear equation and read the charges for five hours. 33. Draw a frequency polygon for the following distribution : Class interval Frequency 10 − 19 20 20 − 29 15 30 − 39 40 − 49 45 − 60 45 60 12 60 − 70 6 70 − 85 15 34. Metal spheres, each of radius 2 cm are packed into a rectangular box of dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed in the box, it is filled with preservative liquid. Find the volume of this liquid to the nearest integer. [use π = 3.14]
MATHEMATICS-IX (Term-II) Model Test Paper-2 (Unsolved) [For S.A.-II (Term - II)] Time : 3 hours M.M. : 90 General Instructions : Same as in Sample Question Paper. SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. Diagonals of a parallelogram ABCD intersect at O. If ∠BOC = 90° and ∠BDC = 50°, then ∠OAB is : (a) 90° (b) 50° (c) 40° (d) 10° 2. In the figure, the area of parallelogram ABCD is : (a) AB × BM (b) BC × BN (c) DC × DL (d) AD × DL 3. In the figure, AB and CD arc two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD respectively, if ∠POQ = 150°, then ∠APQ is : (a) 30° (b) 75° (c) 15° (d) 60° 4. The class mark of the class 90-120 is : (a) 90 (b) 105 5. The total surface area of a cube 96 (a) 8 cm3 (b) 512 cm3 cm2. (c) 115 (d) 120 The volume of the cube is : (c) 64 cm3 (d) 27 cm3 6. In the figure, if ∠ABC = 20°, then ∠AOC is equal to : (a) 20° (b) 40° (c) 60° (d) 10° 7. Base area of a cylinder is 154 sq cm. Its height is 5 cm. Then its volume is : (a) 308 cubic cm (b) 770 cubic cm (c) 525 cubic cm (d) 600 cubic cm 6
8. In a class, there are x girls and y boys. A student is selected at random, then the probability of selecting a boy is : (a) x y (b) x ( x + y) (c) y ( x + y) (d) y x SECTION B (Question numbers 9 to 14 carry 2 marks each.) 9. Write each of the following equations as equations in two variables. (i) x = 17 (ii) y = –5 10. Show that each angle of a rectangle is a right angle. OR The lengths of the diagonals of a rhombus are 24 cm and 18 cm. Find the length of each side of the rhombus. 11. In the figure, ABCD is a parallelogram, if area of ΔAEB is 16 cm2, then find the area of ΔBFC. 12. Calculate the length of a chord which is at a distance 5 cm from the centre of a circle whose radius is 13 cm. 13. The rectangular sheet of paper 22 cm × 15 cm is rolled along its length to form a hollow cylinder. Find the radius of the cylinder thus formed. 14. In a sample study of 420 people, it was found that 240 people were government employees. If a person is selected at random, find the probability that the person is not a government employee. SECTION C (Question numbers 15 to 24 carry 3 marks each.) 15. Draw the graph of the equation 5x – 3y = 1. Find four solutions of the equation. Using the graph check whether x = 2 and y = 3 is a solution of the equation. 16. In a parallelogram, AP and CQ are perpendiculars from A and C on its diagonal BD. Prove that AP = CQ. 17. In the figure, PSDA is a parallelogram, points Q and R are taken on PS such that PQ = QR = RS and PA || QB || RC. Prove that ar (PQE) = ar (CFD). 7
OR In the figure, E is any point on median AD of a ΔABC. Show that ar(ABE) = ar(ACE). 18. Construct a ΔXYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm. 19. Find the points where the graph of the equation 3x + 4y = 12 cuts the x-axis and the y-axis. 20. A sphere of radius r has been cut into two hemispheres. Find the ratio of the surface area of the original sphere to the total surface area of the two hemispheres. OR The radius of a roller, 1.2 m long is 0.42 m. If it takes 200 complete revolutions to level a playground, find the area of the playground. 21. The dimensions of a cuboid are in the ratio 3 : 2 : 1. If the lateral surface area of the cuboid is 360 cm2, find its total surface area. 22. Given below are the seats won by different political parties in the polling outcome of a state assembly elections : Political party A B C D E F Seats won 75 55 37 29 10 37 (i) Draw a bar graph to represent the polling results. (ii) Which political party won the maximum number of seats? OR Find the median of 40, 42, 120, 99, 61, 92, 71, 58, and 58. If 56 is replaced by 85 then find the new median. 23. In a one day cricket match, a batsman played 40 balls. The runs scored are as follows : Runs scored 0 1 2 3 4 6 No. of balls 13 15 5 1 4 2 Find the probability that the batsman will score (i) 6 runs (ii) 0 or 4 or 6 runs. 24. Prove that equal chords of a circle subtend equal angles at the centre. 8
SECTION D (Question numbers 25 to 34 carry 4 marks each.) 25. The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation 5F – 160 . 9 C= (i) (ii) (iii) (iv) If the temperature is 86°F, what is the temperature in Celsius ? If the temperature is 35°C, what is the temperature in Fahrenheit ? If the temperature is 0°F, what is the temperature in Celsius ? What is the numerical value of the temperature which is same in both the scales ? 26. ABC is an isosceles triangle in which AB = AC. A circle passing through B and C intersects AB and AC at D and E respectively. Prove that BC || DE. 27. In the figure, AP || BQ || CR. Prove that ar(AQC) = ar(PBR) 28. Show that the diagonals of a rhombus are perpendicular to each other. 29. A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface area of the solid thus generated. OR A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceeds its height? 30. Draw a frequency polygon for the following distribution. Marks No. of students 0-10 10-20 20-30 30-40 40-50 50-60 3 7 12 8 6 4 31. ABCD is a parallelogram. On diagonal BD are points P and Q such that DP = BQ. Show that APCQ is a parallelogram. 9
OR AD is the median of ∆ABC. E is the mid-point of AD. BE produced meets AC at F. Show that AF = 1 AC. 3 32. Circumference of the base of a cylinder, open at the top, is 132 cm. The sum of radius and height is 41 cm. Find the cost of polishing the outer surface area of cylinder at the 22 ⎤ ⎡ rate Rs 10 per square dm (decimetre). ⎢ use π = 7⎥ ⎣ ⎦ 33. Construct a histogram for the following data : Class interval Frequency 10 − 19 20 20 − 29 15 30 − 39 40 − 49 45 60 50 − 59 75 34. A water tank is getting filled up by water flowing at the rate of 15 cm3/sec. If the volume of water filled in y seconds is x cm3, write a linear equation in two variables to represent this situation. Draw a graph for the equation formed and hence find the volume of water filled in 9 seconds.
