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

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

NAME

PHONE NUMBER

1. Given that
find the value of Q

1/3

1/2

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

4/(x + 1)² +3/x

2/(x+7) - 3/x²- 2/(x + 1)²

x + 2/(x + 1)

3/x + 2/(x + 1) + 4/(x + 1)²

3. Expand (1 + x)⁵ in ascending powers of x.
Without using any calculating device, estimate (1.1)^⁵,
giving your answer correct to 4 decimal places

1 + 5x + 10x3 + 5x4 + x5, 1.6105

1 + 5x + 10x2 + x5, 1.610534

1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.61

1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.6105

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

2x+1

x²+7x-2

7x-2

x²+5x+6

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

45 + 46x² +342x³

2 + 45x + 735x²

3x+ 536x³

1 + 15x + 105x²

6. When the polynomial x³ + mx² + 4x + 2 is divided by x + 2.
What is the value of m?

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

12x²y+6xy+9x+9

-2x²y-4xy-2x-5

-12x²y-6xy-9x-9

-12x²y+6xy+9x+9

8. If

find P + Q + R.

9. Expand (1-x)³, using binomial theorem.

Hence find the value of (0.999)³ correct to five decimal places.

1 - 3x + 3x² - x³, 0.99700

1 - 3x + 3x² - x³, 1

1 - 3x + 3x² - x³, 0.997

1 - 3x + 3x² - x³, 0.10

10. What is the common factor to the binomial expressions 4x²-9y², 8x³+27y³ and (4x+6y)²

2x+3y

4x-6y

2x-3y

4x+6y

11. Find the third term in the binomial expansion of (2-a)¹⁰

11520a²

45332a

11520a

45332a²

12. Find the value of k if the expression kx³ + x² - 5x - 2 leaves a remainder 2 when divided by 2x + 1

-10

-5

13. If

find P+ Q

61/678

41/187

24/362

51/192

14. Factorize the polynomial x³ - x² - 25x + 25

(x - 1)(x + 5)²

(x-5)²

(x - 1)(x + 5)(x - 5)

x²-1(x-5)

15. Resolve

into partial fractions

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

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

7/(x+3) - 4/(x+2)

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

16. Divide 6x² - 13x + 5 by 2x -1

x+7y

2x+5

5x-3

3x-5

17. If (1 + px)ⁿ = 1 + 2x - 3x² + ... where Px<1,

determine the values of p and n, respectively.

3/4, 7

7, 3/4

2/5, 5

5, 2/5

18. If

find the values of the constants P and Q

P = 3, Q = 2

P = 1, Q = 2

P = 2, Q = 2

P = 3, Q = 1

19. Factorize : (4x+3)² - (3x-2)²

x(7x+1)

(x+5)(7x+1)

(x+1)(x+5)

(x-5)(7x-1)

20. Solve the equation 3x³ - 2x² - 4x + = 0

0.752, -3, 0.34

1, -2, -6.62

1, 0.85, -1.18

3, 4.76, -3.53

21. Which of the following polynomials has (a+b) as a factor?

a²+b²

a³-b³

2a²-3ab+b²-a+1

2a³+2a²b-ab+3a-b²+3b

22. Simplify

a/(a+3)(a+7)

(a+3)(a+7)/a

a/(a-3)(a-7)

a/(a-3)(a+7)

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

340

345

140

240

24. What is the common factor to the expressions y²-y, 2y²+y-1 and y²-1?

None

y-1

y+1

25. Factorize the polynomial x² + 5x + 6

(x + 2)(x + 3)

(x + 2)(x + 6)

(x + 2)(8)

(x + 5)(x + 3)

26 out of 25