Free Printable QUARTER 2 Benchmark Review Algebra II

1.

$f\left(x\right)=\frac{7x-1}{7x^2-36x+5}$
Find the horizontal asymptote, the vertical asymptote, and the hole, if they exixt.

a)

HA: y = 0, VA: x = 5, hole: x = 1/7

b)

HA: NONE , VA: x = 5, hole: x = -1/7

c)

HA: y = 0, VA: x = - 5, hole: x = -1/7

d)

HA: y = 7, VA: x = 5, hole: NONE

2.

$y=\frac{2}{x-9}$

Name the domain.

a)

(- ∞, 2) U (2, ∞ )

b)

( - ∞ , - 2 ] U [ - 2 , ∞ )

c)

( - ∞ , 9 ) U ( 9 , ∞ )

d)

( - ∞ , 9 ] U [ 9 , ∞ )

3.

$\frac{3x^2+15x}{x^2+2x-15}$
Simplify.

a)

$\frac{3}{x-1}$

b)

$\frac{3x}{x-3}$

c)

$\frac{1}{x-3}$

d)

$\frac{3x}{x+5}$

4.

$-\frac{2}{x^2}+\frac{1}{7}=\frac{5}{7x}$ Solve.

a)

( 2 , 7 }

b)

{ - 7 }

c)

{ - 7 , 2 }

d)

{ - 2 , 7 }

5.

Which of the following is the graph of
$f\left(x\right)=\frac{x}{x-4}$

a)

b)

c)

d)

6.

$\frac{7x+2}{10}-\frac{x+6}{3}=$

a)

$\frac{11x-76}{13}$

b)

$\frac{31x+54}{30}$

c)

$\frac{11x+66}{30}$

d)

$\frac{11x-54}{30}$

7.

Simplify.
$\frac{x^2-4x+4}{x-8}\cdot\frac{x^2-81}{x^2-11x+18}$

a)

$\frac{\left(x-2\right)\left(x+8\right)}{x-9}$

b)

$\frac{\left(x-2\right)\left(x+9\right)}{x-8}$

c)

$x-2$

d)

$x+8$

8.

$\frac{x-3}{x-5}+\frac{4}{x-8}=\frac{2x-10}{x^2-13x+40}$

a)

x = 5, x = 8

b)

x = 2, x = 7

c)

x = 5, x = 7

d)

x = - 2, x = 9

9.

Factor x³+7x² + 2x - 40 completely, if one of the factors is (x - 2 ).

a)

(x - 2 )(x + 2)(x + 10)

b)

(x - 2 )(x - 2)(x - 10)

c)

(x - 2 )(x + 1 )( x + 20 )

d)

( x - 2 )( x + 5 )( x + 4 )

10.

Simplify. ( 9 + 7i ) ( 4 - 5i )

a)

71 - 17i

b)

1 + 17i

c)

1 - 73i

d)

71 + 73i

11.

Find the EXTRANEOUS solution to
$\sqrt{x+16}=x\ -\ 4$

a)

x = - 9

b)

x = 9

c)

x = 0 and x = 9

d)

x = 0

12.

Factor: x² + 11xy - 12y²

a)

( x + 3y )( x - 4y )

b)

( x + y )( x - 12y )

c)

( x - y )( x + 12y )

d)

( x + 2y )( x - 6y)

13.

Name the domain and the range.

a)

Domain: All real numbers

Range: y > 5

b)

Domain: All real numbers

Range: y > - 5

c)

Domain: All real numbers

Range: y < - 5

d)

Domain: All real numbers

Range: y < 5

14.

Simplify.

a)

b)

c)

d)

15.

Find the perimeter.

a)

b)

c)

d)

16.

$\frac{-2+5\sqrt{7}}{3\sqrt{5}}=$

a)

$\frac{-2\sqrt{5}+25}{15}$

b)

$\frac{-2\sqrt{5}+5\sqrt{35}}{15}$

c)

$\frac{-2+5\sqrt{35}}{5}$

d)

$\frac{-2\sqrt{5}+5\sqrt{7}}{45}$

17.

$\sqrt{64m^9n^6}=$

a)

$8m^{\frac{2}{9}}n^3$

b)

$32m^{\frac{9}{2}}n^3$

c)

$8m^{\frac{9}{2}}n^3$

d)

$32m^{\frac{2}{9}}n^{\frac{1}{2}}$

18.

$\left(\sqrt{3}-4\sqrt{7}\right)$

One side of a square is shown above. Find the area of the square.

a)

$115$

b)

$115-4\sqrt{21}$

c)

$-109-4\sqrt{21}$

d)

$115-8\sqrt{21}$

19.

$\sqrt{5x+17}=\sqrt{7x-9}$

Find the solution.

a)

x = 13

b)

x = - 13

c)

x = 4

d)

x = 6

20.

Solve.

a)

x = 2319

b)

x = 79

c)

x = 19

d)

x = 49

21.

$\sqrt{18}\left(\sqrt{2}+\sqrt{6}\right)+5\sqrt{3}$

Simplify the expression.

a)

$6+2\sqrt{27}+5\sqrt{3}$

b)

$6-11\sqrt{6}$

c)

$18+30\sqrt{3}$

d)

$6+11\sqrt{3}$

22.

$\sqrt{-148}$

Simplify.

a)

$4i\sqrt{37}$

b)

$2i\sqrt{37}$

c)

$-2\sqrt{37}$

d)

$-4\sqrt{37}$

23.

Which equation is graphed here?

a)

b)

c)

d)

24.

Name the domain.

a)

{ x | x < 1 }

b)

{ x | x > 1 }

c)

{ x | x < - 1 }

d)

{ x | x > 2 }

25.

Write with a rational exponent.

a)

$m^{\frac{11}{2}}$

b)

$m^{\frac{11}{6}}$

c)

$m^{\frac{1}{2}}$

d)

$m^3$

26.

$\frac{2}{x}-\frac{1}{5}=6$

a)

$\left\{\frac{31}{10}\right\}$

b)

$\left\{-\frac{7}{10}\right\}$

c)

$\left\{\frac{10}{31}\right\}$

d)

$\left\{0\right\}$

27.

$v=\sqrt{\frac{2K}{m}}$

The formula to find the velocity of an object is shown above. "v" is measured in m/sec, K, kinetic energy, is measured in Joules. "m" is the mass of the object measured in kg. Solve the equation for m.

a)

$m=\frac{K^2}{2}$

b)

$m=\frac{2v^2}{K}$

c)

$m=2Kv^2$

d)

$m=\frac{2K}{v^2}$

28.

$m=\frac{2K}{v^2}$

The formula to find the mass of an object is shown above. "v" is measured in m/sec, K, kinetic energy, is measured in Joules. "m" is the mass of the object measured in kg. Find the mass if the object has a kinetic energy of 2900 Joules and is traveling at a velocity of 15 meters per second.

a)

~ 12.89 kg

b)

~ 25.78 kg

c)

~ 193.33 kg

d)

~ 386.67 kg

QUARTER 2 Benchmark Review Algebra II

Total questions: 28

Worksheet time: 52mins

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