Free Printable Midterm Review

1.

3 x (5 + 2)

a)

17

b)

21

c)

30

d)

14

2.

5 ÷ 1³

a)

1

b)

5

c)

⅕

d)

50

3.

Evaluate the expression:
(23 + m) ÷ 9
m = 4

a)

2

b)

4

c)

3

d)

9

4.

How many terms are in the following expression?
q + 4r − 18 + 2³ - 1
q = 3
r = 2

a)

2

b)

5

c)

3

d)

18

5.

c = 2
Evaluate.

$\left(2\ +c\right)\ \cdot\ c^3$

Use your whiteboard and marker to substitute the variable for the number it equals.

(a)

6.

Simplify the following:
-8 + (15 - 3) ÷ 4

a)

-5

b)

1

c)

-11

d)

11

7.

-2 ⋅ (3 + 8 ÷ 4)²

a)

-16

b)

1.375

c)

4

d)

-50

8.

What does 4⁵ mean?

a)

4x4x4x4x4

b)

4x5

c)

5x5x5x5

9.

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

a)

add

b)

subtract

c)

multiply

d)

divide

10.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

11.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

12.

Solve using the product law of exponents

Resolver utilizando la ley de productos de los exponentes

(5⁵)(5³)

a)

25⁸

b)

5¹⁵

c)

25¹⁵

d)

5⁸

13.

a)

10x⁹

b)

24x¹⁴

c)

24x⁹

d)

10x¹⁴

14.

a)

b)

c)

d)

15.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

16.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

17.

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

a)

add

b)

subtract

c)

multiply

d)

divide

18.

Simplify √72

a)

7√9

b)

4√6

c)

6√2

d)

3√4

19.

In simplest radical form,
2√50 is equivalent to

a)

5√2

b)

7√2

c)

10√2

d)

4√5

20.

In simplest radical form, -5√75 is equivalent to:

a)

5√3

b)

-15√5

c)

√3

d)

-25√3

21.

Simplify √45x⁴y⁷

a)

3x²y³√5

b)

9x²y³√5y

c)

3x²y³√5y

d)

3x⁴y⁷

22.

$\frac{2}{\sqrt[]{8}}$

What's the next step?

a)

Divide numerator and denominator by $\sqrt[]{8}$

b)

Multiply numerator and denominator by $\sqrt[]{8}$

c)

Multiply numerator and denominator by 2

d)

Multiply numerator and denominator by 8.

23.

$\frac{53}{\sqrt[]{2}}$

Which of these equals the above?

a)

$53\sqrt[]{2}$

b)

$\frac{\sqrt[]{53}}{2}$

c)

$\frac{53\sqrt[]{2}}{2}$

d)

$\sqrt[]{\frac{53}{2}}$

24.

$\frac{4}{3-\sqrt[]{2}}$

What's the next step to simplify this?

a)

Multiply numerator by the conjugate $3+\sqrt[]{2}$

b)

Multiply numerator and denominator by the conjugate $3-\sqrt[]{2}$

c)

Multiply numerator and denominator by the conjugate $3+\sqrt[]{2}$

d)

Multiply the denominator by the conjugate $3+\sqrt[]{2}$

25.

$\frac{1+\sqrt[]{5}}{1-\sqrt[]{5}}$

Final result fully simplified?

a)

$\frac{6+2\sqrt[]{5}}{-4}$

b)

$-\frac{6+2\sqrt[]{5}}{4}$

c)

$\frac{5}{-4}$

d)

$-\frac{5}{4}$

26.

Simplify: $\frac{4i}{3i}$

a)

$\frac{4}{3}$

b)

$\frac{4i}{3}$

c)

$\frac{3i}{4}$

d)

$\frac{1}{2}$

27.

Simplify: $\frac{3+i}{2-i}$

a)

$5+i$

b)

$5+5i$

c)

$1+5i$

d)

$1+i$

28.

#6 Simplify $\sqrt[]{-36}$ = (a)

Choose from the below words

6i

36

2

2i

3i

6

-6

29.

#7 Simplify $\sqrt[]{-72}$ = (a) (b) (c)

Choose from the below words

6

i

$\sqrt[]{2}$

-6

$\sqrt[]{36}$

$\sqrt[]{6}$

$\sqrt[]{-2}$

30.

#8 Simplify $\sqrt[]{-12}$ = (a) (b) (c)

Choose from the below words

2

i

$\sqrt[]{3}$

3

$\sqrt[]{2}$

$\sqrt[]{-3}$

-2

6

31.

#13 Simplify (-6 - 7i) + (2 + 6i)

a)

-5

b)

-4 + i

c)

-4 - i

d)

-8 + 13i

32.

Simplify:
2i(4 - 3i)

a)

6 + 8i

b)

6 - 8i

c)

8i - 6i²

d)

8i + 6i²

33.

Simplify:
(4 + 7i) - (3 + 2i)

a)

1 + 5i

b)

7 + 9i

c)

1 + 9i

d)

-1 + 5i

34.

The point where the line crosses the y-axis is called the:

a)

origin

b)

x-intercept

c)

y-intercept

d)

slope

35.

From the equation: y = -2x +6 what is the slope of the line?

a)

y

b)

6

c)

x

d)

-2

36.