MATHEMATICS-IX (Term-II) Model Test Paper-3 (Unsolved) [For S.A.-II (Term - II)] Time : 3 hours M.M. : 90 General Instructions : Same as in Sample Question Paper. SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. The dimensions of a room are 4 m × 3 m × 2 m. The area of the four walls of the room is : (a) 28 m2 (b) 56 m2 (c) 60 m2 (d) 70 m2 2. A coin is tossed 100 times and head appears 64 times. The probability of getting a tail is : 18 9 (a) (b) (c) 0 (d) 1 25 25 3. In the figure, O is the centre of the circle. If ∠AOB = 160°. Then ∠ACB is : (a) 160° (b) 200° (c) 80° (d) 100° 4. The sum of the lengths of bases of a trapezium is 13.5 cm and its area is 54 cm2. The altitude of the trapezium is : (a) 9 cm (b) 6 cm (c) 8 cm (d) 12 cm 5. In the figure, D is the mid-point of AB and DE || BC, then AE is equal to : (a) AD (b) EC (c) DB (d) BC 6. In the figure, O is the centre and AB = BC. If ∠BOC = 80°, then ∠AOB is : (a) 80° (b) 70° (c) 85° (d) 90° 7. The area of the base of a solid hemisphere is 36 cm2. Its curved surface area is : (a) 36 cm2 (b) 72 cm2 (c) 108 cm2 (d) 98 cm2 11
8. The range of the data 25.7, 16.3, 2.8, 21.7, 24.3, 22.7, 24.9 is : (a) 22 (b) 22.9 (c) 21.7 (d) 20.5 SECTION B (Question numbers 9 to 14 carry 2 marks each.) 9. If (2, 5) is a solution of the equation 2x + 3y = m. Find the value of m. 10. In the figure, ΔABC is an equilateral triangle. Find ∠BDC and ∠BEC. 11. In the figure, ABC is a triangle and AD is one of its medians. Find the ratio of areas of triangles ABD and ACD. 12. The class-marks of the distribution are 11, 14, 17, 20, 23, 26 and 29. Find the width of the class and the true class limits. 13. A sphere is inscribed in a cube. Find the ratio of the volume of the cube to the volume of the sphere. 14. Find the measure of each angle of a parallelogram, if one of its angles is 30° less than the twice the smaller angle. OR Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, find the lengths of AC and BD. SECTION C (Question numbers 15 to 24 carry 3 marks each.) 15. For what value of p, the linear equation 2x + py = 8 has equal values of x and y for its solution? 16. Frame a linear equation in the form ax + by + c = 0 by using the given values of a, b and c. (i) a = –2, b = 3, c = 4 (ii) a = 5, b = 0, c = –1 17. In a quadrilateral ABCD, AO and BO are the bisectors of ∠A and ∠B respectively. 1 Prove that ∠AOB = (∠C + ∠D). 2 18. Construct a triangle PQR in which QR = 6 cm, ∠Q = 60° and PR – PQ = 2 cm. 12
19. In a circle of radius 5 cm, there are two parallel chords of length 6 cm and 4 cm. Find the distance between them when they are on opposite sides of the centre. OR In the figure, if AB = AC, ∠BEC = 100° then, find the value of x and y. 20. There are two cones. The curved surface area of one cone is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii. OR The solid sphere of radius 4 cm is melted and then cast into smaller spherical balls of diameter 0.8 cm. Find the number of these balls. 21. The sum of height and radius of the base of a solid cylinder is 37 cm. Total surface area of the cylinder is 1628 cm2. Find its volume. 22. If the mean of the following data is 20.2, find the value of p. x 10 15 20 25 30 f 6 8 p 10 6 23. Following table give the distribution of time taken to solve a problem by 40 students : Time in sec. 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 6 8 12 10 4 No. of students Draw a histogram to represent the above data. OR Thirty children were asked about the number of hours they watched TV programmes in the previous week. The result were found as follows : 1 10 3 6 3 2 2 4 8 3 12 5 5 2 9 12 8 6 5 15 8 8 1 7 4 17 14 8 6 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? 13
24. In the figure, AD is the median. Prove that ar(∆ABD) = ar(∆ACD). SECTION D (Question numbers 25 to 34 carry 4 marks each.) 25. Draw the graph of the equation y = –x + 1 and find the point where the graph meets the axes. 26. In a triangle ABC, median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram. 27. Prove that the parallelograms on the same base and between the same parallels are equal in area. OR Triangles ABC and DBC are on the same base BC with vertices A and D on opposite sides of BC such that ar (ABC) = ar (DBC). Show that BC bisects AD. 28. In the figure, PQ and RS are two parallel chords of a circle. When produced RP and SQ meet at O. Prove that OP = OQ. 29. Water in a rectangular reservoir having base 80 m × 60 m is 6.5 m deep. In what time can the water be emptied by a pipe of which the cross section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km/hr? OR A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm2. 30. Prove that a line segment joining the mid-points of any two sides of a triangle is parallel and half of its third side. 31. Rita and Geeta, two students of class IX, together contributed Rs 100 towards PrimeMinister’s Relief Fund to help the earthquake victims. Write a linear equation with this data satisfied. Draw the graph of the same. 14
32. The runs scored by two teams A and B on the first 60 balls in a cricket match are given below : No. of balls Team A Team B 1–6 2 5 7–12 1 6 13–18 8 2 19–24 9 10 25–30 4 5 31–36 5 6 37–42 6 3 43–48 10 4 49–54 6 8 55–60 2 10 Represent the data of both the teams on the same graph by frequency polygons. 33. Sum of the radius of the base height of a cylinder is 37 cm. Its total surface area is 22 ⎞ ⎛ 1628 sq cm. Find its volume. ⎜ use π = ⎟ ⎝ 7⎠ 34. Mean of 50 observations was found to be 80.4. But later on it was discovered that 96 was misread as 69 at one place. Find the correct mean. If to each observation a constant value k is added, how is the mean affected?
