EXPECTED SAMPLE QUES TIONS FOR MATHEMATIC S 1. 2. 3. 4. 5. 6. In a village a farmer has a field in the shape of a parallelogram while his friend has it in the shape of a triangle. Both the fields have the same size of base equal to 96 m and height 85 m. Both grew wheat in their farms. The one having a triangular field distributed one- fourth of his produce to the poor people in the village. Questions: a. Explain with figure the fields of the farmers. b. Who has more area and by how much? c. What value of the farmer with the triangular field is shown here? A cuboid has total surface area of 40 m2 and lateral surface area 26 m2. Find the area of its base. Also find its volume if its height is .7 cm. A powder tin has square base with side 8 cm and height 13. Another powder tin is cylinder with radius 7 cm and height 15 cm. Which of the two contains more powder? Also find the difference of their capacities. Find mean, mode and median for the following data: 10,15,18,10,10,20,10,20,15,21,15 and 25. In a circle of radius 5 cm, AB and AC are two chords such that AB=AC=6 cm. Find the length of the chord BC. In the given figure, two circles intersect each other at A and B. The centre of the smaller circle is O and lies on the larger circle. If PAC and PBD are straight lines and ∠APB= 700, find ∠AOB, ∠ACB and ∠ADB. C A P 700 O . . B D 7. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices. A and C on diagonal BD as shown in figure. Show that: D C P Q A 8. 9. 10. 11. Life time (in hours) Number of lamps 12. 13. B i) ∆APB ≅ ∆CQD ii) AP = CQ Draw a ∆ABC with base BC=7 and angles in the ratio 3:4:5. Draw the bisectors of its angles. Draw the graph of linear equations y=x and y=-x on the same graph. Find the point of intersection of the two lines. Draw the graph of each of the equation x-2y-3=0 and 4x+3y-1=0 on the same graph. Write the co-ordinates of the point of intersection of these lines. The following table gives life time of 100 neon lamps. Draw an histogram to represent the information: 300-400 12 10 7 Fi 15. 16. 17. 18. 19. 600-700 25 700-800 30 800-900 10 30 8 50 10 70 15 90 10 A dome of a building is in the form of a hemisphere. If it is white washed from inside at Rs/ 5/m 2, total cost of white washing is Rs. 385. Find the inner surface area of the dome and volume of air inside the dome. Construct a ∆ABC in which AB=BC=6 cm and angle AB and BC is 700. Find the area of figure formed by joining the midpoints of adjacent sides 12 cm and 16 cm of a rectangle. Check whether (i) (--2,2) ii) (3,4) iii) (4,4) lies on the linear equation y=x. Give the equations of two lines passing through (4, --2). How many more such lines are there? In rolling a die 500 times the following results were obtained: No. No. of Times 20. 500-600 15 How many metres of cloth of 1.1 m width will be required to make a conical tent whose height is 12 m and base radius is 16 m ? Find also the cost of the cloth used at the rate of Rs. 14 per metre. Find mean of the following distribution: Xi 14. 400-500 8 1 28 2 135 3 142 4 79 5 81 6 35 21. A survey of 500 families was conducted to know their opinion about a particular detergent powder. If 375 families liked the detergent powder and the remaining families disliked it, find the probability that a family chosen at random. i) likes the detergent powder ii) does not like it. Find the median and mode of the data. 2,3,4,5,0,1,3,3,4,3 22. Volume of a hemispherical toy is 23. 24. Draw an angle of 400 and divide it into four equal parts. Draw an angle of measure 1080 and bisect it. 539 6 𝑐𝑚 3, find its curved surface area.