What is the y-intercept?

a)

(5, 0)

b)

(-5, 0)

c)

(0, 5)

d)

(0, -5)

37.

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

a)

A

b)

B

c)

C

d)

D

38.

Which graph represents the equation $y=4x-1$

a)

b)

c)

d)

39.

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

a)

y= -1x+3

b)

y= 4x+3

c)

y=1/4x+3

d)

y= -4x+3

40.

Which equation represents this graph?

a)

$y=\frac{1}{5}x+3$

b)

$y=-5x-3$

c)

$y=5x+3$

d)

$y=-3x+0.5$

41.

What is the correct equation?

a)

x = 5

b)

y = 5

c)

x = - 5

d)

y = -5

42.

What is the solution to the systems of equations shown in the graph?

a)

1 Solution x=-1/2

b)

1 Solution y=-1/2

c)

Many Solutions

d)

No Solution

43.

Solve for x and y.
y = 2/3x - 2
y = -x + 3

a)

(0,3)

b)

(0,-3)

c)

(3,0)

d)

(-3,0)

44.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

45.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

46.

Name the x- and y-intercepts for the equation:
2x - y = 6

a)

(0, 3) and (-6, 0)

b)

(0, -3) and (-6, 0)

c)

(3, 0) and (0, -6)

d)

(-3, 0) and (0, -6)

47.

What is the y-intercept?

a)

(0,7)

b)

(0, 0)

c)

(0,1)

d)

(0, 2)

48.

What are the x- and y -intercepts on this graph?

a)

(0,5), (0,5)

b)

(5,0), (5,0)

c)

(5,0), (0,5)

d)

(0,0), (5,0)

49.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

50.

What is another word that describes the zeroes of a quadratic function?

a)

y-intercepts

b)

vertex

c)

x-intercepts

d)

maximum

51.

To solve a quadratic by graphing is to find where the parabola crosses the x-axis. We call these the ___. Select all that apply.

a)

zeroes

b)

x-intercepts

c)

solutions

d)

roots

52.

Find the roots

a)

x = -1 x = 3

b)

x = -2 x = 3

c)

x = -1 x = 4

53.

Identify a, b and c in the quadratic equation: $2x^2-3x-5=0$

a)

a = 2 , b = 3, c = -5

b)

a = 2, b = -3, c = 5

c)

a = 2, b = -3, c = -5

d)

a = -2, b = 3, c = 5

54.

$b^2-4ac$ is called the . . .

a)

Square root

b)

Quadratic formula

c)

X-intercepts

d)

Discriminant

55.

If the discriminant is equal to -2, how many solutions are there?

a)

No Solutions

b)

1 Solution

c)

2 Solutions

d)

Infinite Solutions

56.

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

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

57.

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)

$x=1,\ x=15$

58.

Solve by completing the square.
$x^2-8x-20=0$

a)

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

b)

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

c)

$x=\left\{-20,\ -8\right\}$

d)

$x=\left\{8,\ 20\right\}$

59.

Solve by completing the square.
$x^2-4x-20=0$

a)

$x=\left\{\pm6\sqrt{2}-2\right\}$

b)

$x=\left\{\pm6\sqrt{2}+2\right\}$

c)

$x=\left\{\pm2\sqrt{6}+2\right\}$

d)

$x=\left\{\pm2\sqrt{6}-2\right\}$

60.

Factor x² - 18x +81

a)

(x+9)(x+6)

b)

(x+18)(x-1)

c)

(x-9)(x-9)

d)

(x-9)(x+9)

61.

Factor x²-2x-15

a)

(x+5)(x-3)

b)

(x-5)(x-3)

c)

(x-5)(x+3)

d)

(x+5)(x+3)

62.

Factor x² + 7x + 12

a)

(x + 2)(x + 10)

b)

(x + 3)(x + 4)

c)

(x + 4)(x + 5)

d)

(x + 4)(x + 6)

63.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

64.

Factor
d² - 10d + 25

a)

(d + 5) (d - 5)

b)

(d - 15) (d + 10)

c)

(d + 5) (d - 20)

d)

(d - 5) (d - 5)

65.

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)

66.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

67.

What is the maximum/minimum of a parabola called?

a)

vertex

b)

point

c)

top

d)

bottom

68.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

69.

Which shows STANDARD FORM of a quadratic?

a)

b)

c)

d)

70.

Which shows VERTEX FORM of a quadratic?

a)

b)

c)

d)

71.

To find the vertex in standard form, you must first find the axis of symmetry. The formula for that is x =

a)

-2b/a

b)

2a/b

c)

-2a/b

d)

-b/2a

72.

The axis of symmetry of this quadratic is: $y=2x^2-20x+47$

a)

x = -10

b)

x = -5

c)

x = 5

d)

x = 4

73.

Which transformation transforms the graph of

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

a)

shift 4 units up

b)

shift 4 units down

c)

shift 4 units to the left

d)

shift 4 units to the right

74.

What are the transformations?

y=(x-2)²+4 (Choose ALL that apply.)

a)

shift right 2

b)

shift left 2

c)

shift up 4

d)

shift down 4

75.

y= -(x-11)²+6

*Mark all that apply.

a)

right 11

b)

reflection across x-axis

c)

VC

d)

up 6

Midterm Review

Total questions: 75

Worksheet time: 3hrs 12mins

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