Free Printable Algebra I Final Review

1.

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

2.

Find the slope from the table.

a)

-4

b)

1

c)

4

d)

-2

3.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

4.

A golf course charges $15 to rent golf clubs and charges $25 per round to play. Write an equation to represent the total cost, T, for one player.

a)

T = 15 + 25r

b)

T = 15g + 25r

c)

T = 40 r

d)

T = 15r + 25

5.

Find the slope and y-intercept of:

2x - 3y = -12

a)

slope = 2/3, y-intercept = -12

b)

slope = -2/3, y-intercept = -3

c)

slope = 2/3, y-intercept = 4

d)

slope = -12, y-intercept = -3

6.

What is the slope:

5x + 10y = 30

a)

m = -1/2

b)

m = 1/2

c)

m = 3

d)

m = 1/3

7.

Write the equation of the line in slope-intercept form.

a)

y = x + 3

b)

y = 1/2x + 3

c)

y = 3x + 2

d)

y = 3

8.

Which equation represents the table?

a)

y = -x

b)

y = x-3

c)

y = 1/2x + 3

d)

y = 3x

9.

6x + 10 > 5x - 12

a)

x > 2

b)

x < -2

c)

x < -22

d)

x > -22

10.

4(2a + 3) < 3(a - 1)

a)

a < -3

b)

a > -3

c)

a < 3

d)

a > 3

11.

Solve the equations:

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

12.

Solve the equation:
3(x - 1) = 2x + 9

a)

x = 12

b)

no solution

c)

x = 10

d)

x = 6

13.

Which expression is equivalent to

(10 + 7r -r²) + (-6r² - 18 + 5r)?

a)

-7r² + 2r + 8

b)

7r² + 12r + 8

c)

-7r² + 12r - 8

d)

7r² +2r - 8

14.

Which expression is eqivalent to $2x^2\ +\left(4x\ -\ 6x^2\right)\ +9\ -\ \left(6x\ +\ 3\right)?$

a)

$-4x^2\ -\ 2x\ +\ 12$

b)

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

c)

$-10x\ +\ 6$

d)

$18x\ +\ 12$

15.

Which expression is equivalent to $\left(h^2\ +\ 9h\ -\ 1\right)\left(-4h\ +\ 3\right)?$

a)

$-4h^3\ -\ 33h^2\ +\ 31h\ -\ 3$

b)

$4h^3\ +\ 39h^2\ -\ 23h\ -\ 3$

c)

$-4h^{3\ }-\ 39h^2\ +\ 23h\ +\ 3$

d)

$4h^{3\ }+\ 33h^2\ -\ 31h\ +\ 3$

16.

The floor plan of a storage facilty shows a length of 5x + 4 and a width of 4x - 4.

All dimensions are given in feet. Which expression represents the are of the storage facility in square feet?

a)

$20x^2\ +\ 36x\ -\ 16$

b)

$20x^2\ -4x\ -16$

c)

$16x^2\ -16$

d)

$9x^2\ -\ 16$

17.

Which expression is equivalent to $35m^2\ -\ 63$

a)

$7\left(5m^2\ -\ 9\right)$

b)

$-7\left(5m^2\ +\ 9\right)$

c)

$7m\left(5m\ -\ 9\right)$

d)

$-7m\left(5m\ -\ 9\right)$

18.

Which expression is equivalent to $210d^2\ -63d?$

a)

$21d\left(10d\ -\ 3\right)$

b)

$21d\left(10d\ +3\right)$

c)

$21\left(10d\ +\ 3\right)$

d)

$21\left(10d\ -\ 3\right)$

19.

Which expression is a factored form of $2x^2\ -\ 25x\ +\ 63?$

a)

$\left(x\ +\ 9\right)\left(2x\ +\ 7\right)$

b)

$\left(x\ -\ 9\right)\left(2x\ -\ 7\right)$

c)

$\left(x\ +\ 7\right)\left(2x\ +\ 9\right)$

d)

$\left(x\ -\ 7\right)\left(2x\ -\ 9\right)$

20.

Which expression is equivalent to $16w^2\ +\ 24w\ +\ 9?$

a)

$\left(4w\ +\ 3\right)^2$

b)

$\left(4w\ -\ 3\right)^2$

c)

$\left(8w\ +\ 3\right)^2$

d)

$\left(8w\ -\ 3\right)^2$

21.

Simplify: (7a³b⁵)³

a)

21 a⁶b⁸

b)

49a⁹b¹⁵

c)

343a⁹b¹⁵

d)

343a⁹b⁸

22.

(-3)⁵

a)

-15

b)

125

c)

2

d)

-243

23.

