ALGEBRA AND GEOMETRY ASSIGNMENT

1.     For each sequence, find the next four terms.
a.     3, 6, 9, 12, ……
b.     1000, 500, 250, …….
2.     Find the first five terms of the following sequence, whose ‘n­th’ term is given.
a.    
b.    
3.     Find the first three terms of the sequcnes for which Sn is given below.
a.    
b.    
4.     Which of the following lists of numbers are Arithmetic Progressions? Justify.
a.     500, 750, 1000, 1250, …….
b.     6, 8, 10, 12, 15, ……….
5.     Write the first five terms of the following Arithmetic Progressions where, the common difference ‘d’ and the first term ‘a’ are given.
a.    
b.    
6.     How many three digit natural numbers are divisible by 3?
7.     How many two digit natural numbers are divisible by 2?
8.     Find the sum of all even natural numbers from 1 to 200.
9.     The sum of the first 55 terms of an A.P. is 3300. Find the 28th term.
10.   Find four consecutive terms in an A.P. whose sum is 12 and the sum of 3rd and 4th term is 14.
11.   Find three consecutive terms in an A.P. whose sum is 27 and their product is 504.
12.   Find four consecutive terms in an A.P. Such that the sum of the middle two terms is 18 and the product of the two end terms is 45.
13.   A farmer borrows Rs. 1000 and agrees to repay with a total interest of Rs. 140 in 12 instalments, each instalment being less then the preceding instalment by Rs. 10. What should be his first instalment?
14.   A man repays a loan of Rs. 3250 by paying Rs. 305 in the  first month and then decreases the payment by Rs. 15 every month. How long will it take to clear his loan?
15.   Which of the following are quadratic equations?
a.    
b.    
16.   Write the following quadratc equations in a standard form
a.    
b.    
17.   Determine whether the given values of ‘x’ are the roots of the given quadratic equation  ,
18.   If one root of the quadratic equation  is 9, then find the value of k.
19.   Solve the following quadratic equations by factorization method.
a.    
b.    
c.     
d.    
e.    
f.     
g.    
20.   Solve the quadratic equations by Completing Square method.
a.    
b.    
c.     
d.    
e.    
21.   Solve the following quadratic equations by using the formula.
a.    
b.    
c.     
d.    
22.   Find the value of discriminant for each of the following equations.
a.    
b.    
c.     
d.    
e.    
23.   Determine the nature of roots of the following equations from their discriminants.
a.    
b.    
c.     
d.    
24.   Find the value of k if the given equation has real and equal roots.
25.   1. Draw the circumcircle of ∆ ABC in which AB = 5 cm, P = 600, M = 500.
26.   2. Construct the circumcircle of ∆XYZ in which XY = 6 cm, Y = 1000, YZ = 4 cm.
27.   3. Construct the circumcircle of ∆PQR, PQ = 6 cm, P = 700 , M = 500.
28.   4. Construct a right angled ∆ABC, Where AB = 7 cm, BAC = 500, ACB = 900. Draw circumcircle of ∆ABC.
29.   5. Construct the incircle of ∆RST in which RS = 7 cm, ST = 8 cm, RT = 6 cm.
30.   6. Construct the incircle of ∆DEF, DE = EF = DF = 6 cm.
31.   7. Construct the incircle of ∆KLM, KL = 3 cm, LM = 4 cm, KM = 5 cm.
32.   8. Draw incircle of ∆DEF, in which DE = EF = 6 cm, DEF = 800.
33.   9. Draw the incircle of ∆ ABC in which AB = 5 cm, P = 600, M = 500.
34.   10. Construct the incircle of ∆XYZ in which XY = 6 cm, Y = 1000, YZ = 4 cm.
35.   11. Construct the incircle of ∆PQR, PQ = 6 cm, P = 700 , M = 500.
36.   12. Construct a right angled ∆ABC, Where AB = 7 cm, BAC = 500, ACB = 900. Draw incircle of ∆ABC.
37.   13. Construct the circumcircle of ∆RST in which RS = 7 cm, ST = 8 cm, RT = 6 cm.
38.   14. Construct the circumcircle of ∆DEF, DE = EF = DF = 6 cm.
39.   15. Construct the circumcircle of ∆KLM, KL = 3 cm, LM = 4 cm, KM = 5 cm.
40.   16. Draw circumcircle of ∆DEF, in which DE = EF = 6 cm, DEF = 800.
41.   17. Draw a tangent at any point M on the circle of radius 4 cm and centre O.
42.   18. Draw a tangent at any point R on the circle of radius 5 cm and centre P.
43.   19. Draw a circle of radius 3.5 cm. Draw a tangent to the circle from any point on the circle using the centre of the circle.
44.   20. Draw a circle with centre P and radius 5 cm. Draw a chord MN of length 7 cm. Draw tangent to the circle through point M and N.
45.   Text Box: Omtex classes21. Draw a tangent at any point A on the circle of radius 5 cm and centre P.
46.   22. Draw a tangent at any point Y on the circle of radius 4.5 cm and centre P.
47.   23. Draw a circle of radius 5.4 cm. Draw a tangent to the circle from any point on the circle using the centre of the circle.
