Free Printable Algebra 1 Semester 2 Final Review

1.

Solve the system using elimination.
$3x-2y=-6$

5x+6y=-10

a)

(-2,0)

b)

(0,-2)

c)

(2,0)

d)

(0,2)

2.

Solve the system using elimination.
$-4x-6y=6$
$4x+6y=-4$

a)

no solution

b)

(2,0)

c)

(-4,0)

d)

(0,0)

3.

Does the system below have one solution, no solution, or infinitely many solutions?
$8x+4y=12$
$y=-2x+3$

a)

(0,3)

b)

(3,0)

c)

No solution(parallel lines)

d)

Infinitely many solutions

4.

Simplify the expression.

$5³\cdot5⁴$

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

5.

Simplify the expression:

$\left(2^8\right)^{2\ }$

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

6.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

7.

Simplify the expression:

$\left(3y^4\right)^2$

a)

9y⁸

b)

9y⁶

c)

6y⁸

d)

6y⁶

8.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

9.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

10.

a)

$x^4y^6$

b)

$\frac{1}{x^4y^6}$

c)

y

d)

1

11.

Simplify the expression.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

12.

Simplify the expression:

(2x²)²(3x³)³

a)

96x¹⁰

b)

96x¹³

c)

108x¹³

d)

108x¹⁰

13.

Simplify the expression.

a)

$\frac{a^6c^6}{b^3}$

b)

0

c)

1

d)

a⁵b³c³

14.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

15.

Simplify the expression.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

16.

SImplify:
3² × 3³³ =

a)

3⁶⁶

b)

3³³

c)

3³⁵

d)

3^-31

17.

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

a)

Growth

b)

Decay

18.

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

a)

Growth

b)

Decay

19.

Is the pictured graph growth, decay, linear or quadratic?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

Quadratic

20.

Is this exponential growth or decay?

a)

Growth

b)

Decay

21.

Suppose a culture of bacteria begins with 5000 cells and decreases in population 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

22.

$f(x)=2\left(\frac{1}{7}\right)^x$

What type of function is this?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

Quadratic

23.

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

24.

Factor x² – 20x + 51

a)

(x-17)(x+3)

b)

(x+17)(x+3)

c)

(x+17)(x-3)

d)

(x-17)(x-3)

25.

Factor x² – 11x – 60

a)

(x-12)(x-5)

b)

(x-15)(x+4)

c)

(x-15)(x-4)

d)

(x+12)(x-5)

26.

Factor the expression:

8r³ + 16r²

a)

4r²(2r + 4)

b)

8r²(r + 2)

c)

8(r³ + r²)

d)

4(r³ + 2r²)

27.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

28.

Factor completely: 3x² - 7x + 2

a)

(x - 1) (3x + 2)

b)

(x - 2) (3x -1)

c)

(x - 1) (3x - 2)

d)

(x + 2) (3x + 1)

29.

Factor completely:

2x² - 7x + 6

a)

(x -1)(2x - 6)

b)

(x - 3) (2x - 2)

c)

(x - 2) (2x - 3)

d)

(x - 6) (2x - 1)

30.

Factor Completely: 4x² - 20x + 25

a)

(4x - 25) (x -1)

b)

(2x + 5) (2x - 5)

c)

(2x - 5)²

d)

(4x - 5) (x - 5)

31.

Factor Completely: 3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

32.

Factor Completely: 6x² + 7x - 3

a)

(2x + 3)(3x-1)

b)

(2x - 3)(3x + 1)

c)

(2x + 3)(6x - 2)

d)

(3x - 3)(2x + 1)

33.

Factor completely: 2x² - 3x - 2

a)

(2x - 2)(x + 1)

b)

(2x + 1)(x - 2)

c)

(2x - 1)(x - 2)

d)

(2x - 1) (x - 1)

34.

Factor Completely: 2x² + x - 6

a)

(x + 2) (2x -3)

b)

(x - 6) (2x + 1)

c)

(x + 1) (2x - 6)

d)

(x - 2) (2x + 3)

35.

Factor the expression:

x² – 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

36.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

37.

Solve the quadratic equation.

a)

±72

b)

±12

c)

12

d)

No real solution

38.

Solve the quadratic equation.

a)

±81

b)

±9

c)

±3

d)

No real solution

39.

Solve the quadratic equation.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

40.

Solve the quadratic equation.

a)

±1.5

b)

1.5

c)

±1

d)

No real solution

41.

What is the discriminant?

a)

b²-4ac

b)

b²/2a

c)

4ac

d)

b²±4ac

42.

If the discriminant equals 0, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

43.

If the discriminant is negative, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solutions

44.

