Thursday, October 22, 2020

Algebra

 Hi friends and my dear students! In this post, I have covered class -7 Algebra (Foundation IIT) Notes After Reading Mathematics Algebra (7th class ) IIT Notes level - I,2 -class work, please do share it with your friends. You can Learn Maths for All Classes here.


LEVEL - I

CLASS WORK

1. Find the sum of :

i) 3x + 2y – 4z and 8x – 5y + 2z.

ii) 2x3 + 3x2 – x – 5, x3 –3x2 +6 and x2 + 2x – 5

iii) 3x2 + 5x – 4, 2x + 3 – x2 and 8 – 3x + 7x2

iv)  3n2 + 5mn – 6m2, 2m2, -3mn –4n2, 2mn –

3m2 – 7n2

2. Subtract :

i) 4p + p2 from 3p2 – 8p

ii) a2 + 2ab from b2 + 4ab

iii) 2abc – a2 – b2 from b2 + a2 – 2abc

3. What expression must be added to 5x2 – 7x + 2to produce 7x2 – 1 ?

4. Find the excess of 4p2 – 2pq + 3q2 over

2p2 - pq + 4q2?

5. How much is x3 – 3x2+ 5x – 2 less than

3 -  2x + x2- x3

6. The perimeter of a triangle is 8 + 13a +7a2

and two of its sides are 2a2 + a + 2 and

3a2  – 4a – 1. Find the third side of the triangle.

7. Two adjacent sides of a rectangle are 6a + 9b and 8a – 4b. Find its perimeter.

8. The perimeter of a rectangle is16x3–6x2+12x+4. If one of its sides is  8x2+3x. Find the other side.

9. Find the products of the following :

i) 9x2 and (5x + 7) ii) (ab + bc) and ab

iii) (5x + 3y) and 2x2 iv) 4mn and (3m – 2n)

v) (-3pq) and (p2q + pq2)

vi) (5ab–7bx) and 4a2 bx2

vii) (6a2bc–7ab2c2) and a2b2

10. Find the products of the following.

i) (2a – 5b) (3a –2b) vii) (2 + x) (4 – 2x)

ii) (2p + 1) (3q – 2) viii) (-x – 16) (x + 8)

iii) (2x – 3) (5x + 4) ix) (2x-3) (x + 8)

iv (a – 2b) (a + 3b) x) (4f –3g) (5f + 6g)

v) (a + b) (7a – 4b) xi) (x3+15) (2x3–3)

vi) (a +2b) (3a + 4b)

11. Expand the following using (a + b) 2 = a2 + 2ab + b2

i) (5m + 3n) 2 ii) (a + 2b) 2

iii) (X/Y+Y/X) 2    iv) (2X +1/2X)2   

v)   (103)2     vi)  (20 ½)2

12. Expand the following using (a – b) 2 = a2 – 2ab + b2

i) (3Y - 1/3Y) 2              ii)  (X/Y - Y/X)2  

iii) (3a/2b - 2b/3a) 2      iv)  (1 - a)2 

 v) ( x - 1/2 ) 2             vi) (97)2

vii) (99 1/2) 2

Also Check

IITJEE 7th class Introduction to Algebra Notes

13. Evaluate, using (a + b) (a – b) = a2 –b2

i) (3p + 2q) (3p – 2q)

ii) (a x + b) (a x – b)

iii) (x+3/4)  (x+3/4)

iv) 101 x 99

v) 8.2 x 7.8

vi. (n + 0.6) (n – 0.6)

viii) 412 - 352

ix) 100 1/2 x 99 ½

 x) (n+1/n) (n-1/n) (n2+1/n2) (n4+1/n4)

xi) (1+p) (1-p) (1+p4) (1+p8)

14. If a + b = 5 and ab = 12 find a2 + b2

15. If x – y = 7 and xy = 7 find x2+ y2

16. If 3x + 4y = 16 and xy = 4 then find value of 9x2 + 16y2

17. Simplify :-

(i) 175 x 175 + 2 x 175 x 25 + 25 x 25

(ii) 322 x 322 – 2 x 322 x 22 + 22 x 22

18. p +1/p =5

(i) p 2 +1/p 2    (ii) p4+1/p4

19. Evaluate using

(a + b + c)2 = a2 + b2 + c2 +2ab +2bc+2ca

i) (2x + 3y + 4z) 2    ii) (x + 2y – 3z) 2

iii) (3x – 4y – z) 2   iv) (2a + 3b – 4c) 2

v) (2a – b – c) 2    vi) (p3 + p2 + 1)

