Free Printable Algebra Review HW #1

1.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

2.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

3.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

4.

Which of the following is a difference of perfect squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

5.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

6.

Factor using sum or difference of cubes. (use your notes!)

a³ + b³

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

7.

Factor the following binomial: 8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

8.

Factor v³+1

a)

(v+1)(v²-v+1)

b)

(v-1)(v²+v+1)

c)

(v-1)(v+1)

d)

(v-1)(v²+1)

9.

Simplify.
$\frac{\frac{1}{x}}{\frac{x-1}{16}}$

a)

$\frac{1}{x}$

b)

$\frac{16x-16}{x^3}$

c)

$\frac{16}{x^2-x}$

d)

$\frac{16}{x^2}$

10.

Simplify.
$\frac{\frac{x+3}{x-5}}{\frac{5}{x+3}+\frac{5}{x-5}}$

a)

$\frac{x-2}{x^2-2x-15}$

b)

$\frac{5x^2-50x+125}{130-x}$

c)

$\frac{x^2+6x+9}{10x-10}$

d)

$\frac{x^2-2x+110}{125}$

11.

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

a)

$\frac{2-x}{3}$

b)

$\frac{4+x^2}{3x+6}$

c)

$\frac{4-x}{3\left(x+2\right)}$

d)

$\frac{3x}{4}$

12.

a)

-2x - x√3

b)

2x + x√3

c)

2x - √(3x)

d)

2x + √(3x)

13.

a)

A

b)

B

c)

C

d)

D

14.

What is the correct equation in
Slope-Intercept Form?
(y = mx +b)

a)

x = 4

b)

y = 4

15.

What is the correct equation?

a)

x = 5

b)

y = 5

c)

x = - 5

d)

y = -5

16.

Given the table, write the equation in the slope-intercept form.

a)

y = 1/3x + 6

b)

y = 3x + 6

c)

y = 2x + 6

d)

y = 1/2x + 6

17.

Write a linear function f with the values f(0) = 6 and f(4) = -6.

a)

y = -3x + 6

b)

y = -6

c)

y = 3x - 6

d)

y = 3x + 6

18.

Find the graph of the standard form equation: 2x + 3y = 3

a)

b)

c)

d)

19.

What is the slope of this line?

a)

m = 0

b)

m = undefined

c)

m = 3

d)

m = ¹/₃

20.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

21.

Give the y-intercept
3x + y = 5

a)

-3

b)

(0,5)

c)

-5

d)

(0, -3)

22.

Find x, if F(x) = 2.

a)

4

b)

-2

c)

-6

d)

8

23.

What is F(-8)?

a)

2

b)

-4

c)

-2

d)

0

24.

What is the domain of F(x)?

a)

-10\le x\le8

b)

$-7\le x\le2$

c)

all real numbers

d)

$-10\le y\le8$

e)

$-7\le y\le2$

25.

What is the range of F(x)?

a)

-10\le x\le8

b)

$-7\le x\le2$

c)

all real numbers

d)

$-10\le y\le8$

e)

$-7\le y\le2$

26.

Graph 2x - y = 4

a)

A

b)

B

c)

C

d)

D

27.

Which of these represents point-slope form?

a)

y - y₁ = m(x-x₁)

b)

Ax + By = C

c)

y = mx + b

d)

a² + b² = c²

28.

What is the VERTICAL asymptote of this function? (click on the graph to enlarge)

a)

x=1

b)

x=-3

c)

y=1

d)

y= -3

29.

What is the HORIZONTAL asymptote of this function? (click on the graph to enlarge)

a)

x=1

b)

x=-3

c)

y=1

d)

y= -3

30.

What is the equation of the rational function graphed?

a)

$f\left(x\right)=\frac{1}{x-2}$

b)

$f\left(x\right)=\frac{1}{x+2}$

c)

$f\left(x\right)=\frac{1}{x}+2$

d)

$f\left(x\right)=\frac{1}{x}-2$

31.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

c)

what's the difference?

d)

it's all waves to me

32.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

33.

Which is the graph of the square root parent function?

a)

A

b)

B

c)

C

d)

D

34.

The graph of y = x² + 1 could be?

a)

b)

c)

d)

35.

Find the y-intercept(s) of the graph shown.

a)

(-3.3, 0)

b)

(5.6, 0)

c)

(-5, 0)

d)

(0, 4)

36.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

37.

What is the equation of the absolute value function?

a)

f(x)= |x+4|

b)

f(x)= |x-4|

c)

f(x)= |x| + 4

d)

f(x)= |x| - 4

38.

Match the graph with the correct equation.

a)

b)

c)

d)

39.

State the domain of the given function.

a)

x ≥ 3

b)

x > 3

c)

x < 3

d)

x ≤ 3

40.

The number (0.01)^-1/2 is equal to

a)

0.1

b)

10

c)

100

d)

1000

Algebra Review HW #1

Total questions: 40

Worksheet time: 1hrs 21mins

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