Free Printable Final Exam Review Part 1

1.

Solve using properties of square roots.

x² - 49 = 0

a)

x = -7, x = 7

b)

x = -7

c)

x = 7

d)

x = 49

2.

Use quadratic formula to solve: $x^2-4x+6=0$

a)

$\left\{\frac{4+\sqrt{8}}{2},\frac{4-\sqrt{8}}{2}\right\}$

b)

$\left\{6\right\}$

c)

$No\ Real\ Solutions$

d)

$\left\{\frac{-4+\sqrt{40}}{2},\frac{-4-\sqrt{40}}{2}\right\}$

3.

Use quadratic formula to solve: $n^2+9n-20=0$

a)

$\left\{\frac{-9+\sqrt{161}}{2},\frac{-9-\sqrt{161}}{2}\right\}$

b)

$\left\{\frac{9+\sqrt{141}}{2},\frac{9-\sqrt{141}}{2}\right\}$

c)

$No\ Real\ Solutions$

d)

$\left\{-10,\ 2\right\}$

4.

Simplify.
$\left(4-5i\right)\left(-2+7i\right)$

a)

$27-38i$

b)

$-27+38i$

c)

$-27-38i$

d)

$27+38i$

5.

Simplify:

-3a²b³(4ab - 7a³)

a)

-12a²b² + 21a⁵b³

b)

-12a²b³- 21a²b³

c)

9a³

d)

-12a³b⁴ + 21a⁵b³

6.

a)

A

b)

B

c)

C

d)

D

7.

Simplify :

(x⁵y¹⁰z¹¹ )⁰=

a)

1

b)

0

c)

(xyz)¹

d)

(x⁵y¹⁰z¹¹)¹

8.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

9.

a)

8

b)

8x

c)

8x²

d)

8x³

10.

Factor with GCF:

a)

3v²( v²−9v−10)

b)

3( v²−9v−10)

c)

3v( v²−9v−10)

d)

9v( v²−3v−10)

11.

True or false:

The solution, root, x-intercept, and zero of a problem are the same.

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

12.

Multiply
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

13.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

14.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

15.

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)

16.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

17.

What is the GCF in this polynomial?
3x²+6x-18

a)

2

b)

3

c)

6

d)

18

18.

What is the GCF of the following polynomial?
2x³+4x²-12x?

a)

2

b)

4x

c)

x

d)

2x

19.

$\left(\left(2x^5-3x^4\right)^3\right)^0=?$

a)

Not enough information

b)

0

c)

1

d)

6

20.

$3x\left(2x\ -5\right)=$

a)

$5x^2-8$

b)

6x - 10

c)

$6x^2-15x$

d)

$6x^2-15$

21.

First thing you do when factoring

5x² - 13x + 6

is

a)

Multiply 5 and -13

b)

Multiply 6 and -13

c)

Multiply 5 and 6

d)

Multiply 5, 6 and -13

22.

Factor: ( Hint: GCF )

17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

x(17y)

23.

Factor:

5x³- 7x²

^{Hint: Try GCF}

a)

x²(5x - 7)

b)

x(5x²- 7x)

c)

x³(5 - 7x)

d)

Cannot be factored

24.

What is the greatest number of solutions that a Quadratic Equation can have?

Remember a quadratic equation is of degree 2.

a)

0

b)

1

c)

2

d)

3

25.

x² + 4 = 68

a)

± 8

b)

± √8

c)

8

d)

± 64

26.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

27.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

28.

Which transformation transforms the graph of
f(x) = x² to the graph of
g(x) = (x + 4)²?

a)

a vertical translation 4 units up

b)

a vertical translation 4 units down

c)

a horizontal translation 4 units to the left

d)

a horizontal translation 4 units to the right

29.

If the blue graph is
f(x) = x²the 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

30.

If the blue graph is

f(x) = x²

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

31.

Does the quadratic have a max/min vertex, and does the graph open up/down?

a)

max/ opens down

b)

min/ opens up

c)

max/ opens up

d)

min/ opens down

32.

Find the equation of the parabola that has moved...

3 units up

a)

$y=x^2+3$

b)

$y=x^2-3$

c)

$y=\left(x+3\right)^2$

d)

$y=3x^2$

33.

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

a)

$y=\left(x+3\right)^2+5$

b)

$y=\left(x+5\right)^2+3$

c)

$y=\left(x-3\right)^2+5$

d)

$y=\left(x+5\right)^2-3$

34.

What is the equation for the axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

35.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

36.

