Free Printable Algebra 2 CP Midterm Review

1.

Simplify the following equation and solve for x:

$3x+2(4x-4)=3$

a)

x = 4

b)

x = 3

c)

x = 2

d)

x = 1

2.

$97=-3\left(6n-5\right)-8$

a)

$-10$

b)

$16$

c)

$-5$

d)

$-2$

3.

solve for m:

\frac{2}{3}\left(9m-6\right)=20

a)

$m=4$

b)

$m=3$

c)

$m=2$

d)

$m=8$

4.

Solve for k, write your answer as a simplified fraction:

-5\left(2k-1\right)\ =\ 17-2k

a)

$k=-1$

b)

$k=-\frac{11}{4}$

c)

$k\ =\ -\frac{2}{3}$

d)

$k=-\frac{3}{2}$

5.

Given $h\left(x\right)=-2\left(x+5\right)^2$ , what is the value of $h\left(7\right)$ ?

a)

$-140$

b)

$-48$

c)

$-8$

d)

$-288$

6.

Which of the following has the smallest value?

Let m(x)= $-3x+5$

a)

m(-1)

b)

m(0)

c)

m(1)

d)

m(2)

7.

$f\left(x\right)=x^2-9x+2$
Evaluate: $f\left(-2\right)$

a)

$f\left(-2\right)=24$

b)

$f\left(-2\right)=-20$

c)

$f\left(-2\right)=16$

d)

$f\left(-2\right)=-12$

8.

What is the y-coordinate to the system of equations below?

-4x + y = 4

4x - 3y = 12

a)

y=3

b)

y=8

c)

y=-3

d)

y=-8

9.

Solve the following system:

-7x-2y=-13

x=2y+11

a)

$\left(3,\ -4\right)$

b)

$\left(3,\ 4\right)$

c)

$\left(-3,\ -4\right)$

d)

$\left(-3,\ 4\right)$

10.

a)

(2, -3)

b)

(3, 2)

c)

(-3, -2)

d)

(-2, -3)

11.

What are the possible ways to successfully do the elimination method for this problem?

(there are more than one correct answer)

a)

Eliminate x by multiplying the top equation by 10 and the bottom equation by 6

b)

Eliminate x by multiplying the top equation by -10 and the bottom equation by 6

c)

Eliminate x by multiplying the top equation by 10 and the bottom equation by -6

d)

Eliminate y by multiplying the bottom equation by 2

e)

Eliminate y by multiplying the bottom equation by -2

12.

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

a)

Sugar Cookies $5
Oatmeal Cookies $3

b)

Sugar Cookies $4
Oatmeal Cookies $8

c)

Sugar Cookies $2
Oatmeal Cookies $6

d)

Sugar Cookies $3
Oatmeal Cookies $6

13.

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

a)

x + y = 1550
y = 4x

b)

x + y = 1550
y = x + 4

c)

y - x = 1550
y = 4x

d)

y = 1550 + x
y = x + 4

14.

Which of the following is not a method for solving systems of equations

a)

Elimination

b)

Substitution

c)

Estimation

d)

Graphing

15.

The difference of a and b is 3. The sum of the variables is 13. Find the numbers.

a)

a = 7
b = 10

b)

a = 8
b = 5

c)

a = 10
b = 13

16.

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

a)

x + y = 1430
20x + 50y = 49

b)

x + y = 49
10x + 5y = 1430

c)

x + y = 49
20x + 50y = 1430

d)

x + y = 49
x + y = 1430

17.

Jack wants to save up money to buy his math teacher a new calculator for the holidays. After 4 weeks, he has $78 saved up. After 9 weeks, he has $138.

How much money does Jack have before he starts saving?

a)

$30

b)

$48

c)

$102

d)

$38

18.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

19.

Jack wants to save up money to buy his math teacher a new calculator for the holidays. After 4 weeks, he has $78 saved up. After 9 weeks, he has $138.

