Free Printable Alg I Study Guide I

1.

The objective when solving an equation is to....

a)

isolate the variable.

b)

check the solution.

c)

guess and check.

d)

Combine Like Terms.

2.

Solve:
6(5x - 3) + 2 = 14

a)

2

b)

.5

c)

-1

d)

1

3.

Solve:
2(2x + 3) = -6(x + 9)

a)

1.2

b)

6

c)

-6

d)

7.5

4.

Solve:
2(a + 4) = 2a - 8 + 4a

a)

3

b)

-3

c)

-4

d)

4

5.

Josh has 2 bags of jelly beans. One bag has 67 jellybeans. The other bag had 43 but he ate x of them. How many jellybeans does he have all together?

a)

3x+8

b)

2*67-43

c)

43+67-x

d)

67 + (43-x)

6.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

7.

Pick the correct letter for:
6 > x

a)

A

b)

B

c)

C

d)

D

8.

What inequality does the number line graph represent?

a)

-x + 4 ≥ -1

b)

-2x + 3 > -7

c)

-x + 1 < -4

d)

2x + 3 ≥ 13

9.

Which is a solution of
5(v + 3) - 10v > -10

a)

v < 5

b)

V > 5

c)

V > -5

d)

v < -5

10.

You take a trip to the bowling alley, where each game cost $2, plus you plan to spend $10 on food. You can spend at most $25. Which inequality models this scenario?

a)

2x + 10 ≥ 25

b)

2x + 10 > 20

c)

2x + 10 ≤ 25

d)

2x + 10 < 25

11.

When graphing an inequality, you use an open dot when you use which symbol?

a)

<, >

b)

≤, ≥

c)

≤, <

d)

≥, >

12.

When you graph an inequality, you used a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

c)

≤, <

d)

≥, >

13.

You flip an inequality symbol when you...

a)

subtract

b)

multiply and divide only

c)

multiple by a negative number

d)

multiple or divide by a negative number

14.

What are the independent quantities in the table?

a)

{5,6,7,8,9}

b)

{0,1,2,3,4}

c)

x

d)

y

15.

What is the algebraic equation for this table?

a)

y = 480x

b)

x = y/480

c)

x + 480 = y

d)

480 - x = y

16.

Which function is linear?

a)

y = 2x + 4

b)

y = 2x² + 4

c)

y = 2x(4 − 3x)

d)

xy = 15

17.

a)

Function

b)

Not a Function

18.

If f(x)=3x-9, find f(5).

a)

f(5) = 6

b)

f(5) = 16

c)

f(5) = -4

d)

f(5) = 24

19.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

20.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

21.

Which of these is NOT the same

a)

Range

b)

Input

c)

Dependent Value

d)

Y-Value

22.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{0, 1, 2, -4}
R:{1, -3, -4}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

23.

What is the range?

a)

-4 < x ≤ 5

b)

-4 ≤ x < 5

c)

-3 < y < 3

d)

-3 ≤ y ≤ 3

24.

What is the DOMAIN of this graph?

a)

-4 ≤ x ≤ 3

b)

-1 ≤ x ≤ 4

c)

4 < x < 3

d)

-1 < x < 4

25.

What is the RANGE of this graph?

a)

y < -3

b)

y ≤ -3

c)

y > 1

d)

y ≥ 1

26.

What variable typically represents the domain?

a)

x

b)

y

27.

What variable typically represents the range?

a)

x

b)

y

28.

What is the correct DOMAIN and RANGE of the above graph?

a)

$All\ real\ numbers$
$y\ge-3$

b)

$All\ real\ numbers$
$y\le-3$

c)

$-4\le x\le2$
$y\ge-3$

d)

$-4\le x\le2$
$y\le-3$

29.

What is the correct DOMAIN of the above graph?

a)

$All\ real\ numbers$

b)

$-6\le x\le6$

c)

$-6<x<6$

d)

$x\ge1$

e)

$x\le-1$

30.

Does the graph have a maximum or minimum?

a)

maximum

b)

minimum

c)

neither

d)

both

31.

Does the graph have a maximum or minimum?

a)

max

b)

min

c)

neither

d)

both

32.

Determine the maximum.

a)

(-3. -2)

b)

(-2, -3)

c)

(1, 3)

d)

(3, 1)

33.

Determine the minimum.

a)

(-3. -2)

b)

(-2, -3)

c)

(1, 3)

d)

(3, 1)

34.

Identify the relative maximum:

a)

(0, 3)

b)

(4, 1)

c)

(3, 0)

d)

(1, 4)

35.

What is the x-intercept?

a)

(12,0)

b)

(0,-3)

c)

(8,-1)

d)

(0,0)

36.

What is the y-intercept?

a)

(0,7)

b)

(0,0)

c)

(1,9)

d)

(2,11)

37.

In which form is the following linear function?

y=2x+4

a)

Slope Intercept Form

b)

Point-Slope Form

c)

Standard Form

38.

In which form is the following linear function?

y-2=3\left(x+1\right)

a)

Slope Intercept Form

b)

Point-Slope Form

c)

Standard Form

39.

In which form is the following linear function?

