Algebra II

Multiple Choice

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15 4x + 2y = 44

• 4x + 2y = 15 x + y = 44

• x = 2y + 44 4x = y + 15

• 2x - 4y = 44 x - y = 15

Multiple Choice

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3 13.5x - 13y = 6

• x + y = 4 x - y = 6

• 4x + 6y = 13 3x + 7y = 13.5

• 4x - 6y = 13 3x - 7y = 13.5

Multiple Choice

A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes. 

 

Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, for a total distance traveled of 141 miles.

This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles.

Which systems of equations can be used to find $$x$$ , the number of miles in the morning and $$y$$ , the number of miles in the afternoon?

• $$12x+16y=141$$

  $$10x+15y=123.75$$

• $$16x+12y=141$$

  $$10x+15y=123.75$$

• $$16x+12y=123.75$$

  $$10x+15y=141$$

• $$16x+12y=141$$

  $$15x+10y=123.75$$

Multiple Choice

How many solutions will this system have?

• No Solution

• Infinitely Many Solutions

• No Clue

• One solution

Multiple Choice

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)

Multiple Choice

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

Multiple Choice

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Multiple Choice

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Multiple Choice

Solve:
y = -1x - 5
4x - 8y = 4

• (-3, -2)

• (5, -7)

• (3, 9)

• (-5, 4)

Multiple Choice

What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 

• 1

• -1

• 3

• 4

Multiple Choice

What is the solution to the following system of equations?

• ( 3 , -1 )

• ( 7 , 7 )

• ( -1 , 3 )

• ( 1 , 1 )

Multiple Choice

Solve  the system of equations.  
   x + 5y = -27
-2x - 5y = 24

• (3, 6)

• (-3, -6)

• (-3, -4)

• (3, -6)

Multiple Choice

What is the solution to this system? Solve by substitution.
y= 4x + 3
2x - 3y = 21

• (3,-9)

• (-3,-9)

• (-3,9)

• (0,1)

Multiple Choice

-4x-2y=-12
4x+8y=-24

• (5,6)

• (6,-6)

• (6,-2)

• (4,-3)

Multiple Choice

Solve the system by elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

Multiple Choice

Solve by elimination
-12x-4y= -8 
  -6x-2y= -4

• no solution 

• (0,0)

• infinite solutions 

• (4,0)

Multiple Choice

Write the matrix that corresponds to the system

• A

• B

• C

• D

Multiple Choice

• a

• b

• c

• d

Multiple Choice

(2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

• None of these

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Multiple Choice

(2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

• None of these

Multiple Choice

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2 

• x + 2

• 2x² + x - 10 

• x - 10 

Multiple Choice

*Remember

1-Match

2-Flip

3-Combine

( 8x³ + 3x² + 4x + 10 ) - ( 3x³ - 4x² + 2x + 1 )

• 11x³ + 7x² + 6x + 12

• 5x³ + 7x² + 2x + 9

• 5x³ - x² - 2x + 11

Multiple Choice

-5x⁶(3x² - 12x + 30)

• -15x⁸ + 60x⁷ - 150x⁶

• 15x⁸ - 60x⁷ - 150x⁶

• 8x⁶ - 17x + 35

• -8x⁶ + 17x - 35x²

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12

• 5x³ + 17x² - 24x +12

• 5x³ - 13x² + 24x +12

• 5x³ +13x² - 24x - 12

Multiple Choice

(x-3)(x²+2x+7)

• x³-x²+x-21

• x³+5x+13x-21

• x³-3x²+7x-21

• x²+2x-3

Multiple Choice

Factor
x² + 9x - 36

• (x + 12)(x - 3)

• (x + 9)(x - 4)

• (x - 12)(x + 3)

• (x - 9)(x - 4)

Multiple Choice

Factor
n² + 16n + 63

• (n-7)(n+4)

• (n+7)(n-9)

• (n-3)(n-10)

• (n+7)(n+9)

Multiple Choice

Factor
x² - 5x - 36

• (x - 4)(x + 9)

• (x - 6)(x + 6)

• (x + 4)(x - 9)

• (x -12)(x + 3)

Multiple Choice

Factor completely: 
3x² + 18x +15
Hint: Factor GCF first.

• 3(x² + 6x + 5)
• (x + 5)(x + 1)
• 3(x + 5)(x + 1)
• Prime

Multiple Choice

Factor: $$3t^2+16t\ -12$$

• (t+18)(t-2)

• (3t-2)(t+6)

• (3t+2)(t-6)

• (3t-4)(t+3)

Multiple Choice

7r³-8r²+42r-48

• (r²+6)(7r+8)

• (r²+6)(7r-8)

• (r²+6)(r²+8)

• (r²+6)(7r+6)

Multiple Choice

20x³-25x²+4x-5

• (5x²-5)(4x+1)

• 5(x²-1)(4x+5)

• (5x²+1)(4x-5)

• (5x²+1)(4x-1)

Multiple Choice

Solve: $$16m^{2\ }-\ 36=0$$

• m=-2/3 & m = 2/3

• m= 6 & m= -6

• m=-3/2 & m = 3/2

• m=0 & m=4

Multiple Choice

Factor completely: $$4a^{4\ }b^6-64a^6b^4$$

• $$4a^4b^4\left(b^2-4a^2\right)$$

• $$4a^4b^4\left(b+4a\right)\left(b-4a\right)$$

• $$\left(2a^2-b^2\right)\left(2b^2+16a^2\right)$$

Multiple Choice

Factor the expression completely:

$$x^2-121$$  

• Not Factorable

• $$\left(x-11\right)^2$$  

• $$\left(x+11\right)^2$$  

• $$\left(x+11\right)\left(x-11\right)$$  

Multiple Choice

Factor the expression completely:

$$25x^2+4$$  

• Not Factorable

• $$\left(5x-2\right)\left(5x+2\right)$$  

• $$\left(5x-4\right)\left(5x-1\right)$$  

• $$\left(5x+4\right)\left(5x+1\right)$$  

Multiple Choice

x³ - 27

• (x - 4)(x² + 4x + 16)

• (x + 3)(x² - 4x + 16)

• (x - 1)(x² + 1x + 1)

• (x - 3)(x² + 3x + 9)

Multiple Choice

x³ + 64

• (x + 3)(x² - 3x + 9)

• (x + 5)(x² - 5x + 25)

• (x + 4)(x² - 4x + 16)

• (x - 4)(x² + 4x + 16)

Multiple Choice

8x³ + 27

• (3x - 2)(9x² + 6x + 4)

• (3x - 1)(9x² + 3x + 1)

• (2x + 3)(4x² - 6x + 9)

• (2x - 1)(4x² + 2x + 1)

Multiple Choice

125x³ - 64

• (5x - 4)(25x² + 20x + 16)

• (5x + 2)(25x² - 10x + 4)

• (3x - 1)(9x² + 3x + 1)

• (4x - 3)(16x² + 12x + 9)