Determine if the sequence is an arithmetic sequence. 10, 12, 15, 19...

a)

no

b)

yes, common difference is -1

c)

yes, common difference is 2

d)

yes, common difference is -2

24.

Solve: 5x - (x-3) - 1 = 18

a)

x = 2

b)

x = 4

c)

x = 8

d)

x = 2/3

25.

0.2m + 0.8 = 1.8

a)

m = 3

b)

m = 5

c)

m = -7

d)

m = -2

26.

Solve for x.

a)

x = 21

b)

x = 7

c)

x = −21

d)

x = 4

27.

a)

2

b)

4

c)

6

d)

8

28.

4m + 5 = 10

Solve for m.

a)

15/4

b)

4/5

c)

5/4

d)

20

29.

Give the solution to the system

a)

(3,1)

b)

(1,3)

c)

(-1,3)

d)

(-3, 1)

30.

a)

Function

b)

Not a Function

31.

a)

Function

b)

Not a Function

32.

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

a)

f(5) = 6

b)

f(5) = 16

c)

f(5) = -4

d)

f(5) = 24

33.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(5, 1)

c)

(-1, -3)

d)

(20, -5)

34.

Which is a zero of the graph?

a)

0

b)

-1

c)

1.5

d)

-3

35.

Identify the common difference.
97, 86, 75, 64, ...

a)

8

b)

11

c)

-11

d)

-8

36.

Is the pictured graph growth, decay, or linear or none?

a)

Growth

b)

Decay

c)

Linear

d)

None

37.

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. When does the rocket hit the ground?

a)

7 seconds

b)

6 seconds

c)

3 seconds

d)

8 seconds

38.

What is the equation for axis of symmetry?

a)

y = 3

b)

x = 3

c)

x = 5

d)

x = 1

39.

Add:

(3x² - 3x + 2) + (x² - 2x + 1)

a)

4x³- 2x² + 2

b)

4x² - 5x + 3

c)

-2x³ + 2x + 2

d)

4x³ - 2x² - 2

40.

Simplify:
5(3x+1)

a)

15x+1

b)

15x+5

c)

8x+1

d)

8x+6

41.

What is the transformation?

a)

Vertical Translation up 2

b)

Vertical Translation down 2

c)

Horizontal Translation left 2

d)

Horizontal Translation right 2

42.

What is the transformation?

a)

Vertical Translation up 1

b)

Vertical Translation down 1

c)

Horizontal Translation left 1

d)

Horizontal Translation right 1

43.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

44.

Is this exponential growth or decay?

a)

Growth

b)

Decay

45.

The graph

g\left(x\right)=2^{\left(x-3\right)}

is shown, which statement best describes the transformation from the parent graph

f\left(x\right)=2^x

.

a)

Vertically shift up 3

b)

Vertically shift down 3

c)

Horizontally shift right 3

d)

Horizontally shift left 3

46.

Which graph best represents

y=2^x-4

a)

b)

c)

d)

47.

Slopes of parallel lines are...

a)

opposite reciprocals.

b)

opposites.

c)

identical.

d)

always 7.

48.

What inequality does the number line graph represent?

a)

x > 5

b)

x < −5

c)

x ≥ −5

49.

The height of an object thrown into the air can be modeled by the formula $y=-16x^2+70x+95$ , where y is in feet after x seconds.
What is the height of the object after 5 seconds?

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

50.

A ball is thrown into the air with an upward velocity. Its height, h, after t seconds is given by the function below.
$h=-16t^2+64t+960$
How many seconds did it take for the ball to reach its maximum height?

a)

10 seconds

b)

64 seconds

c)

960 seconds

d)

2 seconds

51.

A ball is thrown into the air with an upward velocity. Its height, h, after t seconds is given by the function below.
$h=-16t^2+64t+960$
What is the maximum height reached?

a)

1024 feet

b)

64 feet

c)

960 feet

d)

2 feet

52.

What is the Domain?

a)

-10 ≤ y ≤ 6

b)

y ≤ 6

c)

-10 ≤ x ≤ 6

d)

All Real Numbers

53.

Solve for x:

a)

x = yb - v

b)

x = by - v

c)

x = by + v

54.

ax + c = R
(solve for x)

a)

ax = R + c

b)

ax = R - c

c)

x = a(R-c)

d)

x = (R-c) / a

55.

Find the product:

(3x – y)(3x + y)

a)

3x² + 3y2

b)

3x² + y²

c)

3x² -y²

d)

9x²-y²

56.

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

57.

We will start with the explicit formula. Given the following sequence, state the first term and common difference.

