MIDTERM REVIEW

MIDTERM REVIEW

by Kimberlee Joy

​Solving by Opposite Operations

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• ​Equations

Multiple Choice

Solve for x:
5x - 14 = 8x + 4

• x = 6
• x = -6
• x = -18/13
• x = 10/3

Multiple Choice

3y - 8 = 7y

• y = 2

• y = -2

• No Solution

• Infinite Solutions

Multiple Choice

5.3a – 7.9 = 2.6a + 2.9

• 4

• -4

• 1

• 2

​Solving by Opposite Operations

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• ​Literal Equations

Multiple Choice

$$V=\frac{1}{3}Bh$$   Solve for h

• $$h=\frac{1}{3}V-B$$  

• $$h=\frac{\frac{1}{3}V}{B}$$  

• $$h=3V-B$$  

• $$h=\frac{3V}{B}$$  

Multiple Choice

$$S=\frac{1}{2}at^2$$   Solve for  $$t^2$$  

• $$t^2=\frac{2S}{a}$$  

• $$t^2=S-\frac{a}{2}$$  

• $$t^2=2S-a$$  

• $$t^2=\frac{Sa}{2}$$  

Multiple Choice

Solve for y:
5x - y = 16

• y = 5x + 16

• y = -5x - 16

• y = -5x + 16

• y = 5x - 16 

​Solving by Opposite Operations

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• ​Single Inequalities

Multiple Choice

Solve the following Inequality 

$$-3\left(b+5\right)<45$$  

• $$b>-20$$  

• $$b<-20$$  

• $$b<-10$$  

• $$b>-10$$  

Multiple Choice

$$2\left(x-3\right)+9\ge x$$  

• $$x\ge-6$$  

• $$x\ge15$$  

• $$x\le-3$$  

• $$x\ge-3$$  

• $$x\le-6$$  

​Solving by Opposite Operations

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• ​Compound Inequalities

Multiple Choice

$$10\le\frac{x+38}{4}\le20$$   Solve for  $$x$$  

• $$2\le x\le42$$  

• $$.5\le x\le10.5$$  

Multiple Choice

Write the compound inequality to match the graph.

• $$-1\le x\le2$$  

• $$-1<x<2$$  

• $$x<-1\ or\ x>2$$  

• $$x\le-1\ or\ x\ge2$$  

​Solving by Opposite Operations

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• ​Absolute Value Equations HAVE 2 ANSWERS

• ​Absolute Value Inequalities

​ GREATOR

​ LESS THAND

​x > 6 or x < 2

Multiple Choice

|2a - 10| = 6

• a = 8, a = 5
• a = 2
• a = 8
• a = 8, a = 2

Multiple Choice

|v + 8| − 5 = 2 

• {-1,-15}
• {-1,-5}
• {-15,15}
• No Solution

Multiple Choice

Solve -4|x + 1| < -20

• x < -6 or x > 4

• -6 < x < 4

• -4 < x < 4

• x < -4 or x > 4

Multiple Choice

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• no solution

Multiple Choice

Solve for v.

• -6 < v < -4

• -6 < v < -4

• v ≥ -6 or v ≤ -4
• v > -6 or v < -4

Multiple Choice

Solve the following inequality:

−5|x − 4| > −20

• 0 < x < 8

• x > 8 or x < 0

• all real numbers

• no solution

​Writing Equations/Rules

• ​Slope Intercept Form

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​ y = mx + b

​y-intercept is 3

​slope is down 4 right 5

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​y = -4/5x +2

Multiple Choice

Write the equation of the graph.

• $$y=2x+3$$

• $$y=-2x-3$$

• $$y=\frac{1}{2}x+3$$

• $$y=-\frac{1}{2}x-3$$

Multiple Choice

Write the equation of the graph.