Does y = -4x² have a maximum or minimum value?

a)

maximum

b)

minimum

37.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

38.

What is the formula to find the vertex of a parabola?

a)

x = -b/2

b)

x = -b

c)

x = -b / (2a)

d)

x = -b / 2

39.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

40.

Identify the vertex and whether the graph opens up or down.

a)

(-1, 4); opens up

b)

(-1, 4); opens down

c)

(1, 4); opens up

d)

(1, 4); opens down

41.

What is another name for the x-intercepts of a quadratic?

a)

y-intercepts

b)

zeros

c)

x-axis

d)

none of these

42.

solve using the square root method

3x² = 12

a)

± 2

b)

2

c)

± √12

d)

± 4

43.

How many solution does a quadratic equation x² - 9 = 16 have ?

a)

none

b)

1

c)

2

d)

3

44.

What is the standard form of quadratic equations?

a)

$ax^2+bx+c\ =\ 0$

b)

$ax\ +b=c$

c)

$ax^2\ =c$

d)

$ax^2-bx\ =\ c$

45.

First step to solve this quadratic equation?

5m² + 1 = 6

a)

add 1 to both sides

b)

subtract 1 from both sides

c)

divide both sides by 5

d)

take the square root on both sides

46.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

47.

What two numbers when multiplied equals -56, but when you add them equals 1? CHOOSE TWO NUMBERS

(a) (b)

Choose from the below words

-7

8

-8

7

56

1

-56

-1

48.

What are the factors of 25x² + 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

49.

What shape is the graph of a quadratic?

a)

Hyperbola

b)

Parabola

c)

Straight Line

d)

Circle

50.

Parabolas can open which of the following ways?

a)

Up

b)

Down

c)

Right

d)

Left

51.

An axis of symmetry is...

a)

a vertical line

b)

a horizontal line

52.

A positive quadratic will open....

a)

downward

b)

upward

53.

The quadratics we will study have how many real solutions?

a)

Infinite

b)

0

c)

2

d)

at least 2

54.

An x-intercept is also called...

a)

a root

b)

a solution

55.

x-intercepts are also called:

Choose ALL that apply!

a)

Solutions

b)

Roots

c)

Zeros

d)

Parabolas

e)

Puppies

56.

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

a)

Call a friend

b)

Plug into a calculator

c)

Solutions are where the quadratic crosses the x-axis

d)

Magic 8 Ball -_-

57.

What are the solutions, zeros, or x-intercepts of the graph?

a)

(-4,0) and (0,0)

b)

(0,0) and (4,0)

c)

(-2,-2)

d)

None

58.

What are the real roots (solutions) of the quadratic y = 2x²+4x+5

a)

(−1, 3)

b)

(0,5)

c)

(5,0)

d)

(3,-1)

e)

No real roots

59.

Choose the correct values for a, b, and c.

$4x^2-5x\ =\ 9$

a)

a = 4

b)

b = 5

c)

c = 9

d)

b = -5

e)

c = -9

60.

$x=\frac{-\left(b\right)\sqrt{\left(a\right)^2-4ac}}{2b}$ What is wrong with this formula? Check ALL that apply.

a)

Missing $\pm$ after $-\left(b\right)$

b)

The square root should be $\sqrt{\left(b\right)^2-4ac}$

c)

The denominator should be $2a$

d)

There are no errors. It is correct.

61.

Find the axis of symmetry for

f(x) = x²- 4x + 5.

AXIS OF SYMMETRY:

$-\frac{B}{2A}$

a)

x = -2

b)

x = 2

c)

y = 2

d)

y = -2

e)

y= 2x +1

62.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

63.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

64.

What are the zeros of

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

QUADRATIC FORMULA:

$\frac{-b\pm\sqrt[]{b^{2\ }-4ac}}{2a}$

a)

$x=-2,\ -9$

b)

$x=2,\ -9$

c)

$x=-2,\ 9$

d)

$x=2,\ 9$

65.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

66.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

67.

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)

68.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

69.

Factor:

4h² - 12h + 9

a)

(2h - 3)²

b)

4(h + 9)(h + 1)

c)

(2h - 3)(2h + 3)

d)

(h - 9)(4h - 1)

70.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

71.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

72.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

73.

Simplify m¹²/ m³

a)

m^12-3 = m⁹

b)

m^12/3= m⁴

c)

m^-9

d)

-m⁹

74.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

75.

a)

A

b)

B

c)

C

d)

D

Final Exam Review Part 1

Total questions: 75

Worksheet time: 19hrs 45mins

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