Free Printable Honors Algebra 2: Units 1

1.

Which quadratic function is represented by the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

2.

Which of the following is not a solution to this system of inequalities?

a)

(0,-1)

b)

(0,3)

c)

(4,0)

d)

(6,-2)

3.

$\frac{3}{4}x+\frac{2}{5}=x-\frac{7}{10}$

a)

$\frac{22}{5}$

b)

$\frac{5}{22}$

c)

$\frac{22}{15}$

d)

$\frac{11}{4}$

4.

Solve:

$4\left(-8x+5\right)=-32x-26$

a)

x = 54

b)

x = -54

c)

All Real Numbers

d)

No Solution

5.

3 | 2t - 3 | - 5 > 16

a)

No Solution

b)

All Real Numbers

c)

t < -2 or t > 5

d)

-2 < t < 5

6.

a)

all real numbers

b)

$v<0\ or\ v>\frac{6}{7}$

c)

$0<v<\frac{6}{7}$

d)

$0\le v\le\frac{6}{7}$

7.

through (-4, 2), slope = 3/4

a)

$y=\frac{3}{4}x+5$

b)

$y=\frac{3}{4}x-5$

c)

$y=\frac{3}{4}x+2$

d)

$y=-\frac{4}{3}x+\frac{6}{3}$

8.

Determine the equation of the line that is PERPENDICULAR to the line 3x + 12y = 1 and contains the point (-2, 6).

a)

y = 4x + 12

b)

y = 4x + 14

c)

y = 3x + 12

d)

$y=-\frac{1}{4}x+\frac{11}{2}$

9.

Which of the following situations could be descried by the equation y= -25x + 120

a)

There are 120 people in the football stadium, and 25 more are entering each hour.

b)

A plumber charges $25 for a house call and $120 per hour.

c)

A teacher has 120 students. Her third period has 25 students

d)

There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

10.

Solve the system of equations.
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

11.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

12.

What is the value of the y-coordinate of the solution to the system of equations
x-2y=1
x+4y=7

a)

1

b)

-1

c)

3

d)

4

13.

Solve the system.

a)

(3, -5, -2)

b)

(-4, 1, 3)

c)

(3, 5, 8)

d)

(4, 5, 2)

14.

Which graph represents the following equation: $y=-x^2-2x+3$

a)

b)

c)

d)

15.

Identify the vertex and correct graph

a)

A

b)

B

c)

C

d)

D

16.

What is the axis of symmetry for the quadratic

y=2\left(x-3\right)\left(x-2\right)

a)

x=5

b)

x=5/2

c)

x=-5

d)

x=-5/2

17.

Which of the statements about the graph is FALSE?

a)

The vertex is a maximum

b)

There are two zeros at

(-3, 0) and (3, 0)

c)

The y-intercept is (0, 18)

d)

The range is

$y\ge18$

18.

Solve by factoring: 4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

19.

Solve the following quadratics equation by completing the square...

x² + 4x - 1 = 0

a)

$x=-2\pm\sqrt{5}$

b)

$x=5\pm\ \sqrt{2}$

c)

$x=2\pm\sqrt{5\ }$

d)

$x=-5\pm\sqrt{5}\$

20.

What is one of the solutions to this equation?
(2x - 1)² -3= 46

a)

7

b)

-7

c)

-4

d)

-3

21.

Solve the following by completing the square:

2x^2-20x+89=-87

a)

$\left\{5\pm3i\sqrt{7}\right\}$

b)

$\left\{5\pm i\sqrt{63}\right\}$

c)

$\left\{5\pm2i\sqrt{3}\right\}$

d)

$\left\{5\pm4i\sqrt{2}\right\}$

22.

Solve $x^2-4x+18=0$ .

a)

$x=-2\pm i\sqrt{14}$

b)

$x=-2\pm\sqrt{14}$

c)

$x=2\pm i\sqrt{14}$

d)

$x=2\pm\sqrt{14}$

23.

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

a)

2.625

b)

6.25

c)

100

d)

200

e)

210.25

24.

(4 - 2i) - (3 + 6i)

a)

7 - 4i

b)

1 + 4i

c)

1 - 8i

d)

7 - 8i

25.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5 + 12i

c)

13

d)

13 + 12i

26.

a)

A

b)

B

c)

C

d)

D

27.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

28.

$y=-3(x+5)^2-4$
Convert the equation from vertex form to standard form.

a)

y = 9x²- 15x + 21

b)

y = -3x²- 75x - 4

c)

y = 9x²+ 90x + 221

d)

y = -3x²- 30x - 79

29.

