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MATHEMATICS-IX (Term-II) Model Test Paper-4 (Unsolved) [For S.A.-II (Term - II)]Time : 3 hours M.M. : 90General Instructions : Same as in Sample Question Paper. SECTION A N A SH(Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choiceshave been provided of which only one is correct. You have to select the correct choice.) A 1. In the figure, D and E are mid-points of AB and AC respectively. The length of DE is : K (a) 8.2 cm A (b) 5.1 cm (c) 4.9 cm PR (d) 4.1 cm S ER 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 TH (b) 1 cm (c) 2 cm (d) 3 cm O 3. In the figure, if O is the centre of the circle and A is a point R on the circle such that ∠CBA = 40° and AD ⊥ BC, then the value of x is : B (a) 50° L (b) 90° (c) 45° YA (d) 40° O G 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 : 1 13 3 1 (a) (b) (c) (d) 4 40 10 8 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 : N (a) 60 (b) 70 (c) 80 A (d) 100 SH 8. Diameter of the earth is four times (approximately) the diameter of the moon, then the ratio of their surface areas is : A (a) 4 : 1 (b) 8 : 1 K (c) 16 : 1 (d) 64 : 1 A SECTION B PR (Question numbers 9 to 14 carry 2 marks each) S 9. Find the solution of the linear equation 2x + 5y = 10 which represents a point on ER (i) x-axis (ii) y-axis TH10. If the two adjacent angles of a parallelogram are (3x – 20)° and (50 – x)°, then find the value of x. O11. In a parallelogram ABCD, AB = 10 cm. The altitude corresponding to the sides AB and R AD are respectively 7 cm and 8 cm. Find AD. B L12. In the figure, A, B and C are three points on a circle YA with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, O find ∠ADC. G13. 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. N A16. The radius and height of a cylinder are in the ratio 2 : 3. If the volume of the cylinder SH 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. A K18. Give the equations of two lines passing through (2, 14). How many more such lines are there and why? A PR19. 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. S20. The mean of the following distribution is 50. ER x 10 30 50 70 90 TH f 17 5p + 3 32 7p – 11 19 Find the value of p and hence the frequencies of 30 and 70. O OR R B 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 :L YA 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 O Now find the following : G (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 4 5 6 7 8 9 10 11 12 13 Days 50 32 22 18 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) N A24. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and SH DA respectively. Show that the quadrilateral PQRS is a rectangle. OR A In a parallelogram show that the angle bisectors of two adjacent angles intersect at right angles. K A SECTION D PR (Question numbers 25 to 34 carry 4 marks each.) S25. If the work done by a body on application of a constant force is directly proportional ER 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 TH read from the graph the work done when the distance travelled by the body is : (i) 2 units (ii) 0 units. O26. A cylindrical tube opened at both ends is made of iron sheet which is 2 cm thick. If the R outer diameter is 16 cm and its length is 100 cm, find how many cubic centimetres of B iron has been used in making the tube. L OR YA The volume of two spheres are in the ratio 64 : 27. Find the radii, if the sum of their radii is 21 cm. O27. A random survey of the number of children of various age groups playing in a park was G found as follows : Age (in years) Number of children 1–2 5 2–3 3 3–5 6 5–7 12 7 – 10 9 10 – 15 10 15 – 17 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. N A SH A30. ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. K A31. Make a frequency polygon for given frequency table. PR Class interval Frequency 0 − 5 S 2 ER 5 − 10 3 10 − 15 4 TH 15 − 20 1 20 − 25 5 O 25 − 30 3 R B32. Monica has a piece of canvas whose area is 551 m2. She uses it to have a conical tent L made, with base radius of 7 m. Assuming that all the stitching margins and the wastage YA incurred while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with it. O33. The side AB of a parallelogram ABCD is produced to any point P. A line through A and G 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. For FREE ASSIGNMENTS & QUESTION BANK log on to www.GoyalAssignments.com 20