MA112 Chapter 1 Review

Application Problems

100

The UAH bookstore is selling used textbooks at a discounted price. You decide to buy a used math textbook, and you pay a discounted price of $29.75. If the discount was 15% off, what was the original price?

x-x(.15)=29.75

200

You are building a fence and trying to determine what dimensions to make your fence. Your backyard has a length that is 5ft more than twice its width. What are the dimensions of your fence if the perimeter of your backyard is 255 ft.

P= 2W + 2L

P=255

L=5+2W

255=2W+2(5+2W)

300

Ashley invests $20,000, some in stocks and the rest in bonds. If she invests 3 times as much in stocks as she does bonds, how much does she invest in each?

3b + b = 20,000

400

Two twin sisters took turns washing their car on the weekends. Grace can wash their car in 45 minutes and Joann can wash their car in 30 minutes. One weekend, they decide to wash the car together. How long will it take them to wash their car?

x/45 + x/30 = 1

500

How many gallons of 40% sulfuric acid solution should be mixed with 20% sulfuric acid solution to obtain 50 gallons of 25% sulfuric acid solution?

(.40)(x) + (.20)(50-x) = (.25)(50)

Inequalities & Absolute Value

100

How would you write this in interval notation:

-3<x<=0

(-3,0]

200

Answer in interval notation:

-2 < 2x-1 < 5

(-1/2,3)

300

Answer in interval in notation:

7 <= -4x + 3 < 3

(0,-1]

400

Answer in interval notation:

4 | (x/9) | + 7 >= 11

(-infinity, -9]U[9, infinity)

500

Answer in interval notation:

6 | x - 5 | + 6 >= -84

(- infinity, infinity)

Solving Equations

100

Factor:

x²+6x-27

x= -9, 3

200

Solve using Square Root Method:

(x+1)²=4

x = 3, -1

300

Factor:

x⁴+20x²+64

x= 2i, -2i, 4i, -4i

400

Solve using Square Root Method:

(x²+2)²=9

x= -1, 1, root(-5), -root(-5)

500

Solve the rational expression:

(1/x) + (x/x+3) = (2x/x)

x = -5/2 + root (37)/2

x = -5/2 - root(37)/2

Solving Equations Pt.2

100

Solve using Quadratic Formula:

x²+6x+12

x = -3 + i root(3)

x = -3 - i root(3)

200

Solve using Complete the Square:

x²+10x-2

x = -5 + 3i root(3)

x = -5 - 3i root(3)

300

Solve using Quadratic Formula:

2x²-7x+13

x = (7/4) + i root(3)

x = (7/4) - i root(3)

400

Solve using complete the square:

x²-6x-9=0

x = 3 + 3 root2

x = 3 - 3 root2

500

Solve the rational expression:

(1/x-4) + (x/x+1) = (-1/x²-3x-4)

x= 1,2

Complex Numbers

100

Solve:

(3 + 2i)+(-4i + 1)

4 - 2i

200

Solve:

(5+7i)-(-3-i)

8+8i

300

Solve:

(1+3i)(-2-i)

-7i + 1

400

Solve (-2i+5)(4i+1)

18i + 13

500

Solve:

(1+2i) / (4-2i)

i/2