Free Printable Final Exam Review

1.

a)

(-1, -1)

b)

(2, 5)

c)

(5, 11)

d)

(-4, -7)

2.

a)

29.5

b)

-13.5

c)

6

d)

3.25

3.

a)

6

b)

-6

c)

3.5

d)

-3.5

4.

a)

36x⁶

b)

36x⁸

c)

6x⁸

d)

not here

5.

What is the range of y = x²- 2x + 6?

a)

$x\ge5$

b)

$y\ge5$

c)

$All\ Real\ Numbers$

d)

$y\ \le5$

6.

What is the vertex?

a)

(5,2)

b)

(2,5)

c)

(-2,5)

d)

(-5,2)

7.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

8.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

9.

Which answer choice describes y = -3x² +7x - 2 accurately?

a)

opens up with a maximum

b)

opens up with a minimum

c)

opens down with a maximum

d)

opens down with a minimum

10.

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)

11.

Factor completely
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

12.

Factor completely
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

13.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

14.

Solve by factoring
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

15.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

16.

Is this a max or min?

a)

max

b)

min

c)

cannot be determined

17.

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

18.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

19.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

20.

What is the vertex of this quadratic equation?
y = 2(x - 2)² + 5

a)

(-2,5)

b)

(2,5)

c)

(5,-2)

d)

(-5,-2)

21.

Does this graph have a maximum or minimum?

a)

Minimum

b)

Maximum

22.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

23.

What are the Zeroes for this graph?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

24.

Given the equation for this parabola, does this parabola have a maximum or minimum value?

y\ =\ -\left(x-4\right)^2\ -\ 3

a)

Maximum

b)

Minimum

25.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

26.

What is the green dot on the parabola called?

a)

maximum

b)

minimum

c)

roots

d)

zeros

27.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

28.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

29.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

30.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

31.

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

32.

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

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

33.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

34.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

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

35.

What is the axis of symmetry?

a)

the slope of the graph

b)

the dividing line for a parabola

c)

a way to spin my pencil

d)

the x-axis

36.

Solve for x:

3x-5=4

a)

3

b)

2

c)

4

d)

8

37.

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

a)

(0,3)

b)

(3,0)

c)

No solution(parallel lines)

d)

Infinitely many solutions

38.

Which of the following trinomials is a perfect square trinomial?

a)

r² - 6r + 36

b)

4y² + 10y + 25

c)

x² + 16x + 16

d)

9a² - 12a + 4

39.

Factor, if possible: 4x²+36x+81

a)

(4x+81)²

b)

(2x+9)²

c)

Prime /
Not factorable.

d)

(2x-9)²

40.

Solve x² - 5x + 10 = 0

a)

(5 - i√15)/2 , (5 + i√15)/2

b)

(5 - √15)/2 , (5 + √15)/2

c)

(5 - i√65)/2 , (5 + i√65)/2

d)

(5 - √65)/2 , (5 + √65)/2

41.

The solutions of the quadratic equation
x²+2x-15=0 are

a)

x = 3 or x = 5

b)

x = 5 or x = -3

c)

x = -5 or x = 3

d)

x = -3 or x = -5

42.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

43.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

44.

Solve for x:
7 - 5x = 12

a)

1

b)

-6

c)

-1

d)

6

45.

Factor by GCF:
17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

not factorable

46.

Factor
12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

47.

Factor:
b²+ 8b + 7

a)

(b + 4)(b + 3)

b)

(b + 6)(b + 1)

c)

(b + 7)(b +1)

d)

prime

48.

Factor Completely: 6x² + 5x - 6

a)

6(x + 1)(x - 6)

b)

(6x + 6)(x - 1)

c)

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

d)

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

49.

Factor: n²- 2n + 1

a)

(n + 1)(n - 1)

b)

(n + 1)²

c)

prime

d)

(n - 1)²

50.

Factor:
4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

(2h - 2)(2h + 2)

d)

(h - 4)(4h - 1)

51.

a)

x²+4x+8

b)

x²+8x+8

c)

x²+8x+6

d)

x²+6x+8

52.

a)

5x²+16x+8

b)

6x²+12x+8

c)

6x²+16x+6

d)

6x²+16x+8

53.

Simplify:

−3(a + 5)

a)

-3a+15

b)

3a+15

c)

3a-15

d)

-3a-15

54.

Simplify the expression.
(x⁴ )(x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

55.

Simplify the expression.

a)

y¹⁵

b)

y⁵⁰

c)

y²

d)

y⁵

56.