MATHEMATICS-IX (Term-II) Model Test Paper-4 (Unsolved) [For S.A.-II (Term - II)] Time : 3 hours M.M. : 90 General Instructions : Same as in Sample Question Paper. SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. In the figure, D and E are mid-points of AB and AC respectively. The length of DE is : (a) 8.2 cm (b) 5.1 cm (c) 4.9 cm (d) 4.1 cm 2. The areas of a parallelogram and a triangle are equal and they lie on the same base. If the altitude of the parallelogram is 2 cm, then the altitude of the triangle is : (a) 4 cm (b) 1 cm (c) 2 cm (d) 3 cm 3. In the figure, if O is the centre of the circle and A is a point on the circle such that ∠CBA = 40° and AD ⊥ BC, then the value of x is : (a) 50° (b) 90° (c) 45° (d) 40° 4. In a medical examination of students of a class, the following blood groups are recorded : Blood group A AB B O No. of students 10 13 12 5 A student is selected at random from the class. The probability that he/she has blood group B, is : 13 3 1 1 (a) (b) (c) (d) 40 10 8 4 5. The volumes of two spheres are in the ratio 64 : 27. The ratio of their radii is equal to : (a) 4 : 3 (b) 3 : 4 (c) 16 : 9 (d) 16 : 27 16
6. In the figure, O is the centre of the circle. If OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to : (a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm 7. The mean of 10 numbers is 55. If one number is excluded, their mean becomes 50, the excluded number is : (a) 60 (b) 70 (c) 80 (d) 100 8. Diameter of the earth is four times (approximately) the diameter of the moon, then the ratio of their surface areas is : (a) 4 : 1 (b) 8 : 1 (c) 16 : 1 (d) 64 : 1 SECTION B (Question numbers 9 to 14 carry 2 marks each) 9. Find the solution of the linear equation 2x + 5y = 10 which represents a point on (i) x-axis (ii) y-axis 10. If the two adjacent angles of a parallelogram are (3x – 20)° and (50 – x)°, then find the value of x. 11. In a parallelogram ABCD, AB = 10 cm. The altitude corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD. 12. In the figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC. 13. The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110 cm. Find the height of the cylinder. 14. The mean of 10, 12, 18, 13, x and 17 is 15. Find the value of x. OR The points scored by a basket ball team in a series of matches are as follows : 17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28. Find the median for the data. 17
SECTION C (Question numbers 15 to 24 carry 3 marks each.) 15. If the radius of a sphere is increased by 10%, by how much per cent will its volume increase? OR Three solid spheres of iron whose diameters are 2 cm, 12 cm and 16 cm respectively are melted into a sphere. Find the radius of the new sphere. 16. The radius and height of a cylinder are in the ratio 2 : 3. If the volume of the cylinder is 1617 cm3, find its radius and height. 17. Solve the equation 2x + 1 = x – 3 and represent the solution (s) on (i) the number line (ii) the cartesian plane. 18. Give the equations of two lines passing through (2, 14). How many more such lines are there and why? 19. If the mid-points of the sides of a quadrilateral are joined in order, prove that the area of the parallelogram so formed will be half of that of the given quadrilateral. 20. The mean of the following distribution is 50. x 10 30 50 70 90 f 17 5p + 3 32 7p – 11 19 Find the value of p and hence the frequencies of 30 and 70. OR Construct a frequency distribution table for the following data of marks obtained by 25 students in a test in Mathematics in a school. Take 20-30 (30 not included) as one of the classes : 9, 25, 17, 12, 28, 20, 7, 31, 14, 43, 11, 19, 23, 37, 6, 24, 48, 10, 32, 17, 40, 31, 18, 24, 29 Now find the following : (i) the number of students getting less than 40 marks. (ii) the number of students getting 30 or more marks. 21. Over the past 200 working days, the number of defective parts produced by a machine is given below : No. of defective parts 0 1 2 3 Days 4 50 32 22 18 5 6 7 8 9 10 11 12 13 12 12 10 10 10 8 6 6 2 2 Determine the probability that tomorrow’s output will have : (i) no defective part (ii) not more than 5 defective parts (iii) more than 13 defective parts? 18
22. Construct a rhombus whose side is of length 3.4 cm and one of its angles is 45°. 23. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD. (see figure) 24. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. OR In a parallelogram show that the angle bisectors of two adjacent angles intersect at right angles. SECTION D (Question numbers 25 to 34 carry 4 marks each.) 25. If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 3 units. Also read from the graph the work done when the distance travelled by the body is : (i) 2 units (ii) 0 units. 26. A cylindrical tube opened at both ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimetres of iron has been used in making the tube. OR The volume of two spheres are in the ratio 64 : 27. Find the radii, if the sum of their radii is 21 cm. 27. A random survey of the number of children of various age groups playing in a park was found as follows : Age (in years) Number of children 1–2 2–3 3–5 5–7 7 – 10 10 – 15 15 – 17 5 3 6 12 9 10 4 Draw a histogram to represent the data above. 19
28. Triangles ABC and DBC are on the same base BC with vertices A and D on opposite sides of BC such that ar (ABC) = ar (DBC). Show that BC bisects AD. OR Show that the diagonals of a parallelogram divide it into four triangles of equal area. 29. In the figure, ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC = 30°, find ∠BCD. Further, if AB = BC, find ∠ECD. 30. ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. 31. Make a frequency polygon for given frequency table. Class interval Frequency 0 − 5 2 5 − 10 3 10 − 15 4 15 − 20 1 20 − 25 5 25 − 30 3 32. Monica has a piece of canvas whose area is 551 m2. She uses it to have a conical tent made, with base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with it. 33. The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that ar(ABCD) = ar(PBQR). 34. 4 years before, age of a mother was 3 times the age of her daughter. Write a linear equation to represent this situation and draw its graph.
MATHEMATICS-IX (Term-II) Model Test Paper-5 (Unsolved) [For S.A.-II (Term - II)] Time : 3 hours M.M. : 90 General Instructions : Same as in Sample Question Paper. SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is : (a) 55° (b) 40° (c) 25° (d) 50° 2. The median of a triangle divides it into two : (a) triangles of equal area (b) congruent triangles (c) right triangles (d) isosceles triangles 3. In the figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to : (a) 30° (b) 60° (c) 90° (d) 45° 4. The radius of a sphere is 2r, then its volume will be : (a) 4 3 πr 3 (b) 4πr3 (c) 32 3 πr 3 (d) 8 3 πr 3 5. The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is : (a) 38 (b) 30 (c) 35 6. Which of the following is not true for a parallelogram? (d) 28 (a) opposite sides are equal (b) opposite angles are equal (c) opposite angles are bisected by the diagonals (d) diagonals bisect each other 7. In a cylinder, radius is doubled and height is halved. The curved surface area will be : (a) halved (b) doubled (c) same (d) four times 8. A bag contains x white, y red and z blue balls. A ball is drawn at the random, then the probability of drawing a blue ball is : 21
