Unit 1 Study Guide

Unit 1 Study Guide

for Integrated Math 1 Students

Literal Equations​

Here is an example of using opposite operations to solve for a​

Multiple Choice

IR = V
(solve for R) 

• R = IV
• R = I/V
• R = V/I
• R = V - I

Multiple Choice

ax + c = R
(solve for x) 

• ax = R + c
• ax = R - c
• x = a(R-c)
• x = (R-c) / a 

Multiple Choice

$$\ u\ =\ bak\$$    Solve for  a

• $$a=\frac{u}{bk}$$  

• $$a\ =\ \frac{bk}{u}$$  

• $$a\ =\ -\frac{bk}{u}$$  

• $$a=-\frac{u}{bk}$$  

Multiple Choice

$$P=2l+2w\$$                Solve for  $$l$$  

• $$l=2P-4w$$  

• $$l=\frac{P-2w}{2}$$  

• $$l=P-2w$$  

• $$a=-\frac{u}{bk}$$  

Proportions​

Multiple Choice

Solve the proportion

• x = -1/4

• x = 1/3

• x = -3/4

• x = 3/4

Multiple Choice

Solve the proportion

• x = 3
• x = -3
• x = 1
• x = -1

Multiple Choice

Emily's original painting has a width of 3 inches and a height of 4 inches. She enlarged the size of the painting so that it has a width of 15 inches. What is the new height?

Which of these proportions correctly represents the situation?

• $$\frac{3\ in\ width}{4\ in\ height}=\frac{15\ in\ width}{x\ in\ height}$$

• $$\frac{3\ in\ width}{15\ in\ height}=\frac{4\ in\ width}{x\ in\ height}$$

• $$\frac{3\ in\ width}{5\ in\ height}=\frac{4\ in\ width}{15\ in\ height}$$

• $$\frac{3\ in\ width}{4\ in\ height}=\frac{x\ in\ height}{15\ in\ width}$$

Multiple Choice

20 Fuji apples cost $12. How many Fuji apples can you buy for $3?

Select the proportion that represents the situation correctly.

• $$\frac{20\ apples}{12\ dollars}=\frac{x\ apples}{3\ dollars}$$

• $$\frac{20\ apples}{3\ dollars}=\frac{x\ apples}{12\ dollars}$$

• $$\frac{12\ dollars}{20\ apples}=\frac{x\ apples}{3\ dollars}$$

• $$\frac{3\ dollars}{12\ dollars}=\frac{20\ apples}{x\ apples}$$

Conversions​

Multiple Choice

A football field is 120 yards long, including its end zones. How many feet long is that?

• 40 feet

• 300 feet

• 360 feet

• 3,600 feet

Multiple Choice

#15) Convert 45 miles per hour to feet per second.

• 66 ft/s

• 45 ft/s

• 30.6 ft/s

• 56.7 ft/s

Multiple Choice

#16) If an object can travel 26 centimeters per second, what is its speed in meters per minute?

• 18.7 m/min

• 43.3 m/min

• 15.6 m/min

• 21 m/min

Solving Single Inequalities​

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10
• x ≤ -10
• x ≥ 10
• x ≤ 10

Multiple Choice

Solve:
6x+10>5x-12

• x>2
• x<2
• x<-22
• x>-22

Multiple Choice

Solve:
3(x - 2) < 2(x + 9)

• x<24
• x>12
• x<12
• x>24

Multiple Choice

Which graph matches the inequality
-2 ≥ n?

• A
• B
• C
• D

Multiple Choice

$$5\left(x+2\right)\le5x+30$$  

• all real numbers

• no solution 

Multiple Choice

$$2x-3>2x+9$$  

• all real numbers

• no solution

Multiple Choice

A wager was placed on the DANCE COUPLE that they could not get an average score of at least a 7 out of 10 at the contest. 

The first 3 judges scored:  6.7, 6.8 and 6.8. 

What are the possible scores that the LAST JUDGE could give that would allow the couple to win the bet?

• x > 7.3

• x > 7.5

• x > 7.7

• x > 7.9

Solving Compound Inequalities​

​

Multiple Choice

x + 8 < 3 or - 8x < -40 

• x > -5 or x < 5
• x < -5 and x > 5
• x < -5 or x > 5 
• x > -5 and x < 5 

Multiple Choice

−6 < 2t − 5 < 3

• −0.5 < t < 4

• 0.5 < t < 4

• −11/2 < t < 2

• 11/2 < t < −2

Multiple Choice

Which graph represents the inequality -5 ≤ x < 0 ?

Absolute Value Inequalities​

​

Multiple Choice

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and
• or

Multiple Choice

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x ≤ -1

• 1 ≤ x ≤ 5

Multiple Choice

| x + 3 | > 8

• No Solution
• All Real Numbers
• x < -11  or  x > 5
• -5 < x < 11

Multiple Choice

What is the correct first step?

• divide by 10
• multiply by 10
• make it two inequalities with an "or"
• make it two inequalities with and "and

Multiple Choice

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

Multiple Choice

| 2w - 1 | < 11

• No Solution
• All Real Numbers
• -5 < w < 6
• -6 < w < 5

Multiple Choice

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

Multiple Choice

Solve for n.

• n ≥ 10 and n ≤ -6
• n > 10 and n < -6
• n ≥ 10 or n ≤ -6
• n > 10 or n < -6

Multiple Choice

Solve for v.

•  -6 < v ≤ -4

• -6 < v < -4

• v ≥ -6 or v ≤ -4
• v > -6 or v < -4