Free Printable Algebra 1 Final Review 2024

1.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

2.

a)

b)

c)

d)

3.

a)

b)

c)

d)

4.

Simplify
(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

5.

Simplify.

a)

b)

c)

d)

6.

a)

x⁴y⁴

b)

x⁸y⁴

c)

x^-4y¹²

d)

x⁸y¹²

7.

This is an example of: $f\left(x\right)=\ \left(\ 0.20\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

8.

How do you know that this was exponential growth? $f\left(x\right)=\left(1.3\right)^x$

a)

Because the 0.25 was bigger than one

b)

Because the 1.3 was bigger than one

c)

Because the 0.25 was less than one

d)

Because the 1.3 was less than one

9.

This is an example of: $f\left(x\right)=\left(\frac{1}{2}\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

10.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

11.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

12.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

13.

Give the y-interecept

3x + y = 5

a)

y = 0

b)

y = 5

c)

y = -3

d)

y = -5

14.

Give the x-intercept

3x + 8y = 24

a)

x = 8

b)

x = 0

c)

x = 3

d)

x = 24

15.

Find the slope of the line that passes through:
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

16.

Which of these represents slope-intercept form?

a)

y - y₁ = m(x-x₁)

b)

Ax + By = C

c)

y = mx + b

17.

What is the x and y intercept for the following equation ?
4x - 10y = 20

a)

x - int = 4
y-int = -10

b)

x-int = 5
y-int = 2

c)

x - int = 5
y int = -2

d)

x -int = 4
y -int = -10

18.

Given a graph, how can you find the "solutions" to a quadratic?

a)

Copy off neighbor

b)

Plug into calculator

c)

Solutions are where the quadratic crosses the x axis

d)

Magic 8 Ball

19.

What are the green dots called?

a)

roots

b)

vertex

c)

solutions

d)

x intercepts

20.

What are the x- intercepts?

a)

(0,0) and (0,4)

b)

(0,0) and (4,0)

c)

y= 0

d)

x= 2

21.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

22.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3
*remember right side should =0

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

23.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

24.

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)

$x=2,\ 9$

25.

Which answer shows the quadratic formula being plugged in correctly for the following problem?
$x^2+6x-16=0$

a)

$\frac{\left(6\right)\ \frac{+}{-}\sqrt{\left(6\right)^2-4\left(1\right)\left(-16\right)}}{2\left(1\right)}$

b)

$\frac{-\left(6\right)\ \frac{+}{-}\sqrt{\left(6\right)^2-4\left(1\right)\left(16\right)}}{2\left(1\right)}$

c)

$x=\frac{-\left(6\right)\ \frac{+}{-}\sqrt{\left(6\right)^2-4\left(1\right)\left(-16\right)}}{2\left(1\right)}\$

d)

$\frac{\left(6\right)\ \frac{+}{-}\sqrt{\left(6\right)^2-4\left(1\right)\left(16\right)}}{2\left(1\right)}$

26.

Solve the following equation using the quadratic formula:

$3x^2+16x+5=0$

a)

$x=\frac{1}{3},\ x=5$

b)

$x=-\frac{1}{3},\ x=-5$

c)

$x=-1,\ x=-15$

d)

$x=1,\ x=15$

27.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

28.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

a)

8 seconds

b)

1 second

c)

1.5 seconds

d)

1/4 second

29.

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t² + 80

About how long did it take for the balloon to hit the ground?

a)

1.73 seconds

b)

2.24 seconds

c)

2.45 seconds

d)

2.83 seconds

30.

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t² + 45

When is the ball at ground level?

a)

only at t = 0 seconds

b)

only at t = 3 seconds

c)

only at t = 9 seconds

d)

at both t = 0 seconds and t = 3 seconds

31.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

-2 seconds

c)

-6 seconds

d)

6 seconds

32.

Solve

2x² + 7x - 15 = 0

a)

x = -1.5 and x = 5

b)

No Solution

c)

x = -5 and x = 1.5

d)

x = 0.7 and x = 5

33.

Is this a maximum or minimum?

a)

minimum

b)

maximum

c)

cannot be determined

34.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

35.