(a) z x+y+z (b) y x+y+z (c) x x+y+z (d) 0 SECTION B (Question numbers 9 to 14 carry 2 marks each.) 9. In the figure, if AOB is a diameter and ∠ADC = 120°, find ∠CAB. OR Prove that the cyclic parallelogram is a rectangle. 10. In the figure, ABCD is a parallelogram. Find the value of x and y. 11. In the figure, P and Q are mid-points of sides AB and AC respectively of ΔABC. If PQ = 2.5 cm and AB = AC = 7 cm, then find the perimeter of ΔABC. 12. Marks obtained by 50 students in a class test of 100 marks are given below : Marks No. of students 0-25 25-50 50-75 75-100 4 12 18 16 Find the probability that a student obtains less than 50% marks. 13. Check whether the graph of the linear equation x + 2y = 7 passes through the point (0, 7). 14. A cone, a hemisphere and a cylinder stand on equal bases and have same height. Find the ratio of their volumes. 22
SECTION C (Question numbers 15 to 24 carry 3 marks each.) 15. Draw the graphs of the equations x + y = 6 and 2x + 3y = 16 on the same graph paper. Find the coordinates of the points where the two lines intersect. 16. Find three solutions of 5x – y + 6 = 0 after reducing it to y = mx + c form. 17. Bulbs are packed in cartons, each containing 40 bulbs. Seven hundered cartons were examined for defective bulbs and the results are given in the following table : No. of defective bulbs Frequency 0 1 2 3 4 5 6 more than 6 400 180 48 41 18 8 3 2 One carton was selected at random, what is the probability that it has : (i) no defective bulbs ? (ii) defective bulbs from 2 to 6 ? (iii) defective bulbs less than 4 ? 18. If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 11. Find the mean of first three observations. OR The observations 10, 13, 15, x + 1, x + 5, 30, 32, 36 are in ascending order with median 20. Find the value of x. 19. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC. (ii) MD ⊥ AC 20. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also find the ratio between their surface areas. 21. A heap of wheat is in the form of a cone. Diameter of the base of the heap is 8 m and height is 3 m. Find its volume. The heap is to be covered to protect it from rain, find the area of canvas required. OR Two solid spheres made of the same metal have weights 5920 g and 740 g respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm. 22. Construct a triangle ABC such that AB = BC = 6 cm and median AD = 4 cm. 23. D and E are points on sides AB and AC respectively of ΔABC such that ar (DBC) = ar (EBC). Prove that DE || BC. 23
24. Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other. OR Prove that the diagonal of a parallelogram divides it into two congruent triangles. SECTION D (Question numbers 25 to 34 carry 4 marks each.) 25. The taxi For the Rs 6 per equation fare in a city is as follows : first kilometre, the fare is Rs 8 and for the subsequent distance it is km. Taking the distance covered as x km and total fare as Rs y, write a linear for this information and draw its graph. 26. A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs 498.96. If the cost of whitewashing is Rs 2.00 per square metre, find (i) the inside surface area of the dome. (ii) volume of air inside the dome. OR A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 5 m, what will be the cost of painting it on the outside at the rate of Rs 10 per square metre? 27. AB and CD are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre, prove that 4q2 = p2 + 3r2. OR If a line drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral so formed is cyclic. 28. In the figure, BD || CA, E is the mid-point of CA and BD = 1 CA. Prove that ar (ABC) = ar (DBC). 2 29. In the figure, PQRS is a parallelogram in which PQ is produced to T such that QT = PQ. Prove that ST bisects RQ. 30. Draw a histogram and frequency polygon on the same graph for the data given below : Marks No. of students 60-90 90-120 12 7 120-150 150-180 180-210 210-240 240-270 10 24 3 15 4 2
31. Draw the graph of the equation 2x + 3y – 6 = 0. (i) Using graph paper determine whether x = 3 and y = 0 is a solution. (ii) Find the value of y, if x = –3 and (iii) Find the value of x, if y = –2 from the graph and verify. 32. In the figure, ABCD and AEFD are two parallelograms. Prove that ar(PEA) = ar(QFD). 33. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite. 34. The heights of 50 students, measured to the nearest centimetres, have been found to be as follows : 135, 162, 173, 151, 176, 165, 162, 145, 171, 172, 157, 161, 172, 158, 163, 175, 148, 173, 163, 159, 160, 162, 172, 175, 176, 168, 167, 170, 172, 173, 165, 151, 149, 169, 173, 138, 156, 148, 159, 166, 176, 151, 139, 146, 164, 173, 141, 142, 150, 159. Represent the data given above by a grouped frequency distribution table, taking class intervals as 160 – 165, 165 – 170 etc.
SCIENCE-IX (Term-II) MODEL TEST PAPER – 1 (UNSOLVED) Maximum Time : 3 hours Maximum Marks : 90 Instructions : Same as in Sample Question Paper. SECTION A 1. In the figure given below, if the bob of the pendulum swings from P to Q, what is the kinetic energy at Q?  Support Q P 2. What is ammonification?  3. Name one control measure for overcoming the problem of ozone depletion.  4. Draw a sketch of Bohr’s model of an atom with three shells.  5. Name the group of plants with the following characters :  (a) Plants with seeds (b) Plants without roots, stem, leaves or flowers (c) Plants having seeds with two cotyledons (d) Plants visible with naked eye but having no chlorophyll. 6. Name and define the force experienced by a body when immersed in a fluid. What is the direction of this force?  7. Why does the percentage of gases like oxygen, nitrogen and carbon dioxide remain almost the same in the atmosphere?  8. What is the qualitative meaning of the symbol of chlorine (Cl) of atomic mass 35.5 u?  9. (a) Mention the postulate of Dalton's Atomic Theory that explain the Law of Constant Proportion.  (b) Mention any two rules to write a chemical formula. (c) Write the chemical formulae of the following compounds : (i) Calcium hydroxide (ii) Ammonium sulphate 1
