Algebra II(Senior Class Math Study by Topics Test ) : GATE Academy

Welcome to your Algebra II(Senior Class Math Study by Topics )

NAME

EMAIL

PHONE NUMBER

1. Find the second term in the expansion of (2+3x)¹²

334

4096

73728x

22x²

2. Given that (1 + 3x)⁴ = 1 + Px + Qx² ...

find 3P + 2Q.

72

144

24

12

3. Expand completely (1 - 3x)⁵ in ascending powers of x.

1 - 5x + 67x² + 270x3 + 405x4 - 243x5

1 - 15x + 90x² + 270x3 + 405x4 - 243x5

1 - 5x² + 270x3 + 405x4 - 243x5

1 - 5x + 67x² + 270x3

4. Subtract the polynomials: (- 7 x²y + xy + 3x + 2) - (5 x²y - 5 xy - 6x - 7)

-12x²y+6xy+9x+9

12x²y+6xy+9x+9

-2x²y-4xy-2x-5

-12x²y-6xy-9x-9

5. Given that

where A and B are constants, find the value of (A + B)

2

4

3

1

6. Subtract the polynomials: (9 x - 6) - (- 5x + 7)

4x + 1

14x - 13

-4x + 13

-4x - 13

7. Find the remainder when
12x⁴-9x²-2x-1 is divided by 2x+1

0

x-1

1+x

1/x

8. Add the polynomials: (x²y + 3x + 2) + (2 + 2 xy² + 3x)

3x²y+6x+4

3x²y²+6x+4

3xy²+6x+4

x²y+2xy²+6x+4

9. Divide 6x² - 13x + 5 by 2x -1

x+7y

2x+5

3x-5

5x-3

10. Find the term independent of x in the expansion of
(x²- 2/x)⁶

140

345

240

340

11. Add the polynomials: (xy + 3x + 2) + (3x² + y)

3x²+4xy+2

3x²+5xy+2

3x²+xy+3x+y+2

3x²+2xy+3x+2

12. Use binomial theorem to expand (1 - 4x)³ in ascending powers of x

1 - 12x + 64x3

1 - 12x + 48x2

1 - 2x + 8x2 + 14x3

1 - 12x + 48x2 + 64x3

13. Decompose into partial fractions : (8x + 14) / (x + 1)(x + 5)

13/(2(x + 5))

3/2(x+5)

3/(2(x + 5)) + 13/(2(x + 6))

3/(2(x + 1)) + 13/(2(x + 5))

14. Find a positive value of p if the expression 2x² - px - + p leaves a remainder 6 when divided by x-p

5

4

2

3

15. Express

in partial fractions.

4/(3x+2) + 3/(x+1) + 1/(x+3)

7/(x+2) - 2/(x-2)

2/(x+1) + 3/(x-2) + 2/(x+2)

4/(x+1) + 3/(x+3)

16. Multiply (x + 3y + 5) by (2x² + 5y + 2)

x²+31y+18x+2x+9

2x³+6yx²+5xy+15y²+31y+10x²+2x+10

2x³+6yx²+5xy+15y

2x²+6y²x+4xy+12x²+31y+18x+2x+9

17. Subtract the polynomials: (x²y + 3x + 2) - (2 + xy² + 3x)

-2x²y

0

x²y+xy²

x²y-xy²

18. Find the value of M if

2/3

5/3

-5/3

-2/3

19. Find the binomial expansion of (0.7)⁵

5.8589

45.075

108.67

0.16807

20. Simplify

2x-y

3/5

2/5

1

21. Subtract the polynomials: (-x² + 5 x) - (6 x² + x - 2)

-7x²+4x+2

5x²+6x-2

5x²+6x

-5x²+6x+2

22. Decompose into partial fractions : (5x² + 12x + 3) / x(x + 1)²

3/x + 2/(x + 1) + 4/(x + 1)²

x + 2/(x + 1)

2/(x+7) - 3/x²- 2/(x + 1)²

4/(x + 1)² +3/x

23. Find the third term in the expansion of (1-2x)¹⁰

180x²

123x²

12

20x

24. Divide 2x³ + 11x² + 17x + 6 by 2x + 1

7x-2

x²+7x-2

2x+1

x²+5x+6

25. Use Bionomial Theorem to find the first three terms in the expansion of
(1 + x)¹⁵

2 + 45x + 735x²

3x+ 536x³

1 + 15x + 105x²

45 + 46x² +342x³