IIT JEE 7th class Mathematics Algebra Notes,level - I,2 -class work

Algebra

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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

Introduction To Trigonometry

SSC (10th class) Trigonometry Exercise - 11.1 Solution

SSC(10th class) Trigonometry Exercise - 11.1 Solutions

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 + a^m x (a ≠ 0) ii) a²x² – 1

iii) xⁿ iv) 1 –a^x (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).