10. In the following table the mass number and the atomic number of certain elements are given.  Elements A B C D E Mass No. 1 7 14 40 40 At. No. 1 3 7 18 20 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. (a) Select a pair of isobars from the above table. (b) What would be the valency of element C listed in the above table? (c) Which two subatomic particles are equal in number in a neutral atom? Which do you think is a more basic characteristic for classifying organisms—the place where they live or the kind of cells they are made of ? Why?  (i) What do you mean by disease symptoms?  (ii) Suggest two lines of treatment given to patients suffering from infectious diseases. What precautions will you take to justify “prevention is better than cure"?  (a) Name any two air-borne diseases. How does the disease causing microbes spread through air?  (b) How does the immune system of our body function? What happens when : (a) Buoyant Force exerted by the fluid is less than the weight of the body?  (b) Buoyant Force exerted by the fluid is equal to the weight of the body? (a) The potential energy of a freely falling object decreases progressively. What happens to its (i) kinetic energy (ii) total mechanical energy? State the law on which your answer is based.  (b) A household consumes 1 kWh of energy per day. How much energy is this in joule? 50 sound waves pass through a point in 0.1 s. If the distance between one compression and the subsequent rarefaction is 0.34 m, calculate (a) frequency (b) wavelength (c) wave velocity of the longitudinal wave in air.  Represent graphically by two separate diagrams in each case.  (i) Two sound waves having the same amplitude but different frequencies. (ii) Two sound waves having the same frequency but different amplitudes. (iii) Two sound waves having different amplitudes and also different wavelengths. Explain with the help of a labelled diagram carbon cycle in nature.  Give reasons for the following :  40 40 (a) 18 Ar and 20 Ca are called isobars. (b) 'He' and 'Ne' have zero valency. (c) An atom is neutral. (d) Nucleus is positively charged. (e) Isotopes have similar chemical properties. OR (a) What are isobars? Give one example. (b) Write any two uses of isotopes.  (c) Write two differences between isobars and isotopes. 2
21. (a) Draw a well labelled diagram of Euglena. (b) Name the kingdom to which it belongs.  OR Pick the odd one out and justify your choice by giving reasons. (a) Moss, Fern, Pinus, Spirogyra.  (b) Sea cucumber, Octopus, Feather star, Star fish. 22. (a) Derive the formula of kinetic energy of an object of mass ‘m’ moving with a uniform velocity ‘v’.  (b) A force acting on a 20 kg mass changes its velocity from 5 ms–1 to 3ms–1. Calculate the work done by the force. OR (a) Define power. (b) State and define the S.I. unit of power. (c) A force applied on a body of mass 4 kg for 5 seconds changes its velocity from 10 ms–1 to 20 ms–1. Find the power required. 23. (i) How the bats make use of ultrasonic waves to catch their prey? Explain.  (ii) A radar signal is reflected by an aeroplane and is received 2 × 10–5 s after it was sent. If the speed of these waves is 3 × 108 ms–1, how far is the aeroplane? OR (i) What causes reverberation of thunder sound? (ii) A SONAR device on a submarine sends a signal and receives an echo 5 s later. Calculate the speed of sound in water if the distance of the object from the submarine is 3625 m. 24. (a) How can we prevent the loss of top soil? Discuss.  (b) Why are root nodules useful for plants? OR (a) What is biogeochemical cycle? Describe the oxygen-cycle with the help of a labelled diagram. SECTION B 25. Which of the following information is not conveyed by a chemical equation?  (a) The reactants taking part in the reaction (b) The products formed in the reaction (c) The speed of the reaction (d) The ratio of the weights of reactants and products taking part in the reaction 26. Observe the following pictures. The common feature that assigns them to the same phylum is :  (a) wings (b) three pairs of legs (c) jointed appendages (d) antennae 3
27. Which one of the following characteristics can be used to distinguish gymnosperms from angiosperms?  (a) Presence of pollen chamber in gymnosperms (b) Presence of naked ovules in gymnosperms (c) Presence of stomata in angiosperms (d) Absence of naked ovules in gymnosperms 28. Parallel venation is the characteristic feature of  (a) monocots (b) dicots (c) both (a) and (b) (d) none of these 29. In Pinus, the fertilisation takes place in the :  (a) 1st year cone (b) 2nd year cone (c) 3rd year cone (d) microsporangia 30. Scales are present in :  (a) fish (b) reptiles (c) both (a) and (b) (d) none of these 31. A female Anopheles lays the eggs about :  (a) one at a time (b) 5 at a time (c) 50 to 200 at a time (d) None of the above 32. The readings of the spring balance will be :  (a) equal to each other in all cases A, B and C (b) equal to each other in cases B and C only (c) equal to each other in cases A and C only (d) different in every case. 33. The density of which of the following cannot be measured accurately using a spring balance and a measuring cylinder?  (a) A ball filled with a liquid having a leakage (b) A block of ice at 0°C (c) A small porous solid (d) All of these 34. The principle of a spring balance is :  (a) the extension produced in spring is directly proportional to the square of the stretching force (b) the extension produced in spring is directly proportional to the stretching force (c) the extension produced in spring is inversely proportional to the stretching force (d) the extension produced in spring is inversely proportional to the square of the stretching force. 4
35. If the reflecting body is covered with a loose woollen cloth, the reflected sound :  (a) heard will be more louder (b) heard will be less louder (c) heard will be of the same loudness (d) will not be heard. 36. The figure given below shows a line diagram  for the verification of laws of reflection of a sound wave. The vibrating tuning fork should be held at : (a) A (b) B (c) D (d) C 37. It is easier to lift a heavy stone in water because :  (a) the stone loses its mass in water (b) the stone loses its weight in water (c) the stone experiences an upthrust equal to the volume of water displaced (d) the stone experiences an upthrust equal to the weight of water displaced. 38. During the formation of a pulse, most of the medium at any time is :  (a) in the state of rest (b) in the state of motion (c) some parts in the state of rest and some parts in the state of motion (d) none of the above. 39. A pulse travels through a slinky 10 m long from one end to the other end and then back to the point of origin in 3 s. The velocity of the pulse in the slinky is :  (b) 4.5 ms–1 (c) 6.00 ms–1 (d) 6.66 ms–1. (a) 3.33 ms–1 40. In which case is the pressure exerted by the brick on the ground maximum? (a) A C (b) B A (c) C B (d) none of these  41. During sharpening of a knife we :  (a) decrease the surface area of the cutting edge (b) increase the surface area of the cutting edge (c) remove rust from the cutting edge (d) none of the above 42. The tuning fork in the experiment to prove laws of reflection of sound has to be placed with its prongs.  (a) Vertical near the tube (b) Horizontal near the tube (c) Vertically or horizontally near the tube makes on difference (d) Inclined near the tube. ANSWERS 16. 23. 30. 38. 3.6 × 106 J (ii) 3 km OR ((ii) (c) 31. (c) (a) 39. (d) 17. 500 Hz, 0.68 m, 340 m/s 22. (b) 210 J OR (c) 40 W 1450 m/s 25. (c) 26. (c) 27. (b) 28. (a) 29. (b) 32. (b) 33. (d) 34. (b) 35. (d) 36. (a) 37. (d) 40. (a) 41. (a) 42. (b)