How much money does Jack save per week?

a)

$5 per week

b)

$60 per week

c)

$12 per week

d)

$15 per week

20.

The money I have is represented by the equation:

y = 95x + 23 where x = number of weeks and y = money remaining.

How much money do I have initially?

a)

$95

b)

$95 in debt

c)

$23

d)

$23 in debt

21.

The money I have is represented by the equation:

y = 10x + 100 where x = number of weeks and y = money remaining.

How does my money CHANGE each week?

a)

increases by $10 each week

b)

decreases by $10 each week

c)

increases by $100 each week

d)

decreases by $100 each week

22.

a)

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

b)

$y=\frac{2}{5}x$

c)

$y=\frac{2}{5}x-1$

d)

$y=-x-3$

23.

a)

$y=3x-1$

b)

$y=-9x-1$

c)

$y=\frac{1}{3}x+2$

d)

$y=-\frac{1}{3}x-9$

24.

Write the equation of the line shown in point slope form.

a)

$y-7=\frac{3}{4}x\left(x-0\right)$

b)

$y-0=-\frac{3}{4}\left(x-7\right)$

c)

$y+4=-\frac{3}{4}\left(x+4\right)$

d)

$y-4=-\frac{3}{4}\left(x-4\right)$

25.

Find the rate of change/slope.

Then write the point-slope equation using the first point given in the table.

a)

-2 minutes per gallon

y - 80 = -2 (x - 10)

b)

-20 minutes per gallon

y - 80 = -20 (x - 10)

c)

-2 gallons per minute

y -80 = -2 (x - 10)

d)

-20 gallons per minute

y - 80 = -20 (x - 10)

26.

Which equation is written in point-slope form?

a)

$y=mx+b$

b)

$y-y_1=m\left(x-x_1\right)$

c)

$Ax+By=C$

27.

A man is climbing down from 100 feet high descending 30 feet per minute. Which function models his descent?

a)

y = 100 - 30x

b)

y = 100 + 30x

c)

y = 100x + 30

d)

y = 100x - 30

28.

What is the slope (or rate of change)?

a)

$2/1 mile drive

b)

$1/2 miles driven

c)

2 miles driven/$1

d)

1 mile driven/$2

29.

Sonia has $40 in her lunch account and pays $2 each day to eat lunch.
How long till her account has no money left?

a)

y= 2x + 40, 20 days

b)

y = -2x + 40, 20 days

c)

y = 40x + 2, 10 days

d)

y = - 40x + 2, 15 days

30.

Describe the transformation from the parent absolute value function:

$y=\left|x\right|-5$

a)

Shift up 5 units

b)

Shift down 5 units

c)

Shift right 5 units

d)

Shift left 5 units

31.

Describe the transformation from the parent absolute value function:

$y=-\left|x+4\right|-3$

* Select THREE answers *

a)

Reflection over the x-axis

b)

Translation 4 units left

c)

Translation 4 units up

d)

Translation 3 units left

e)

Translation 3 units down

32.

a)

y = Ix + 2I - 1

b)

y = -Ix + 2I - 1

c)

y = -Ix - 2I - 1

d)

y = -Ix + 1I - 2

33.

Describe the transformation on the parent function: $f\left(x\right)\ =\ 2\left|x-3\right|-2$ (a) (b) (c)

Choose from the below words

Vertical Stretch

Horizontal Translation Right

Vertical Translation Down

Refection across the x-axis

Reflection across the y-axis

Vertical Translation Up

Horitzontontal Translation Left

Vertical Compression

Horizontal Stretch

34.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

35.

Consider the graph of the equation below. Where would the VERTEX be?

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

a)

(0, 0)

b)

( 3, 4)

c)

(-3, 4)

d)

(4, -3)

36.

Describe the transformation from the parent graph

a)

Reflect over x, right 3, down 4

b)

Reflect over y, right 3, down 4

c)

Reflect over x, right 3, up 4

d)

Reflect over y, left 3, down 4

37.