If the discriminant is positive, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

45.

Factor the equation x²-9x+20=0 to solve.

a)

x=-2, 10

b)

x=-5, -4

c)

x=4, 5

d)

Not factorable

46.

Solve the equation:

5 = –2x + x²

a)

No Solution

b)

-3.5 or 1.5

c)

2 or 3

d)

-1.5 or 3.5

47.

Solve the equation:

10x² = 8x

a)

0 or 0.8

b)

-0.8 or 0

c)

No Solution

d)

0

48.

Solve the equation:

2x² - 32 = 0

a)

-16 or 16

b)

-4 or 4

c)

No Solution

d)

-8 or 8

49.

Solve the quadratic.

a)

±23.25

b)

±5

c)

±25

d)

No real solution

50.

Find the discriminant.
2x² + 7x - 15 = 0

a)

169, No Real Solutions

b)

169, Imaginary solutions

c)

169, 1 real solution

d)

169, 2 real solutions

51.

Solve by taking square roots:
(x - 7)² = 99

a)

x = 7 ± 3√11

b)

x = -7 ± 3√11

c)

x = -11 ±√7

d)

x = 11 ±√7

52.

Solve.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

53.

Solve by factoring.
x² + 2x - 8 = 0

a)

4 and 2

b)

4 and -2

c)

-4 and 2

d)

-4 and -2

54.

Solve by factoring.
3a² - 12a + 12 = 0

a)

-2

b)

2

c)

2/3

d)

5

55.

Solve by factoring.
z² - 6z - 27 = 0

a)

z = 3 or z = 9

b)

z = 3 or z = -9

c)

z = -3 or z = 9

d)

z = -3 or z = -9

56.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

57.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

58.

Solve by factoring

6x² + 17x + 12 = 0

a)

x = -4/3, x = -3/2

b)

x = 9, x = 8

c)

x = 4, x = 3

d)

x = -4, x = -3

59.

Solve using the square root method:

x² - 49 = 0

a)

x = -7, x = 7

b)

x = -7

c)

x = 7

d)

x = -7, x = 1

60.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

61.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

62.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

63.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

64.

How does the parabola open? y = 4x - x² - 1

a)

up

b)

down

c)

left

d)

right

65.

Which of the following parabolas will have a minimum?

a)

y = -x² + 4

b)

y = -x² + x - 3

c)

y = -x² - 2

d)

y = x² + 2x - 8

66.

What do we call the graph of a quadratic function?

a)

parabola

b)

linear

c)

cubic

d)

sinusoidal

67.

How do you know if a parabola has a minimum?

a)

When ‘a’ is positive there is a minimum

b)

When ‘a’ is negative there is a minimum

c)

When all the numbers in the equation are negative there is a minimum

d)

When all the numbers in the equation are positive there is a minimum

68.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

69.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

70.

What are the zeros of the function?
f(x) = (x - 3)(x +7)

a)

x = 3 and x = -7

b)

x =-3 and x = 7

c)

x = -21 and x = 10

d)

x = 21 and x = -10

71.

Simplify:
√45

a)

9√5

b)

3√5

c)

5√9

d)

3√15

72.

Simplify:
√200

a)

10√2

b)

2√10

c)

50√2

d)

2√50

73.

√125

a)

5√5

b)

25√5

c)

5√25

d)

5√2

74.

Simplifying the following

a)

√4

b)

2

c)

(√100 )/ 5

75.

Is this a perfect square trinomial?
x² + 14x + 49

a)

Yes

b)

No

76.

Factor:
n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

77.

Find the missing value "c" to create a perfect square trinomial:
x² – 4x + ___

a)

4

b)

8

c)

-4

d)

-2

78.

Find the missing value "c" to create a perfect square trinomial:
x² – 32x + ___

a)

256

b)

200

c)

32

d)

16

79.

What is the axis of symmetry for this graph?

a)

y=2

b)

x=2

c)

x=0

d)

y=0

80.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

81.

The line that goes through the vertex of a parabola is called the...

a)

Vertex

b)

Axis of Symmetry

c)

x-intercept

d)

y-intercept

82.

The vertex of this quadratic is...

a)

(1,16)

b)

(-3,0)

c)

(5,0)

d)

(0,15)

83.

Which graph represents a system of equations with no solution?

a)

b)

c)

d)

None of the above

84.

Solve the system using substitution.

$x=2y$
$-3x+5y=17$

a)

(-34, -17)

b)

(8, 4)

c)

(10, 20)

d)

No solution

e)

Infinite solutions

Algebra 1 Semester 2 Final Review

Total questions: 84

Worksheet time: 3hrs 46mins

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