SCIENCE-IX (Term-II) MODEL TEST PAPER – 2 (UNSOLVED) Maximum Time : 3 hours Maximum Marks : 90 Instructions : Same as in Sample Question Paper. SECTION A 1. How will the kinetic energy of an object change, if its velocity is halved?  2. What are the two forms of oxygen found in the atmosphere?  3. What is biological fixation?  4. Draw a sketch of Bohr’s model of an atom with four shells.  5. Give two characteristics of the class Amphibia.  6. Define density. What is its unit in SI system?  7. How do the rivers from land, add minerals to sea water?  8. Calculate :  (i) The percentage of hydrogen in ammonium sulphate [(NH4)2 SO4]. (ii) The percentage composition of water present in washing soda [Na 2CO3. 10H2O]. (iii) The mass of oxygen contained in 72 g of pure water. [N = 14 u, H = 1 u, S = 32 u, O = 16 u, Na = 23 u, C = 12 u] 9. What is Avogadro number? How many atoms of each element are present in 6.3 g of nitric acid (HNO3)?  [H = 1.0, N = 14.0, O = 16, NA = 6.022 × 1023 mol–1] 10. An element X has a mass number 27 and it contains 13 protons.  (i) Write the symbolic representation of the element. (ii) Find the number of neutrons and electrons in the element. (iii) Write the electronic configuration of the element. 11. Give three criteria for classification of organisms belonging to the kingdom Monera. 12. Give two symptoms of each of the following diseases : (a) Malaria (b) Typhoid 13. Define health. List four factors affecting health.  (c) Marasmus.  14. A doctor/nurse/health-worker is exposed to more sick people than others in the community. Find out how she/he avoids getting sick herself/himself.  6
15. You have a bag of cotton and an iron bar, each indicating a mass of a 100 kg when measured on a weighing machine. In reality, one is heavier than the other. Can you say which one is heavier and why?  16. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?  17. Define : (i) wavelength (ii) frequency (iii) amplitude of a sound wave. 18. (a) What is meant by 'compression' and 'rarefaction' of longitudinal wave?   (b) Give well labelled graphical representation of a longitudinal wave. 19. (a) With the help of well labelled diagram explain water cycle in nature.  (b) How is greenhouse effect related to Global warming? Explain. 20. (i) On the basis of Thomson’s model of an atom, explain how the atom is neutral as a whole.  (ii) For the symbol H, D and T, tabulate three subatomic particles found in each of them. OR Explain with examples (i) atomic number (ii) mass number (iii) isotopes and (iv) isobars. Give any two uses of isotopes. 21. (a) List any two main characteristics of chordates.  (b) In which class would you place any organism which has – (i) four chambered heart and lay eggs. (ii) skeleton made up of both bones and cartilage and are cold blooded. OR Differentiate between annelida and nematoda. 22. (i) About how many kg of boiled potatoes would you have to eat to supply energy for half hour of swimming. Assume that your body utilises only 20% of the energy stored in potatoes. Energy content of potatoes is 3.7 × 106 J/kg and the energy used in swimming is 25.6 kJ/minute. (ii) A rocket of 3 × 106 kg mass takes off from a launching pad and acquires a vertical velocity of 1 kms –1 at an altitude of 25 km. Calculate (a) Potential energy (b) Kinetic energy. [Take the value of g = 10 ms–2]  OR (i) Distinguish between work, energy and power. State the SI units for each of these quantities. (ii) A dog of mass 16 kg is running at a constant speed of 12 ms–1. Calculate the kinetic energy of the dog. 23. (a) Why the stage of an auditorium has curved background, curtains, carpets and false ceiling?  7
(b) The sound of a ringing bell inside a vacuum chamber cannot be heard. Why? OR State the relationship between frequency and time period of a wave. The wavelength of vibrations produced on the surface of water is 2 cm. If the wave velocity is 16 m/s find the frequency and time period. 24. What is the role of the following in soil formation?  (i) Water (ii) Lichens (iii) Sun OR (i) All living organisms are basically made up of C, N, S, P, H and O. How do they enter the living forms? Discuss. (ii) Lichens commonly grow in Manali or Darjeeling but not in Delhi. Explain. SECTION B 25. Sudden and non-repetitive single disturbance in the medium is :  (a) Propagation (b) Wave (c) Pulse (d) Jerk 26. Skiers use long and wide skies while gliding on the snow, because :  (a) it exerts maximum pressure on the ground. (b) it exerts least pressure on the ground. (c) it cuts a lot of snow (d) it provides more stability. 27. The S.I. unit of thrust is :  (a) kgf (b) gf (c) Pa (d) N 28. The weight of a body felt in tap water and salty water are WA and WB respectively, then :  (c) WA < WB (d) WA = 2WB (a) WA = WB (b) WA > WB 29. Three students used three different containers A, B and C of different shapes, for finding the loss in weight of a solid when dipped in water. On dipping a solid sphere in these containers they would observe that the loss in weight is :  (a) maximum in (A) (b) minimum in (A) (c) maximum in (B) (d) same in all 8
30. Four measuring cylinders with different least counts are shown in figures A, B, C and D. The most suitable cylinder for determining the volume of a cube of side 1 cm is :  (a) A (b) B (c) C (d) D 31. The figure given below represents a graph between the angle of incidence and the angle of reflection for a sound wave. From the graph we can say :  (a) (b) (c) (d) Angle of incidence decreases with the increase in angle of reflection Angle of incidence increases with the decrease in angle of reflection Angle of incidence is always equal to the angle of reflection Angle of incidence sometimes increases and sometimes decreases, depending upon the loudness of sound. 32. In the experiment of verification of reflection of sound, the incident sound is directed along :  (a) the axis of the tube (b) the normal to the axis of the tube (c) at an angle of 30° from the axis of the tube (d) at an angle of 45° from the axis of the tube 33. For producing a transverse wave along a string /slinky, a student should : (a) compress the free end of string /slinky. (b) jerk the free end of string/slinky at right angle to its length. 9 
(c) pull the free end of string /slinky. (d) do all the above. 34. A student sets up a slinky on a smooth table top in the manner shown here. He can produce a pulse in the slinky by giving a jerk to its free end :  (a) at an angle 45° with the table top (b) backward and forward along the length of the slinky Smooth Table (c) downwards (d) towards left 35. The correct way of reading the liquid level is shown in : (a) figure a (b) figure b (c) figure c  (d) figure d 36. A student found the posterior part of a male cockroach in his house. After drawing the following sketch he compares it with the sketch given in the book and found that a part is missing. The missing part as per the sketch is :  (a) brood pouch (b) antenna (c) anal cerci (d) anal style 37. Figures of two plants are given. Observe them carefully and select the option which correctly gives their identification and names of the groups to which they belong :  (a) (i) moss : bryophyta (ii) fern : pteridophyta (b) (i) pine : gymnosperm (ii) leafy plant : angiosperm (c) both (i) and (ii) are mosses and belong to bryophyta (d) both (i) and (ii) are ferns and belong to pteridophyta 10