Match the equation with the graph:

a)

y = (x - 2)² + 4

b)

y = -(x - 4)² + 2

c)

y = -(x - 2)² + 4

d)

y = -(x + 2)² + 4

38.

Describe the transformation from the parent quadratic function:

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

a)

Shift up 2 units

b)

Shift down 2 units

c)

Shift right 2 units

d)

Shift left 2 units

39.

If $f\left(x\right)=a\left(x-h\right)^2+k$ has a horiz. shift of -2, a vert. shift of 3 and a vert. stretch of 4, what is the equation for $f\left(x\right)$ ?

a)

$f\left(x\right)=4\left(x+2\right)^2+3$

b)

$f\left(x\right)=4\left(x-2\right)^2+3$

c)

$f\left(x\right)=3\left(x+2\right)^2+4$

d)

$f\left(x\right)=2\left(x-4\right)^2+3$

40.

Which description best fits the transformation of f(x)=x² into f(x) =(x-5)²+3 ?

a)

Opens up, shifts to the right 5, and shifts up 3

b)

Is narrow, shifts left 5 and up 3

c)

Shifts right 5 and down 3

d)

Opens down and shifts up 3

41.

Which of the following equations best fits the graphs of the transformed function shown in red?

a)

$f\left(x\right)=\left(x-1\right)^2-3$

b)

$f\left(x\right)=\left(x+3\right)^2-1$

c)

$f\left(x\right)=-\left(x-3\right)^2+1$

d)

$f\left(x\right)=\left(x-3\right)^2-1$

42.

What is the equation of this parabola?

a)

x² + 2x + 3

b)

-x² - 2x + 3

c)

x² + 2x - 3

d)

-x² - 2x - 3

43.

If the red parabola is f(x) = x², what is the best equation for the blue parabola?

a)

f(x) = 0.25x²

b)

f(x) = x² - 3x + 4

c)

f(x) = 5x²

d)

f(x) = 0.5x²

44.

What is the axis of symmetry of the parabola?

a)

(2, -8)

b)

x = 2

c)

y = 2

d)

z = 2

45.

For the equation y = ax²+ bx + c, what is used to solve for the x-coordinate of the vertex?

a)

-a

b)

-b/a

c)

b/2a

d)

-b/2a

46.

What is the vertex of y = x²+ 4x + 3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

47.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

48.

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

49.

Find the vertex of

f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(-2, 22)

d)

(-2, 4)

50.

Does this graph show a maximum or a minimum?

a)

Maximum

b)

Minimum

51.

What is the range of the parabola?

a)

$\left[-4,\infty\right)$

b)

$\left(-\infty,\infty\right)$

c)

$\left(-4,\infty\right)$

d)

$\left[-1,3\right]$

52.

The graph of y = x² + 1 could be?

a)

b)

c)

d)

53.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

54.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

55.

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

56.

Given the diagram below find the value if x if the area is 21 square meters.

a)

7

b)

-3

c)

3

d)

-7

57.

The dimensions of a rectangle can be given by x +7 and x + 2. If the ares of the rectangle is 66 square inches, what are the dimensions of the rectangle.

a)

4 X 13

b)

-6 X -11

c)

11 X 6

d)

20 X 15

58.

The length of a rectangle is 6 meters more than its width. If the area of the rectangle is 135 square meters, find its dimensions.

a)

15 X 21

b)

9 X 15

c)

-9 X -15

d)

6 X 12

59.

If path of a projectile is modeled by:
h(t) = -16t² + 20t +6, what is the height after 1 second?

a)

6 feet

b)

20 feet

c)

10 feet

d)

4 feet

60.

When a cannonball is fired the equation of its pathway can be modeled by h = -16x² + 128t. Find the maximum height of the cannonball

a)

8 ft.

b)

0 ft.

c)

256 ft.

d)

4 ft.