How do you find the vertex of a quadratic function?

a)

Find $x=-\frac{b}{2a}$

b)

Find $x=-\frac{b}{2a}$ and the plug that value of x into the function to find y.

c)

Find the value of c

d)

Set the function equal to zero and solve for x.

36.

What does the y-intercept represent?

a)

The number of seconds that the water is in the air

b)

The velocity of the water

c)

The maximum height that the water reaches

d)

The height of the water when it was launched

37.

The math club launched a rocket and recorded its height and distance travelled. What was its maximum height?

a)

4 feet

b)

8 feet

c)

10 feet

d)

14 feet

38.

The math club launched a rocket and recorded its height and distance travelled. At what height did they start shooting it from?

a)

4 feet

b)

8 feet

c)

10 feet

d)

14 feet

39.

The math club launched a rocket and recorded its height and distance travelled. How far did the rocket travel overall?

a)

4 feet

b)

8 feet

c)

10 feet

d)

14 feet

40.

If I want to find out when an object hits the ground, I should _________.

a)

Use x = (-b/2a) as my answer.

b)

Set my equation = 0 and solve.

c)

Replace x with 0 and evaluate.

d)

Find the y-coordinate of the vertex.

41.

If I want to see the initial (starting) height of an object, I should _____________.

a)

Use x = (-b /2a) as my answer.

b)

Find the y-intercept of the quadratic.

c)

Set my equation = 0 and solve.

42.

What is the vertex of the graph?

a)

x = -2

b)

(-2, -3)

c)

(-3, -2)

d)

x = -3

43.

Which equation has a vertex of (-3, 4)?

a)

y = 2(x+3)²+ 4

b)

y = (x+3)² - 4

c)

y = (x-3)² + 4

d)

y = 2(x - 3)² + 4

44.

What is the vertex?

a)

(-1,-2)

b)

(-2,-1)

c)

(-3,-1)

d)

(2,1)

45.

Convert the equation
x²-12x+40
into vertex form

a)

(x+6)²-4

b)

(x+6)²+4

c)

(x-6)²-4

d)

(x-6)²+4

46.

Convert the equation y= x²+ 4x + 11 into vertex form.

a)

y = (x + 2)² - 4

b)

y = (x + 2)² + 7

c)

y = (x + 2)²

d)

y = (x - 2)² - 7

47.

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

a)

f(x) = (x - 4)² - 15

b)

f(x) = (x - 4)² + 17

c)

f(x) = (x - 4)² - 17

d)

f(x) = (x - 4)² + 65

48.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

f(x) = (x + 6)² + 34

49.

If A = {1, 2, 3, 4, 5, 6} and B = {1, 2, 3, 5, 7, 9} What is A ⋂ B?

a)

{1, 2, 3, 4, 5, 6, 7, 9}

b)

{1, 2, 3, 5}

c)

{4, 6, 7, 9}

d)

{ }

50.

If A={3,4,7,9}, B={1,3,5,8,9,11} and C={2,3,5,6,9,12}. What is A∩C?

a)

{3}

b)

{2,3,4,5,6,7,9,12}

c)

{3,9}

d)

{3,5,9}

51.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

52.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

53.

A = {1, 3, 5, 7, 9}

B = {2, 3, 5, 7}

What is A ∪ B ?

a)

{3, 5, 7}

b)

{2, 3, 5, 7, 9}

c)

{2, 3, 5, 7}

d)

{1, 2, 3, 5, 7, 9}

54.

Write a line equation in standard form given the point and slope: (3, -8); slope = -3

a)

$3x+y=1$

b)

$y=-3x+9$

c)

$y+8=-3\left(x-3\right)$

d)

$y=-3x+1$

55.

What is the equation of the line that passes through the points (1, -3) and (4, 0)

a)

-3x +2y = -6

b)

3x + 2y = 6

c)

-3x + 2y = -12

d)

3x - 2y = 12

56.

Which is correctly written in standard form of y=-6/7x+12

a)

6x+7y=84

b)

6/7x-y=12

c)

7x+6y=72

d)

y-6/7x=12

57.

write the equation of a line that goes through the points (7, 7) and (14, 8)

a)

y = 1/7x + 6

b)

-1/7x + y = 6

c)

x - 7y = 42

d)

x + y = 6

58.