48.   24. Draw a circle with centre P and radius 5 cm. Draw a chord MN of length 6 cm. Draw tangent to the circle through point M and N.
49.   25. Draw an angle of 500 and bisect it.
50.   26. Draw seg MN = 7 cm and draw a perpendicular bisector of seg MN.
51.   27. Draw an angle of 1250 and bisect it.
52.   28. Draw perpendicular bisector of seg AB of length 9 cm.
53.   29. Draw ∆ ABC with AB = 4 cm, BC = 6.5 cm and ABC = 800. Draw the circumcircle of ∆ ABC.
54.   30. Draw ∆ PRS with PR = 5.4 cm, RS = 4.5 cm, PS = 6.7 cm. Draw the circumcircle of ∆ PRS.
55.   31. Draw ∆ ABC, with BC = 6 cm, AB = 4.8 cm and AC = 5 cm. Draw the circumcircle of ∆ ABC.
56.   32. Draw ∆ ABC with AB = 4 cm, BC = 6.5 cm and ABC = 800. Draw the incircle of ∆ ABC.
57.   33. Draw ∆ PRS with PR = 5.4 cm, RS = 4.5 cm, PS = 6.7 cm. Draw the incircle of ∆ PRS.
58.   34. Draw ∆ ABC, with BC = 6 cm, AB = 4.8 cm and AC = 5 cm. Draw the incircle of ∆ ABC.
59.   35. Draw an angle of 700 and bisect it.
60.   36. Draw seg MN = 8 cm and draw a perpendicular bisector of seg MN.
61.   37. Draw an angle of 1750 and bisect it.
62.   38. Draw perpendicular bisector of seg AB of length 6.5 cm.
63.   39. Construct ∆ LMN, such that LM = 6 cm, MN = 4 cm, LN = 5 cm.
64.   40. Construct ∆ PQR, such that PQ = 5 cm, P = Q = 500.
65.   41. Draw the circumcircle and the incircle of an equilateral triangle, ∆ ABC, with side 6.6 cm.
66.   42. Draw a tangent to a circle with centre O and radius 3.1 cm at any point R on the circle.
67.   43. Draw a circle of radius 3.6 cm. Take any point M on it. Draw a tangent to the circle at M, without using the centre of the circle.
68.   44. Draw a circle of suitable radius. Draw a chord XY of length 4.6 cm. Draw tangents at points X and Y, without using the centre of the circle.
69.   45. Draw a circle with radius 3 cm. Draw a chord AB of length 5 cm. Draw tangent at points A and B, without using the centre of the circle.
70.   46. Construct tangents to the circle with centre A and radius 3.5 cm, from a point B at a distance of 7.6 cm from the centre.
71.   47. Draw tangents to the circle with centre O and radius 5 cm, from a point C at a distance of 8 cm from the centre.
72.   48. Draw a tangent to the circle with centre C and radius 4 cm, from a point B at a distance of 8 cm from the centre.
73.   49. ∆ ABC ∆ LMN. In ∆ ABC, AB = 5.1 cm, B = 550, C = 650 and , construct ∆LMN.
74.   50. ∆ XYZ ∆ DEF. In ∆ DEF, DE = 5.5 cm, E = 400, EF = 4 cm, and  . Construct ∆ XYZ.
75.   51. Construct ∆ ABC in which BC = 4cm, B = 500, AB = 3.5 cm. ∆ ABC ∆ PBQ. Construct ∆ PBQ such that  .
76.   Find the slopes of lines with inclinations (i)  (ii)  (iii)  (iv) .
77.   Show that □ABCD is a parallelogram if A = (4,8) , B = (5,5) , C = (2,4) , D = (1,7).
78.   If the slope of the line is 2 and y intercept is 5 then write the equation of that line.
79.   Write the equation  in the slope intercept form. Write the slope and y – intercept.
80.   P(2,3) is a point on the line find c.
81.   Two points of each of the line are given below write the equation of these lines.
a.     A(1, 1) &  B(2,2)
b.     P(5,5) & (3, -1)
c.      A(9, 2) & (4, 7)
82.   Find and  intercepts of each of the following line.
a.    
b.    
83.   them are right angled triangles.
a.     8, 15, 17.
b.     9, 40, 41.
c.      11, 12, 15.
84.  
a.     If , DE = 5.6 cm then find AB.
b.     If BC = 2.2. cm then find EF.
c.      If , , find the ratio of the area of  and .
85.   The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.
86.   The areas of two similar triangles are 81 sq. Cm. And 49 sq. Cm. Reapectively. Find the ratio of their corresponding heights. What is the ratio of their corresponding medians?
87.   A ladder of 10m long reaches a window 8 m above the ground. Fid the distance of the foot of the ladder from the base of the wall.
88.   Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
89.   Prove that three times the square of any side of an equilateral triangle is equal to four times the square of an altitude.
90.   Find the length of the altitude of an equilateral triangle, each side measuring ‘a’ units.
91.   Find the side of a square whose diagonal is  cm.
92.   Write the equation of X – axis and Y – axis.
93.   Find the equation of the line passing through the origin and the point (-3, 5).