vii) (X+1+1/X)2

20. If a + b + c = 0 and a2 + b2 + c2 = 16 find the   Value of ab + bc + ca.

21. If x2 + y2 + z2 = 16 and xy + yz + zx = 10 Find the value of x + y + z

22. If a + b + c = 9 and ab + bc + ca = 23 Find   the value of a2+ b2 + c2

23. Expand the following, using (a + b)3 = a3 + 3a2b + 3ab2 + b3 (or) (a + b)3 = a3 + b3 + 3ab (a + b).

i) (a + 2)3 ii) (a+1/a)3

iii) (2x + 1)3 iv) (2x + 3y) 3

v) (2x + y) 3

24. Expand the following using (a – b)3 =

a3 – 3a2b + 3ab2 – b3 (or) (a – b)3 = a3–b3–3ab(a–b)

i) (3x – 5y) 3 ii) (3x – 2y) 3

iii) 993

HOME  WORK

1. Find the sum of :

i) 3a – 5b + 2c and 2a + 3b – c

ii) a2 + a – 3, 2a + 3a2 + 6 and 4a2 – 5a + 8

iii) 5a + 6b – 3c, 4b + c – 3a and a – 6c – 3b.

 2. Subtract :

i) 5a – 3b + 2c from 4a – b - 2c

ii) a2 + 3a – a3 – 6 from 2a2 + a – 2a3 + 3

3. Find  the perimeter of triangle whose sides are

2y + 3z, z – y,  4y – 2z.

4. Find the products of the following :

i) 2x and (x + y) ii) 2p and (3p + 4q)

iii) xy and (x – 2y)

5. Find the products of the following.

i) (x + 2) (x + 3)       iv) (c + 7) (c- 5)

ii) (x + 6) (x – 6)       v) (x + a) (x –b)

iii) (x – a) (x + b)       vi) (x –a) (x – b)

vii) (x + a) (x + b)

6. Expand the following using (a + b)2 = a2 + 2ab + b2

i) (a – 1/a) 2

ii) (3p – 4q) 2

iii) (49) 2

8. Evaluate, using (a + b) (a – b) = a2 – b2

i) (x + a) (x – a)             ii) (2x + 7) (2x – 7)

iii) (7m– 4n) (7m + 4n)    iv) 442 - 392

v) 20.5 - 19.5

9. If 2x – 3y = 8 and xy = 2 then find the value of

4x2 + 9y2

10. Evaluate using

(a + b + c) 2 = a2 + b2 + c2 +2ab + 2bc + 2ca

i) (a + 2b + c) 2       ii) (x – y + z) 2

iii) (x2 + x – 1) 2     iv) (x – 2y – 3z) 2

11. Solve (x + a) 3 by using suitable formula

12. Expand the following using (a – b) 3 = a3 – 3a2b+ 3ab2 – b3 (or) (a – b)3 = a3–b3–3ab(a – b)

i) (x – a)3 ii) (x – 2y)3

iii) (2x – 1)3

13. If x + y = 10 and xy = 21 then find the value of x3 + y3.

14. Divide :

i) –28p2qr3 by –7pqr

ii) 9p2q3r4 by – 12pq4r2

15. Divide the given polynomial by the given monomial

i) 15(a3b2c2 – a2b3c2 + a2b2c3) ÷ 3abc

ii) (3p3 – 9p2q – 6pq2) ÷ (–3p)

 LEVEL - II

CLASSWORK

1. Multiply together :

a) x3- 7x + 5, x2- 2x + 3

b) x – 2y + 6, x – 2y – 6

c) a – 2b + c, a + 2b – c

d) 3x2 – 2x – 5, 2x – 5

e) x4- x2y2 + y4, x2+ y2

f) x2+ x – 2, x2 + x – 6

2. Add the following :

a) 5x2 – 2xy + 8y2, 3xy-7y2 – 2x2

and y2 + xy – 4x2

b) p2 + 2q2 – 5r2 + 2pqr, q2 – 3p2 + 2r2

– 5pqr and r2 – p2 – 2q2 + pqr

3. Subtract:

3xy2 – 3x2y + x3 – y3 from x3 + 3x2y + 3xy2 + y3

4.Find (i) A + B + C (ii) 3A – 2B – C

5. Find the zeros of the following:

i) an + am x (a ≠ 0) ii) a2x2 – 1

iii) xn iv) 1 –ax (a ≠ 0)

6. Find the degree of

[1 + 2x + 3x2 + 4x3 + ……….(999 terms)].

7. If two polynomials of degrees m, n are

multiplied, then find the degree of the resultant polynomial. Explain with one example.

8. How much is 4a2 – 5ab + 9b2 greater then

10b2 – 5a2 + 11ab?

9. If A = a + b + c, B = a – b + c and C = a + b – c

and D = -a + b + c, find (A + C) – (B + D).


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