38. The structure associated with earthworm, cockroach, bony fish and birds are given below in a series. Choose the correct series :  (a) Pneumatic bones, gills, Chitinous plates, metameres (b) Gills, metameres, chitinous plates, pneumatic bones (c) Metameres, gills, chitinous plates, pneumatic bones (d) Metameres, chitinous plates, gills, pneumatic bones 39. Mosquitoes use their siphon tube for :  (a) sucking the blood (b) drinking water (c) swimming (d) breathing 40. A plant showing reticulate venation and a woody stem is a : (a) Pteridophyta (b) Gymnosperm (c) Monocot  (d) Dicot 41. Jointed appendages are characteristic of : (a) Amphibia (b) Reptilia (c) Arthropoda  (d) Mammalia 42. Elements X and Y react to form Xa Yb. Elements P and Q react to form PmQn. The formula of the compound formed between X and Q is.  (a) XbQm (b) XmQb (c) XaQn (d) XnQa ANSWERS 8. 9. 16. 22. 23. 30. 38. (i) 6.06% (ii) 62.93% (iii) 64 g. 6.022 × 1022 atoms of H, 6.022 × 1022 atoms of N, 1.8066 × 1022 atoms of O 208416.685 J (i) 5.185 kg (ii) (a) 7.5 × 1011 J (b) 1.5 × 1012 J OR (ii) 1152 J OR 800 Hz; 0.00125 s 25. (c) 26. (b) 27. (b) 28. (b) 29. (d) (a) 31. (b) 32. (a) 33. (c) 34. (b) 35. (a) 36. (d) 37. (a) (d) 39. (d) 40. (d) 41. (c) 42. (b)
SCIENCE-IX (Term-II) MODEL TEST PAPER – 3 (UNSOLVED) Maximum Time : 3 hours Maximum Marks : 90 Instructions : Same as in Sample Question Paper. SECTION A 1. Calculate the work done by a machine of 50 W power rating in 30 s.  2. What is greenhouse effect?  3. Name one process which increases the percentage of carbon dioxide in the atmosphere.  4. With the help of the given table, find the mass number of oxygen and sulphur atom. Element Symbol No. of Protons No. of Neutrons No. of Electrons Oxygen Sulphur O S 8 16 8 16 8 16 5. Name the phylum to which each of the following animals belong : Sea horse, silver fish, cuttle fish, jelly fish.  6. Give one example each where the same force acting on (i) a smaller area exerts a larger pressure (ii) a larger area exerts a smaller pressure.  7. How are clouds formed?  8. (a) What mass of silver nitrate will react with 5.85 g of sodium chloride to produce 14.35 g of silver chloride and 8.5 g of sodium nitrate?  (b) On what law is the above reaction based and state the law. 9. Calculate :  (a) number of molecules in 90 g of H2O (b) number of mole in 19 g of H2O2 (c) formula unit mass of Al2(CO3)3 (Atomic mass : Al = 27 u, C = 12 u, O = 16 u, H = 1 u, NA = 6.022 × 1023 mol–1) 10. Define (a) Atomicity  (b) Valency (c) Molecule 11. (i) What are the divisions of living organisms?  (ii) How is classification and evolution interrelated with each other? 12. (i) What is a disease?  (ii) Which bacterium causes peptic ulcer? (iii) Who discovered the above pathogen for the first time? 12
13. What are chronic diseases and acute diseases? Which one causes more damage to our body and how?  14. (a) What are anitibiotics  (b) How do they work? (c) How is penicillin effective in controlling bacterial diseases? 15. Give reasons :  (a) It is easier to lift a heavy stone under water. (b) A block of plastic released under water come up to the surface of water. 16. (a) The potential energy of a freely falling object decreases progressively. What happens to its (i) kinetic energy (ii) total mechanical energy? State the law on which your answer is based.  (b) A household consumes 1 kWh of energy per day. How much energy is this in joule? 17. (i) How does a sonar detect the depth of submerged objects?  (ii) Which property determines the pitch of sound? 18. (i) If velocity of sound in air is 340 ms–1, calculate :  (a) wavelength when frequency is 256 Hz. (b) frequency when wavelength is 0.85 m. (ii) Draw a curve showing density or pressure variations with respect to distance for a disturbance produced by sound. Mark the position of compression and rarefaction on this curve. 19. (a) What are the forms of oxygen found in the atmosphere?  (b) “Forests influence the quality of our air, soil and water resources”. Justify the statement. 20. Compare Thomson’s, Rutherford’s and Bohr’s Model of an Atom.  OR (i) The ratio of the radii of hydrogen atom and its nucleus is 105. Assuming the atom and the nucleus to be spherical what will be the ratio of their sizes? (ii) If an atom is represented by the planet earth (‘Re’ = 6.4 × 106 m) estimate the size of the nucleus. (iii) How many neutrons are present in each of the three isotopes of hydrogen? 21. Name the phylum to which this organism belongs. Write any two characteristic features of the phylum.  13
OR Differentiate between the following, giving one main point of difference.  (a) Gymnosperm and Angiosperm (b) Diploblastic and Triploblastic animals (c) Dicotyledons and Monocotyledons 22. (a) Derive the formula of kinetic energy of an object of mass 'm' moving with a uniform velocity 'v'.  –1 –1 (b) A force acting on a 20 kg mass changes its velocity from 5 ms to 2 ms . Calculate the work done by the force. OR (i) Two bodies A and B of masses 4 kg and 16 kg respectively have the same kinetic energy. Calculate the ratio of their velocities. (ii) A mass of 10 kg is dropped from a height of 50 cm. Find : (a) kinetic energy, and (b) velocity, just as it reaches the ground. Does the velocity depend on the mass of the particle? Explain. 23. Distinguish between the following : (a) Mechanical waves and electromagnetic waves (b) Loudness and intensity (c) Crest and compression OR (a) What is audible range of the average human ear? (b) Explain how ultrasound is used to clean spiral tubes and electronic components? 24. (i) What is the greenhouse effect?  (ii) Explain the carbon-cycle with the help of a labelled diagram. OR How are living organisms dependent on the soil? Are organisms that live in water totally independent of soil as a resource?  SECTION B 25. The amount of reflection, a sound wave undergoes depends upon (a) Speed of sound (b) Density of the medium (c) Both (a) and (b) (d) None of these 26. The force acting on a body perpendicular to its surface is called : (a) frictional force (b) thrust (c) pressure (d) all of these 14 
27. A cuboid has dimensions 30 cm × 20 cm × 5 cm. If it exerts maximum pressure, what should be its surface area of contact?  2 2 2 (a) 600 cm (b) 150 cm (c) 100 cm (d) none of these 28. Students are interested to observe gills of a mushroom, which part they should be shown by the label.  (a) (iv) (b) (iii) (c) (i) 29. While locating the stem of a fern, the students find that it is : (d) (ii) (a) underground rhizome (b) coiled like spring (c) totally absent  (d) branched and filamentous 30. You can observe only one cotyledon in the embryo of :  (a) maize (b) gram (c) soyabean (d) bean 31. Seeta was doubtful whether the cactus present in her garden was a xerophyte or not. Which of the following characters will confirm that the cactus is a xerophyte?  (a) Succulent leaves and deep root system (b) Fleshy stem and spiny leaves (c) Green stem and branched root system (d) Woody stem and spiny leaves. 32. Which of the following is not an aerial adaptation?  (a) presence of feathers (b) forelimbs modified into wings (c) presence of gills (d) hollow bones 33. Which of the given mosquito lay its eggs on damp soil ? (a) Anopheles (b) Culex (c) Aedes  (d) None 34. In the experiment to establish the relation between loss in weight of an immersed solid with the weight of water displaced by it, the upthrust experienced by the object in the tap water and in salty water are Uw and Us respectively.  then : (a) Uw = Us (b) Uw > Us (c) Us = 2Uw (d) Uw < Us 35. Four students a, b, c and d while performing an experiment on establishing the relation between the loss of weight of a small solid when fully immersed in tap water, and the 15