Example 1: 4, 7, 10, 13, 16, …

a)

$a_1\ =\ 3,\ \ \ d\ =\ 4$

b)

$a_1\ =\ 16,\ \ \ d\ =\ 3$

c)

$a_1\ =\ 4,\ \ \ d\ =\ 3$

d)

$a_1\ =\ 16,\ \ \ d\ =\ 13$

58.

Now, write the explicit formula for the given sequence.

Example 1: 4, 7, 10, 13, 16, …

a)

$a_n\ =\ 1+3n$

b)

$a_n\ =\ 0+4n$

c)

$a_n\ =\ 3\ +\ 3n$

d)

$a_n\ =\ 16\ +\ 4n\$

59.

Write an explicit rule to model the following sequence:

Example 2: 21, 19, 17, 15, …

a)

$a_n=21-2n$

b)

$a_n=21+2n$

c)

$a_n=23+2n$

d)

$a_n=23-2n$

60.

Sequences that increase or decrease by MULTIPLYING the previous term by a fixed number are called _________ sequences.

a)

arithmetic

b)

geometric

c)

logarithmic

d)

mathematic

61.

Find the common ratio of the following geometric sequence

-250,\ -50,\ -10,\ 2

a)

r = 5

b)

r = -5

c)

r = 1/5

d)

r = -1/5

62.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

63.

Factor completely: 2x²+22x+60

a)

(2x+10)(x+6)

b)

(x+5)(x+6)

c)

2(x+1)(x+30)

d)

2(x+5)(x+6)

64.

Factor completely: x²-6x+8

a)

(x-2)(x-4)

b)

(x-1)(x-8)

c)

(x+2)(x+4)

d)

(x+1)(x+8)

65.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

66.

Factor out the GCF:
12x + 6

a)

6(2x + 1)

b)

3(4x + 2)

c)

6x(2x + 1)

d)

2(6x + 3)

67.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

68.

How do you find the median of a data set that has two middle numbers?

a)

You pick the higher middle number

b)

You pick the lower middle number

c)

Add the two middle numbers and divide it by 2

d)

Subtract the two middle numbers and divide by 2

69.

Which measure of central tendency would best represent this data?

a)

Mean

b)

Median

c)

Mode

d)

Range

70.

Which measure of central tendency best represents this data?

a)

Mean

b)

Median

c)

Mode

d)

Range

71.

The mean of this data set is 17.8. What would happen to the mean if 40 was added to the data set?

a)

The mean would not change

b)

The mean would go up

c)

The mean would go down

72.

Which class has the higher median?

a)

1st period

b)

2nd period

c)

They have the same median

73.

How is the data distributed in this histogram?

a)

Symmetrically

b)

Skewed Right

c)

Skewed Left

74.

How is the data distributed in this histogram?

a)

Symmetrically

b)

Skewed Right

c)

Skewed Left

75.

What is the transformation?

a)

Vertical Translation up 2

b)

Vertical Translation down 2

c)

Horizontal Translation left 2

d)

Horizontal Translation right 2

76.

What is the transformation?

a)

Vertical Translation up 1

b)

Vertical Translation down 1

c)

Horizontal Translation left 1

d)

Horizontal Translation right 1

77.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

78.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

79.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

80.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

81.

Is this exponential growth or decay?

a)

Growth

b)

Decay

82.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

83.

Linear, exponential, or neither?

a)

Linear

b)

Exponential

c)

Neither

d)

All of the above

84.

What type of function does this table represent?

a)

Linear

b)

Exponential

c)

Neither

85.

Write an equations that models the data shown.

a)

$y=3x+6$

b)

$y=3\cdot2^x$

c)

$y=2x+3$

86.

What type of pattern do linear functions have?

a)

Adds or subtracts by the same number every time

b)

Multiplies or divides by the same number every time

c)

Square roots all the inputs

87.

Suppose the population of a species of insects doubles every year. There are 1600 insects initially. The function for the scenario would be?

a)

$f\left(x\right)=2x+1600$

b)

$f\left(x\right)=1600\times2$

c)

$f\left(x\right)=1600\cdot2^x$

88.

X intercepts are also called....

a)

Solutions

b)

Parabolas

c)

Roots

d)

Puppies

89.

What are the green dots called?

a)

roots

b)

vertex

c)

solutions

d)

x intercepts

90.

Identify a, b, and c in: x²−6x+14

a)

a=3,b=5,c=9

b)

a=1,b=-6,c=14

c)

a=1,b=-6,c=-14

d)

a=1,b=6,c=14

91.

What are the zeros of

$f\left(x\right)=x^2+7x-18$ ?

a)

$x=-2,\ -9$

b)

$x=2,\ -9$

c)

$x=-2,\ 9$

d)

$x=2,\ 9$

Algebra I Final Review

Total questions: 91

Worksheet time: 4hrs 40mins

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