Class : VIII Worksheet 4 Annual Exam March 2016 Sub: Math

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1 Class : VIII Worksheet 4 Annual Exam March 2016 Sub: Math 1. Find the area of the triangle whose sides are 13cm, 20cmand 21cm. Also find the length of the height corresponding to the largest side of the triangle. 2. If the area of an equilateral triangle is 36 3 cm 2, find its perimeter 3. Find the area of a circular ring whose external and internal radii are 40cm and 37cm respectively. 4. Find the area of a triangle whose sides are 17cm, 25cm and 26cm. 5. The area of a triangle is 216cm 2. One side of the triangle measures 24cm. Find the corresponding height. 6. The base and height of a triangle are in the ratio 7:4. If the area of the triangle is 87.5cm 2, find its base and height. 7. The perimeter of a rectangle is 36cm and its breadth is 8.4cm. Find the length and area of the rectangle. 8. The area of a rectangle is 20m 2 and its length is 8m. Find the diagonal and perimeter of the rectangle. 9. The length of a rectangle is 12 and its diagonal is 15m. Find the breadth and area of the rectangle. 10. The area of a rectangular park is 2160m 2. The length and breadth of the park are in the ratio 5:3. Find the cost of fencing the park at Rs5 per metre. 11. A rectangular lawn measuring 38m by 25m has been surrounded externally by a 2.5m wide path. Calculate the cost of gravelling the path at the rate of Rs4.50 per sqm 12. A rectangular field is 50m by 40.5m. It has two crossroads through its centre, running parallel to its sides. The width of the longer and the shorter roads are 1.8n and 2.5m respectively. Find the total expense involved in cementing the road at Rs 24 per sqm and laying grass in the remaining part at Rs 1.60 per sqm. 13. The length of the diagonal of a square is 32cm. Find the area and perimeter of the square ( Take 2 = 1.41) 14. A room 9.5m long and 6m wide is surrounded by a verandah 1.25m wide all round it on the inside. Find the cost of leveling the path at Rs1.80 per sqm.

2 15. A square field has an area of 625 sqm. Find the cost of putting a fence round it at Rs per metre. 16. Find the area of a parallelogram whose base is 3.5m and height is 80 cm. 17. The base of a parallelogram is twice its height. If the area is 98 sqcm, find the base and the height. 18. Find the area of a rhombus whose diagonals are 25cm and 16.8cm. 19. Find the area of a rhombus having each side equal to 13cm and one of its diagonals equal to 24cm. 20. The parallel sides of a trapezium are 18cm and 15cm and the distance between them is 5.6cm. Find the area of the trapezium. 21. The lengths of the parallel sides of a trapezium are in the ratio 5:3 and the distance between them is 12.5cm. If the area of the trapezium is 450 sqcm, find the lengths of its parallel sides. 22. PQRS is a parallelogram with PQ = 26cm and QR = 20cm. If the distance between its longer sides is 12.5cm, find i) the area of the parallelogram ii) the distance between its shorter sides. 23. Find the radius and circumference of a circle whose area is 154 sqcm. 24. Find the area of a circle whose circumference is 55cm. 25. A wall of length 13.5m, width 60cm and height 1.6m is to be constructed by using bricks, each of dimensions 22.5cm by 12cm by 8cm. How many bricks will be needed? 26. The volume of cuboid is 972cm 3. If is length and breadth be 16m and 13.5m respectively, find its height. 27. The dimensions of a room are 8m by 6.5m by 3.5m, find i) area of 4 walls of the room ii) the area of the floor of the room. 28. A room 9m long, 6m broad and 3.6m high has one door 1.4mby2m and two windows, each 1.6m by 75cm. Find i) area of 4walls excluding doors and windows ii) the cost of white washing the walls at the rate of Rs2.50m 2 iii) the cost of painting its ceiling at Rs 5 per sqm 29. The length, breadth and height of a cuboid are in the ratio 7:6:5. If the surface area of the cuboid is 1926 sqcm, find its dimensions.

3 30. A closed wooden box 80cm long, 64cm wide and 45cm high, is made up of wood 2.5cm thick. Find i) the capacity of the box ii) the weight of the box if 100cm 3 of wood weighs 8 grams. 31. The external dimensions of a wooden box, open at the top are 54cm by 30cm by 16cm. It is made of wood 2cm thick. Calculate the capacity of the box ii) the volume of wood. 32. Five cubes each of edge 7cm are joined side by side to form a cuboid. Write the dimensions of the resulting cuboid obtained. Also, find the total surface area and thevolume of the resulting cuboid. 33. Using the class intervals 0-4, 5-9, 10-14, construct the frequency distribution for the following data: Find the median : 4, 0, 9, 6, 11, 7, 3, 8, Construct a histogram for the following data. Marks No of students 36. The marks obtained by 12 students in a test are 13, 15, 10, 17, 16, 8, 7, 20, 12, 11, 12 and 9. Find the mean and median. 37. Find the mean of the following distribution x f Find the mean, median and mode for the following data :11, 8, 3, 3, 2, 5, 10, 12, 9.

4 39. The following table gives the daily wages of 50 workers of a factory. Calculate the mean daily wages of workers of the factory. Wages(in Rs) No of workers The mean of numbers 6, 1, 9, 0, 3, 8, x, 6, 12 is 6. Find the value of x. 41. If A = { 7, 9, } B = { 2, 3} and C = { 8, 9, 10} Find i)b C ii) A (BC) I iii) (A B) (A C). Is A (BC) = (A B) (A C). 42. A = { 0, 1, 2} B= { 1,2,4} Find i)(n-m) (NM) ii) (MN) (M-N) Let A = {5, 6, 7} and B={3, 4, 5, 6, 7. Let R = {(a, b) : a A, b B and a b}. Write R in roster form. Find its domain and range. 44. Let P = {6, 7, 8, 9} and Q={ 4, 6, 8, 10}. Let R = {(x, y) : x P, y Q and x y}. Write R in roster form. Find its domain and range. 45. Let A = { 7, 8, 9, 10} and B= { 4, 5, 6, 7, 8}. Let R be a relation is 2 greater than from A to B. Represent R in roster form and arrow diagram. 46. Let A = {2, 3, 4, 5} and {5, 8, 11}. Let f = {(2, 5), (3, 8), (4, 11), (5, 11)}. State whether f is a mapping from A to B or not. Give reason. 47. Which of the following relations are functions? Give reasons i) R1= {(2, 8), (3, 8), (5, 8), (7, 8)} ii)r2 = {(2, 3), (2, 4), (2, 5), (2, 6)} iii) R3 = {(a, b), (b, c), (c, d), (d, e)} 48. Let A = { 2, 1, 0, 1, 2} and B = { 1, 0, 1, 2, 3}. Consider the rule, f(x) = x 2-1, x A Represent the function in roster form and arrow diagram.

5 49. Let A = { 1, 3, 5, 7} and B = { 1, 3, 7, 11 }. f is a function from A to B defined by f(x) = 2x 3, x A. Represent the function in roster form and arrow diagram 50. Given F(x) = 4x 7, x R Find i) f(4) ii) f(-4) iii) f(3) + f(-3) 51. Let f(x) = 2x2 3, x R Find i)f(1) ii) f(-1) iii) f(2) iv) 52. The following table shows the number of cars of different colours in a parking space. Draw a pie graph for the data.

SA-II Model Exam - II

Student Name : Date : 08/05/2017 SA-II Model Exam - II Question 1 Name the rays given in the picture Question 2 How are the following names related? a) Trapezium b) Parallelogram c) Rhombus d) Rectangle