weight of water displaced by it, used four different shapes of overflow cans containing water as shown :  The arrangement, that would give correct results is that of student : (a) a (b) b (c) c (d) d 36. While determining the density of the material of a sphere, using a spring balance and measuring cylinder, a student noted the following readings :  (i) mass of the sphere = 81 g (ii) reading of water level in the cylinder without sphere in it = 54 ml (iii) reading of water level in the cylinder with sphere in it = 63 ml On the basis of these observations, the density of the material of the sphere is : (a) 1500 kg/m3 (b) 6000 kg/m3 (c) 7000 kg/m3 (d) 9000 kg/m3 . 37. While calculating the density of a stone with the help of a spring balance and measuring cylinder, few air bubbles were seen sticking to the stone when immersed in water. The presence of air bubbles will lead to the :  (a) increase in density (b) decrease in density (c) no change in density (d) none of these. 38. Which of the following arrangements is best suited for verifying the laws of reflection of sound?  (a) 1 (b) 2 (c) 3 (d) 4 39. Metallic tubes are employed in the verification of laws of reflection of sound waves. These tubes are highly polished because they make the sound waves :  (a) move in straight lines (b) concentrate into powerful beam 16
(c) have multiple reflections and prevent spreading of sound (d) none of the above 40. In the experiment of finding speed of a pulse propagated through a slinky, the pulse is produced :  (a) by pulling the slinky towards us. (b) by pushing the slinky so as to compress it. (c) by giving a jerk to the slinky in a vertically upward direction. (d) by giving a jerk to the slinky in a direction perpendicular to its length. 41. A pulse was created in a slinky/string of length 4 m by a group of students. They observed that it returned, after reflection, at the point of creation 6 times in 10 seconds and calculated the speed as follows :  Students A B C D Speed m/s 0.4 2.4 4.8 9.6 The correct speed was calculated by the student : (a) A (b) B (c) C (d) D 42. Atomic number of an element X is 9. Which of the following represents the correct equation for the ion formation of an atom of X?  (b) X + e– → X– (c) X – e– → X+ (d) X + e– → X+ (a) X – e– → X– ANSWERS 1. 20. (b) 31. 39. 1500 J 4. 16 u, 32 u. 18. (a) 1.33 m (b) 400 Hz OR (i) 1015 : 1 (ii) 64 m 22. (b) 210 J OR (i) 2 : 1 (ii) (a) 50 J 3.16 m/s 25. (c) 26. (b) 27. (c) 28. (d) 29. (a) (b) 32. (c) 33. (c) 34. (d) 35. (c) 36. (d) 37. (b) (c) 40. (a) 41. (b) 42. (b) 30. (a) 38. (b)
SCIENCE-IX (Term-II) MODEL TEST PAPER – 4 (UNSOLVED) Maximum Time : 3 hours Maximum Marks : 90 Instructions : Same as in Sample Question Paper. SECTION A 1. Write an expression for the work done, when a force is acting on an object in the direction of its displacement.  2. Name four pollutants released due to burning of fossil fuels.  3. Why do plants not utilise nitrogen directly from the atmosphere?  4. Give one use of the isotope of (i) cobalt (ii) iodine.  5. How are pteridophytes different from phanerogams?  6. Why is it difficult to hold a school bag having a strap made of thin and strong string?  7. Give four ways in which you can reduce water pollution.  8. (i) Define one mole of an element.  (ii) What is the relation between mole and gram atomic mass of an element. (iii) Gram atomic mass of an element X is 27 g. How many moles of X are in 54 g? 9. Calculate the number of particles in each of the following : (a) 46 g of Na atoms.  (b) 8 g of O2 molecules. (c) 0.1 mole of carbon atoms 10. (a) Illustrate Rutherford’s experiment to explain the model of an atom.  3+ (b) If an ion M contains 10 electrons and 14 neutrons. What are the atomic number and mass number of the element M? 11. How do gymnosperms and angiosperms differ from each other?  12. (i) Why is the immune system essential for health?  (ii) Why are antibiotics not effective for viral diseases? (iii) Give two examples of non-infectious diseases. 13. What are the various means by which infectious diseases spread? Explain giving examples.  14. Give reasons :  (i) Social harmony and good economic conditions are necessary for good health. 18
(ii) Our surroundings should be free of stagnant water. (iii) Balanced diet is neccessary for maintaining a healthy body. 15. (a) Explain why wide sleepers are placed below railway lines?  (b) When we jump into a swimming pool we feel lighter. Why? 16. (a) Define work and write its SI unit.  (b) State three conditions for which mechanical work is zero. 17. How does the sound produced by a vibrating object in a medium reach your ear?  18. A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these frequencies? Take the speed of sound in  air as 344 ms–1. 19. (a) Draw Carbon-cycle (any six labellings).  (b) State two effects of depletion of ozone layer. 20. (a) What is an octet? How do elements reach an octet? (b) Make a schematic atomic structure of magnesium or phosphorus. (given : number of protons of magnesium = 12, phosphorus = 15)  79 (c) Bromine atom is available in the form of two isotopes 35 Br and 81 Br in 49.7% and 35 50.3% respectively. Calculate the average atomic mass of bromine. OR (a) What are canal rays? (b) If an atom contains one electron and one proton, will it carry any charge? Identify the element. (c) 'X' and 'Y' are isobars. 'X' has mass number 14 and atomic number 6. 'Y' has 7 neutrons. Predict the atomic number and mass numbers of 'Y' 21. You are given leech, Nereis, Scolopendra, prawn and scorpion; and all have segmented body organisation. Will you classifiy them in one group? If no, give the important characters based on which you will separate these organisms into different groups.  OR Which organism is more complex and evolved among bacteria, mushroom and mango tree? Give reasons. 22. (i) A body has a mass m and velocity v. If the mass is increased four times and velocity is decreased two times, calculate the ratio of the kinetic energies in the above cases.  (ii) Why does a truck moving at 18 kmh–1 cause far more serious accident than a cycle moving at the same speed? (iii) What kind of energy transformation takes place when a sparkle is lighted? 19
OR State in each of the following cases, if work is done/not done and why?  (a) A girl climbing a staircase. (b) A man standing and holding a briefcase in hand. (c) A porter carrying a heavy load and going down the stairs. (d) A boy preparing for examination. (e) A planet going
CBSE Class IX Term I Summative assessment I Solutions to Sample paper 2 SECTION A 1. The gravitational force of earth that acts on an object of mass 1 kg.
Cbse-spot.blogspot.com 1 SUMMATIVE ASSESSMENT I 2013 ENGLISH COMMUNICATIVE - Class IX SAMPLE QUESTION PAPER Maximum Marks: 90
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