• $$y=\frac{6}{5}x+2$$

• $$y=-\frac{6}{5}x+2$$

• $$y=\frac{5}{6}x+2$$

• $$y=-\frac{5}{6}x+2$$

​Writing Equations/Rules

• ​Slope Intercept Form

Multiple Choice

Write equation of the line containing (0,-3) and (4,1)

• y = 1x + 1
• y = 1x - 3
• y = -1x + 1
• y = -1x - 3

Multiple Choice

Write equation of the line containing (0,5) and (2,-1)

• y = -2x + 5
• y = -3x +5
• y = 2x + 5
• y = 3x + 5

​Writing Equations/Rules

• ​Arithmetic Sequence Rule

Multiple Choice

If the first term of an arithmetic sequence is 5 and the common difference is 6, what are the first five terms?

• 5, 11, 17, 23, 29

• 6, 11, 16, 21, 26

• 5, 10, 15, 20, 25

• 5, 11, 15, 20, 26

Multiple Choice

Identify the common difference. 
10, 20, 30, 40, ...

• 5
• 10
• 15
• 20

Multiple Choice

What is the 67^th term of the following arithmetic sequence.

13, 22, 31, 40, ...

• -445

• 67

• 625

• 607

​Writing Equations/Rules

• ​Arithmetic Sequence Word Problems

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​         Write out a sequence of #s

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​          0.15, 0.30, 0.45, 0.6.....

 $9.75

Multiple Choice

There are 125 passengers in the first carriage, 150 passengers in the second carriage and 175 passengers in the third carriage, and so on in an arithmetic sequence. What is the total number of passengers in the 7th carriage?

• 225

• 250

• 275

• 300

Solving Systems

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• ​Creating Opposites

Multiple Choice

What is the solution to this system of equations?

4x + y = 6

x - 2y = 6

• (2,-2)

• (1,2)

• ( 1/2 , 4 )

• (-2,2)

• (2, 4)

Multiple Choice

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 

• y = 9.65 + x
  y = 8.40 + x
• y = 9.65x + 43
  y = 8.40x + 58
• y =9.65x
  y = 8.40x
• y = 9.65x - 43
  y = 8.40x - 58

​Proportions and Conversions

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• ​Set up and Solve a Proportion

Multiple Choice

Solve for k

• 165
• 17
• 1/17
• 1/165

Multiple Choice

A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him?

• 24 Weeks
• 24-ounce bottle
• 10.6 Weeks
• 10.6-ounce bottle

​Proportions and Conversions

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• Converting Units

Multiple Choice

Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)

5,280 feet = 1 mile

• 95 feet per second

• 59 feet per second

• .45 feet per second

• 40 feet per second

​Functions

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• Is it a Function??

​No Yes

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

• Function
• Not a Function

​Functions

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• Function Notation

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​       Remember if you get stuck:

​       type the equation into the y = 

​       of your calculator and use your

​       table!!

Multiple Choice

If h(x) = -5x + 7,

Evaluate h(2).

• -2

• 3

• -18

• -3

Multiple Choice

The function h(t) represents the height in inches of a plant after t weeks. What does the notation h(4) = 5 mean?

• After 5 week the plant is 4 inches tall
• The plant grows at a rate of 5/4 inch per week
• After 4 weeks the plant is 5 inches tall
• The plant grows at a rate of 1 inch per week

Multiple Choice

Given the function f(x) = -2x + 7, find the value of x that makes f(x) = 23.

• x = -39

• x = -15

• x = -8

• x = 8

​Functions

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• Reasonable Domain and Range

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​       Remember:

​       type the equation into the y = 

​       of your calculator and use your

​       table!!

Multiple Choice

P(c) = 8c represents profit based on the number of cars washed (soap donated).  If you have enough soap to wash 50 cars, write the reasonable domain and range.

• 0 < c < 50

  0 < P(c) < 400

• 0 < c < 8

  0 < P(c) < 400

• 0 < c < 8

  0 < P(c) < 64

• 8 < c < 50

  64 < P(c) < 400