4x+2y=8

a)

Slope Intercept Form

b)

Point-Slope Form

c)

Standard Form

40.

Name the x- and y-intercepts for the equation:
2x + y = 6

a)

(0, 3) and (6, 0)

b)

(0, -3) and (-6, 0)

c)

(3, 0) and (0, 6)

d)

(-3, 0) and (0, -6)

41.

Which equation is being represented by this line?

a)

y = -1x + 2

b)

y = 1/2x + 2

c)

y = 3x -4

d)

y = -3x +2

42.

For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

43.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, -7); m = -1/4

a)

y + 7 = -1/4(x - 4)

b)

y - 4 = -1/4(x + 7)

c)

y + 7 = 4(x - 4)

d)

y - 7 = -1/4(x - 4)

44.

Write the following equation in slope-intercept form:
4x - 3y = 12

a)

y = -4/3x + 3

b)

y = -4x + 12

c)

y = 4/3x - 4

d)

y = 4/3x - 12

45.

Write an equation
m = 5 through (-1, -3)

a)

y = 5x + 2

b)

y = -5x - 5

c)

y = -5x + 2

d)

y = 2x - 5

46.

Write the equation of the line that passes through the points (0, -5) and (4, 3)

a)

y=2x-5

b)

y=1/2x-5

c)

y=2x+5

d)

y=1/2x+5

47.

What is the equation of the graphed line?

a)

y = 3

b)

y = 3x

c)

x = 3

d)

x = 3y

48.

Does the following equation represent a vertical line, a horizontal line, or neither?

y = −3

a)

vertical

b)

horizontal

c)

neither

49.

Does a line with the following slope represent a vertical line, a horizontal line, or neither?

Slope of 0

a)

vertical

b)

horizontal

c)

neither

50.

Does a line with the following slope represent a vertical line, a horizontal line, or neither?

Undefined slope

a)

vertical

b)

horizontal

c)

neither

51.

Slopes of parallel lines are...

a)

opposite reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

52.

Slopes of perpendicular lines are...

a)

opposite reciprocals.

b)

opposites.

c)

identical.

d)

always 7.

53.

What is the slope of a line perpendicular to 5?

a)

5

b)

1/5

c)

-1/5

d)

-5

54.

Write an equation for a line perpendicular to
y = -5x + 3 through (-5, -4)

a)

y = -3x + 1/5

b)

y = -3x - 1/5

c)

y = 1/5x - 3

d)

y = -1/5x - 3

55.

Convert the equation of the line

y + 5 = -3(x - 6)

into slope intercept form.

a)

y = -3x - 23

b)

y = -3x - 13

c)

y = -3x - 11

d)

y = -3x + 13

56.

f(x) = 5x² + 2

a)

Stretch of 5
Up 2

b)

Shrink of 5
Up 2

c)

Stretch of 5
Down 2

d)

Shrink of 5
Down 2

57.

.
If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

58.

.
If the blue is f(x)=x^2,the red must be

a)

g(x)=(x+3)²

b)

g(x)=(x-3)²

c)

g(x)=x²+3

d)

g(x)=x²-2

59.

What are the following transformations?
- f(x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

60.

What are the following transformations:
f(-x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

61.

Which equation describes the transformation of shifting f(x)=x³ seven units up?

a)

x³+7

b)

x³-7

c)

(x-7)³

d)

(x+7)³

62.

Which equation describes the transformation of shifting f(x)=x³ three units left?

a)

x³ + 3

b)

x³ - 3

c)

(x + 3)³

d)

(x - 3)³

63.

Which equation represents this graph.

a)

f(x)=(x - 4)² - 3

b)

f(x)=-(x - 4)² + 3

c)

f(x)=(x - 4)² + 3

d)

f(x)=-(x + 4)² + 3

64.

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation for C, the total cost, to rent the boat for h hours.

a)

h = 2C + 15

b)

C = 15h + 2

c)

h = 15C + 2

d)

C = 2h + 15

65.

At Joe's Clown Car Rental Agency, renting a car costs $35 plus $0.75 for every mile it is driven. What is an equation that can be used to find the number of miles, m, a vehicle was driven, if the total rental charge was $222.50?

a)

222.5 = m(35 + 0.75)

b)

222.5 = 35 + 0.75m

c)

222.5 = 0.75 + 35m

d)

222.5 = 0.75(m + 35)

66.

Which statement below accurately represents the graph?

a)

$100 is earned for each hour worked

b)

$100 is earned for every 2 hours worked

c)

$500 is earned for every 8 hours worked

d)

$200 is earned for every 3 hours worked

67.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?

a)

200

b)

150

c)

300

d)

75

68.

Given the equation y = 2x + 5 , where x is the number of homework questions and y is the number of minutes it takes to do all the homework, what does the y-intercept of the line mean in real world context.

a)

For every homework assignment, it takes 5 more minutes to complete.

b)

For every homework assignment, it takes 2 more minutes to complete.

c)

It initially takes 5 minutes to get homework out and start working.

d)

It initially takes 2 minutes to get homework out and start working.

Alg I Study Guide I

Total questions: 68

Worksheet time: 16hrs 58mins

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