61.

When a cannonball is fired the equation of its pathway can be modeled by h = -16x² + 128t. Find the time it will take for the cannonball to reach the ground.

a)

8 sec.

b)

0 sec.

c)

256 sec.

d)

4 sec.

62.

When Joey dives of a diving board, the equation of his pathway can be modeled by h = -16t²+ 15t + 12. Find Joey's maximum height.

a)

0.52 ft.

b)

1.45 ft.

c)

0.46 ft.

d)

15.52 ft.

63.

When Joey dives of a diving board, the equation of his pathway can be modeled by h = -16t²+ 15t + 12. Find the time it will take Joey to reach the water.

a)

0.52 sec.

b)

1.45 sec.

c)

0.47 sec.

d)

15.52 sec.

64.

At the end of the school year, Rachel and Amber go to the roof of a 12-story building and throw their Algebra book off the edge. The equation of the pathway that each girl's textbook takes is given below.

Rachel: h = -16t² + 36t + 160

Amber: h = -16t²+ 50t + 160

By how many seconds does Rachel's textbook beat Amber's to the ground?

a)

0.61 sec.

b)

4.48 sec.

c)

5.09 sec.

d)

0.27 sec.

65.

Find the zeros of the function. Choose all thaty apply.

y = 2x² - x - 15

a)

x = 3

b)

x = 5

c)

x = -5/2

d)

x = -3/2

e)

x = -3

66.

Find the zeros of the function. Choose all that apply.

f(x) = 4x² - 5x - 6

a)

x = -4/3

b)

x = -3

c)

x = 2

d)

x = 4/3

e)

x = -3/4

67.

How many solutions does this quadratic have?

a)

Two Real Solutions

b)

One Real Solution

c)

No Real Solutions

d)

I don't know

68.

The discriminant is

a)

ax² + bx + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

69.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

70.

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

a)

76

b)

-7

c)

9

d)

none of these

71.

A function has a discriminant of -3.
______________
How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

3

72.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

73.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

74.

Simplify
(-6 - 2i)²

a)

32

b)

36-4i

c)

36+24i

d)

32+24i

75.

(4-5i)(4+5i)

a)

41

b)

-9

c)

41+40i

d)

-9+40i

76.

$\sqrt{-48}$

a)

$4i\sqrt{3}$

b)

$3i\sqrt{12}$

c)

$-4\sqrt{3}$

d)

$-8\sqrt{6}$

77.

$3\sqrt{-90}$

a)

$3i\sqrt{10}$

b)

$9i\sqrt{10}$

c)

$27i\sqrt{10}$

78.

$\sqrt{-80}$

a)

$2i\sqrt{20}$

b)

$4i\sqrt{5}$

c)

$-8\sqrt{10}$

79.

Add:

\left(-6\ +\ 10i\right)\ +\ \left(8\ +\ 4i\right)

a)

$14+14i$

b)

$2+14i$

c)

$16i$

80.

Subtract:

\left(8+7i\right)-\left(6+3i\right)

a)

$2+4i$

b)

$2+10i$

c)

$14+10i$

d)

$14+2i$

81.

$\left(2i\right)\left(-9i\right)$

a)

$18$

b)

$-18$

c)

$-18i^2$

d)

$18i$

82.

$\left(2+3i\right)\left(3+7i\right)$

a)

$6+21i^2$

b)

$-15+23i$

83.

$-3+6i-\left(-5-3i\right)-8i$

(a)

84.

$\left(1-7i\right)^2$

(a)

85.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

86.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

87.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

88.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

89.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

90.

a)

A

b)

B

c)

C

d)

D

91.

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)

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

92.

Solve by completing the square.
$x^2-4x-21=0$

a)

$x=\left\{-7,\ 3\right\}$

b)

$x=\left\{3,\ 7\right\}$

c)

$x=\left\{-3,\ 7\right\}$

d)

$x=\left\{-7,\ -3\right\}$

93.