Add the polynomials.

(2xy - 3x² + 4y - 5) + (-3xy + 4y² - 3y + 8)

a)

-1xy - 3x² + 4y² + 1y + 3

b)

-1xy + 1x² + 1y + 3

c)

-1xy + 1y² + 1y + 3

d)

1xy + 3x² + 4y² + 1y + 3

e)

None of these

59.

(2x + 5y - z) + (-6x - 4y + 7z)

a)

-4x +6y + 6z

b)

4x + y + 6z

c)

-4x - y + 6z

d)

-4x + y + 6z

60.

6v(2v + 3)

a)

12v+18

b)

15v² + 8v

c)

12v² + 18v

d)

12v² + 18v²

61.

Multiply: (r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

d)

$r^2+14r-49$

62.

(x+10)(x-10)

a)

x² - 100

b)

x² + 100

c)

x² + 20x - 100

d)

x² -20x + 100

63.

Multiply

a)

b)

c)

d)

64.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

65.

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)

66.

Factor:

2x² + 3x - 9

a)

2(x + 3)(x - 3)

b)

(2x - 3)²

c)

(x + 3)(2x - 3)

d)

(2x + 3)(x - 3)

67.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁵)

d)

3x²(80x³-40-60x⁵)

68.

Factor by grouping:

4p^3+8p^2+3p+6

a)

$\left(2p^2+3\right)\left(p+2\right)$

b)

$\left(2p^2+6\right)\left(p+4\right)$

c)

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

d)

$\left(4p^2+8p\right)\left(3p+6\right)$

69.

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)

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

70.

4x²- 64y²

a)

Unfactorable

b)

( 2x - 32y) (2 x + 32y)

c)

( 2x - 8y) (2 x - 8y)

d)

( 2x - 8y) (2 x + 8y)

71.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Unfactorable

72.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

73.

Factor completely
2c² + 2c - 84

a)

(c-6)(2c+14)

b)

(c+7)(2x-12)

c)

(c-4)(2c+21)

d)

2(c+7)(c-6)

74.

$\frac{8x^2y^3}{2xy^3}$

a)

$\frac{x}{2}$

b)

$4x$

c)

$4xy$

d)

0

75.

Simplify: $\frac{x^2y^5}{x^9y^5}$

a)

$x^2$

b)

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

c)

$\frac{1}{x^7}$

d)

$x^7$

76.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n=a_n-1+11
a₁=6

b)

a_n=a_n-1-4
a₁=6

c)

a_n=a_n-1+9
a₁=6

d)

a_n=a_n-1+6
a₁=6

77.

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

a)

a_n = a_n-1 + 16
a₁=17

b)

a_n = a_n-1 - 17
a₁=17

c)

a_n = a_n-1 - 15
a₁=17

d)

a_n = a_n-1 - 16
a₁=17

78.

Write the recursive formula for the following sequence?
6, 4, 2, 0, . . .

a)

a_n = -2n + 8

b)

a₁=6, a_n = a_n - 1 - 2

c)

a₁ = 6, a_n = a_n-1 + 2

d)

a₁ = 6, a_n = a_n-1 - 2

79.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n=a_n-1+11
a₁=6

b)

a_n=a_n-1-4
a₁=6

c)

a_n=a_n-1+9
a₁=6

d)

a_n=a_n-1+6
a₁=6

80.

Find the given term for the sequence.
Find a₆₄ for a_n = 5n + 4

a)

9

b)

324

c)

320

d)

cannot be determined

81.

A sequence is given by the function $a_n=3\left(n-1\right)+9$

What is the value of a₇?

a)

30

b)

27

c)

24

d)

33

82.

What function best models the data in the table?

a)

linear

b)

exponential

c)

quadratic

83.

What function model best represents the data in the table?

a)

linear

b)

exponential

c)

quadratic

84.

Is the table linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

85.

Which function best models this data?

a)

Linear

f(x) = -19.9x + 221

b)

Quadratic

f(x) = -0.29x² - 17.8 + 218.0

c)

Exponential

f(x) = 235.7(0.87)^x

d)

Linear

f(x) = -18x + 220

Algebra 1 Final Review 2024

Total questions: 85

Worksheet time: 5hrs 55mins

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