6⁰

a)

1

b)

0

c)

6

57.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

58.

According to exponent rules, when we multiply the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

59.

When dividing exponential expressions with the same base, what always happens to the exponents?

a)

they are added together

b)

they are subtracted

c)

they are divided

d)

they are multiplied

60.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

61.

Simplify with no negative exponents:
x^-3

a)

-3x

b)

x³

c)

1/ x^-3

d)

1/ x³

62.

Evaluate, follow the Order of Operation

(3x – 5)(y + 2) when x = 2, y = 3

(a)

63.

Evaluate, follow the Order of Operation

2x – 3y + 2 when x = -4, y = 2

(a)

64.

Evaluate

15 – 2x² when x = 2

(a)

65.

Evaluate when x = -4, y = 2

(a)

66.

Is 7 a solution of the equation x² – x + 2 = 42?

a)

yes

b)

no

67.

Is 5 a solution of the inequality 13 + 2x ≤ 23 ?

a)

yes

b)

no

68.

Simplify

-2-(-7)

(a)

69.

A rectangle has a width of 2x + 1 . It has a length of 4x + 2. Write an expression for the perimeter of this rectangle.

(a)

70.

What is the DOMAIN?

a)

[0, ∞)

b)

(-∞, 0)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

71.

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

72.

Find the zeros.

a)

0 and 4

b)

0 and -4

c)

0

d)

-4

73.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

74.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

75.

Factor:
2x² + 13x + 15

a)

(2x + 1)(x + 15)

b)

(x + 3)(x + 5)

c)

(2x - 3)(x - 5)

d)

(2x + 3)(x + 5)

76.

a)

A

b)

B

c)

C

d)

D

77.

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

78.

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

79.

Simplify.
a² b⁰ a^-3

a)

a

b)

1/a

c)

ab

d)

1/(a³)

80.

If g(x) = 2x² - 4, find g(-2)

a)

-8

b)

-12

c)

4

d)

0

81.

a)

5^-8

b)

5²

c)

25^-8

d)

25²

82.

a)

8

b)

1/8

c)

8⁷

d)

all of the above

83.

The growth factor for this table is

a)

2

b)

4

c)

12

d)

144

84.

Is the Equation Linear or Exponential?

a)

Linear

b)

Exponential

85.

Describe the function:
y = 57(1/3)^x

a)

growth by factor of 1/3

b)

decay by factor of 1/3

c)

growth by 2/3

d)

decay by 1/3 %

86.

Which scatter plot shows a linear relationship between x and y?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

87.

In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that models this situation. After how many months will the total cost be $58?

a)

7 months

b)

6 months

c)

5 months

d)

4 months

88.

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)

89.

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)

90.

Factor Completely: 9x² - 49

a)

(3x + 7)(3x + 7)

b)

(3x + 7)(3x - 7)

c)

(3x - 7)(3x - 7)

d)

Prime

91.

Solve
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

92.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

93.

Solve
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

94.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

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

95.

Identify the 'c' value: y = 16x² -8x -24

a)

16

b)

-8

c)

24

d)

-24

96.

-5x⁶(3x² - 12x + 30)

a)

-15x⁸+ 60x⁷- 150x⁶

b)

15x⁸- 60x⁷- 150x⁶

c)

8x⁶- 17x + 35

d)

-8x⁶+ 17x - 35x²

97.

Factor completely:
x² - 121

a)

(x + 11)(x - 11)

b)

(x + 11)(x +11)

c)

(x - 11)(x - 11)

d)

x(x - 121)

98.

Classify the polynomial by its degree:

25x³+ 3y⁶+ 2x³y⁴

a)

25

b)

7

c)

6

d)

2

99.

Simplify:

a)

81√3

b)

9√3

c)

3√3

d)

√3

100.

Simplify:

a)

2√3√14

b)

4√42

c)

2√42

d)

4√3√14

101.

√5 + √20

a)

5

b)

25

c)

3√5

d)

2√3

102.

The number under the radical sign or square root sign is called the ______.

a)

radical sign

b)

radicand

c)

factor

d)

exponent

103.

Simplify
-11√21 - 11√21

a)

0

b)

-22√21

c)

√21

d)

Already simplified

104.

Simplify the expression

a)

49

b)

7

c)

√98/√2

d)

It's already simplified

Final Exam Review - Algebra I

Total questions: 104

Worksheet time: 5hrs 19mins

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