What are the solutions to the system of equations graphed below?

a)

(2, 0)

b)

(2, 0), (-2, 0)

c)

(-2,0)

d)

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

e)

No Solution

94.

y²- x = 4

x² + y²= 4

a)

(0, 2), (0, -2)

b)

(-1, √3), (-1, -√3)

c)

(0, 2), (0, -2), (-1, √3), (-1, -√3)

d)

(2, 0), (0, -2), (√3, ±1)

95.

Find the solution(s) to the system.

a)

(0,-3) and (1,-2)

b)

(0,-3)

c)

(-2,0) and (2,0)

d)

No solution

96.

What are the solutions to the system:

y = x² + 3x - 5

y = x + 3

a)

(-4, 2) and (-1, 5)

b)

(-4, -1) and (2, 5)

c)

(2, -1 and (-4, 5)

d)

(-4, 1) and (2, -1)

97.

$y=-\left(x-2\right)^2+4$
$y=-5$

Solve the system by graphing.

a)

(-1,-5)

b)

(5,-5)

c)

(-1,-5) and (5,-5)

d)

(-5,5)

98.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

99.

Find ALL solutions to the system of non-linear equations:

y=x^2+6x-9

y=6x

a)

$\left(3,18\right)\&\left(-3,-18\right)$

b)

$\left(3,18\right)$

c)

$\left(-3,-18\right)$

d)

No Solutions

100.

Factor and Solve

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

101.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

102.

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

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

103.

Solve the equation:
5x² - 35x + 60 = 0

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

104.

Use the square root property to solve the Quadratic Equation.
2(x - 4)² = 200

a)

±10

b)

-14, 6

c)

-6, 14

d)

100

105.

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

106.

What is this?

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.

107.

Solve
16a² - 9 = 0

a)

a = ^-3/₄, ³/₄

b)

a = ^-4/₃, ⁴/₃

c)

a = ^-9/₁₆, ⁹/₁₆

d)

a = ^-16/₉, ¹⁶/₉

108.

Solve for x:

(x + 6)²- 49 = 0

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

109.

Solve and find your x-intercepts:
0=x(x - 6)

a)

x=0 and x=-6

b)

x=1 and x=-6

c)

x=0 and x=6

d)

x=6

110.

Solve the following quadratic equation: $x^2-6x-7=0$

a)

$x=7\ \ \ \&\ \ \ x=-1$

b)

$x=1\ \ \ \&\ \ \ x=-7$

c)

$x=0$

d)

$x=\frac{-7}{5}$

111.

Solve the following quadratic equation by factoring. $2x^2-5x+2=0$

a)

$x=\frac{-1}{2}$ & $x=-2$

b)

$x=-1$ & $x=-4$

c)

$x=4$ & $x=1$

d)

$x=\frac{1}{2}\ \&\ x=2$

112.

Solve the following quadratic equation: $4x^2-9=0$

a)

$x=\frac{3}{2}$ & $x=-\frac{3}{2}$

b)

$x=\frac{2}{3}$ & $x=\frac{-2}{3}$

c)

$x=\frac{9}{4}$

d)

$x=\frac{4}{9}$

113.

$x^2-7x=0$

Solve by the method of your choice.

a)

x = 7 only

b)

x = 0 only

c)

x = 0 and 7

d)

There is no real answer for this equation.

114.

Fill in the formula

$x^2-6x-40=0$

BLUE= (a) RED= (b)

GREEN= (c)

Choose from the below words

-6

1

-40

-1

6

40

115.

$2x^2-36=x$

a)

$x=\frac{-9}{2}and\ 4$

b)

$x=\frac{9}{2}\ and\ -4$

c)

$x=4\ and\ -4$

d)

No real solution

Algebra 2 CP Midterm Review

Total questions: 115

Worksheet time: 10hrs 35mins

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