Convert to vertex form.

a)

y=-(x-5)² + 21

b)

y=-(x+5)² + 21

c)

y=-(x+10)² + 21

d)

y=-(x-10)² + 21

30.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

31.

(5x⁴- 4x³- 2x² + x - 19) - (x⁴+ 5x³ + 8x² + x + 5)

a)

4x⁴- 9x³- 10x²- 24

b)

4x⁴- 9x³ - 10x²- 2x - 24

c)

4x⁴ - 9x³ - 10x² + 2x - 24

d)

-4x⁴ - 9x³ - 10x² - 24

32.

(2x + 3)(x² + 4x + 1)

a)

2x³ + 10x² + 14x + 4

b)

2x³ + 11x² + 14x + 3

c)

-2x³ - 11x² + 14x + 5

d)

x³ - 11x² + 14x + 3

33.

Use polynomial long division: (3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

$3x^2-3x+8-\frac{9}{x+1}$

c)

$3x^2+2x-\frac{1}{x+1}$

d)

$3x^3+3x^2+\frac{7}{x+1}$

34.

Find the quotient:

$\left(4x^4-8x^3-3x^2+7x-2\right)\div\left(2x-1\right)$

a)

$2x^3-3x^2-3x+2$

b)

$2x^3+3x^2+3x+2$

c)

$4x^3-6x^2-6x+4$

d)

$2x^3+2$

35.

What is the factored form of $5n^3-10n^2+3n-6$ ?

a)

$\left(5n^2+3\right)\left(n-2\right)$

b)

$\left(5n^2-3\right)\left(n-2\right)$

c)

$\left(5n^3-3\right)\left(n+2\right)$

d)

$10n\left(n^2-6\right)$

36.

Factor by grouping:
$x^3-4x^2-4x+16$

a)

$\left(x+4\right)\left(x+2\right)$

b)

$\left(x-4\right)\left(x-2\right)\left(x+2\right)$

c)

$\left(x+4\right)\left(x-2\right)\left(x+2\right)$

d)

$\left(x-4\right)\left(x-2\right)$

37.

Factor the following expression:
$100y^4-16y^2$

a)

$4y^2\left(5y+2\right)\left(5y-2\right)$

b)

$4y^2\left(5y+4\right)^2$

c)

$4y^2\left(25y+4\right)^2$

d)

$4y^2\left(-5y+2\right)\left(5y-2\right)$

38.

Factor the following expression:
$3v^3-24v^2-27v$

a)

$3v\left(v+1\right)\left(v-9\right)$

b)

$3v\left(v-1\right)\left(v+9\right)$

c)

$v\left(v-6\right)\left(v-7\right)$

d)

$v\left(v+1\right)\left(v-9\right)$

39.

Determine whether $3x+1$ is a factor of $3x^3+16x^2-x-2$ . Explain how you know.

a)

No. There was a remainder when the two polynomials were divided.

b)

Yes. There was no remainder when the two polynomials were divided.

c)

Yes. $3x$ divides evenly into $3x^2$ .

d)

No. The dividend is a cubic polynomials, whereas the divisor is only a linear polynomial.

40.

Determine where the graph of $f\left(x\right)$ is increasing.

a)

$\left(-1.5,\ 2\right)\cup\left(4.1,\infty\right)$

b)

$\left(-\infty,\ -1.5\right)\cup\left(2,\ 4.1\right)$

c)

$\left(-\infty,\ \infty\right)$

d)

$\left(-1.5,\ 2\right)$

41.

Describe the end-behavior of the graph.

a)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty.\$ $As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty.\$

b)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty.\$ $As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty.\$

c)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty.\$

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty.\$

d)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty.\$

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty.\$

42.

Solve the equation $2x^3+5x^2=2x+4$ by graphing.

a)

{-2.588, -0.836, 0.924}

b)

{2.588, 0.836, -0.924}

c)

{-2.427}

d)

no real solution

43.

Solve the system of equations:

y = x² + 3x - 5

-x + y = 3

a)

(-4, -1) and (2, 5)

b)

(-4, 2)

c)

(4, 7) and (-2, 1)

d)

no real solution

44.

Expand

a)

A

b)

B

c)

C

d)

D

45.

Solve the quadratic inequality:

$x^2-4x-32<0$

a)

$x<-4\ ,\ \ x>8$

b)

$-8<x<4$

c)

$-4<x<8$

d)

$x<-8\ ,\ \ x>4$

Honors Algebra 2: Units 1 - 5 Review

Total questions: 45

Worksheet time: 24mins

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