College Algebra Review

College Algebra Supplementary Review for test 1

Some text here about the topic of discussion

Multiple Choice

Linear Equations:

solve for m:

$$\frac{2}{3}\left(9m-6\right)=20$$  

• $$m=4$$  

• $$m=3$$  

• $$m=2$$  

• $$m=8$$  

Solving rational equations

• 1. Factor the DENOMINATORS only

• 2. Multiply each side of the equation by the least common multiple (LCM) this should get rid of the fraction

• 3. Solve

• 4. Check to make sure your answers work (you don't divide by zero)

Multiple Select

Solve

$$\frac{x+1}{x-3}=-\frac{x^2-6x+1}{\left(x-3\right)\left(x-1\right)}$$  

• -5

• -2

• 0

• 1

• 4

check

Multiple Choice

Parker can ride his bike 4 mph faster than Libby. If Parker can travel 30 miles in the same time that Libby can go 15 miles, what speeds is Parker riding his bike at?

• 2 mph

• 4 mph

• 6 mph

• 8 mph

Solution

​ Rate times Time = Distance

​

Parker L + 4 30 miles

Lilly​ L 15 miles

Solution

​ Rate times Time = Distance

​

Solution

Multiple Choice

It takes Burt three times as long Carl to set up a new alarm system. Together they can set it up in 90 minutes. How long would it take Burt to set it up by himself?

• 180 minutes

• 120 minutes

• 45 minutes

• 360 minutes

Multiple Choice

How many liters of a 24% glucose solution must be added to two liters of a 9% glucose solution to obtain a 12% glucose solution?

• 0.5 liters

• 1 liter

• 1.5 liters

• 15 liters

Draw

Match an expression in column A with an equivalent expression in column B.

Multiple Choice

Evaluate $$i^{79}$$  

• $$i$$  

• $$1$$  

• $$-1$$  

• $$-i$$  

Multiple Choice

$$\left(-2+5i\right)\left(8-3i\right)$$  

Simplify

• $$21+35i$$  

• $$-1+46i$$  

• $$-9+46i$$  

• $$-16+13i$$  

Multiple Choice

$$\frac{-2-6i}{-3+5i}$$  : what do you do to divide?

• Multiply the top and bottom by

  -3-5i

• Multiply the top and bottom by

  -3 + 5i

• multiply the top by -2+6i

  and the bottom by -3-5i

Multiple Choice

What is $$\frac{-2-6i}{-3+5i}$$  ?

• 15i

• $$-\frac{12}{17}+\frac{14}{17}i$$  

• Unknown

• $$\frac{1}{8i}$$  

Multiple Choice

A ball is thrown into the air with an upward velocity of 56 ft/s. Its height, h, after t seconds is given by the function  h = -16t² + 56t + 6. When did the ball hit the ground?

• 3.6 seconds

• 2 seconds
• 5 seconds
• 7.6 seconds

Example 3.

​The area of a rectangle is 40 cm². If the length is 3 cm longer than the width, find the dimension of the rectangle.

Solution:

​

Let A = the area of the rectangle

w = width of the rectangle​​

l = w + 3 = length of the rectangle

​

​

The area of a rectangle is 40 cm². If the length is 3 cm longer than the width, find the dimension of the rectangle.

Solution:

​

A = lw

A = (w + 3)w

40 = w² + 3w

w² + 3w - 40 = 0

(w + 8)(w - 5) = 0​

​

w + 8 = 0​

w = -8​

​

w - 5 = 0​

w = 5​

​

w + 8 = 0​

w = -8​

​

Thus, the width is 5 cm and the length is w + 3 = 5 + 3 = 8 cm.

Multiple Choice

$$64>-2+2\left(4x-7\right)$$  

• $$x<0$$  

• $$x>0$$  

• $$x>10$$  

• $$x<10$$  

Match

Match the following

• |x| = 5

• |2x| = 4

• |x+2| = 6

• |x-3| = 2

• $$\left|\frac{x}{5}\right|=-6$$  

x = 5, -5

x = 2, -2

x = 4, -8

x = 1, 5

No Solution

• x = 5, -5

• x = 2, -2

• x = 4, -8

• x = 1, 5

• No Solution

Multiple Choice

Solve and graph:

• A

• B

• C

• D

Multiple Choice

Let's solve:      $$2\left|x-5\right|>10$$  First do Step 1:  Isolate the | |.

What will we have to do?

• Subtract 2

• Divide by 2

• Add 4

• Ready to make 2 cases!

Step2:  Write 2 inequalities.  

Multiple Choice

For this problem, $$\left|x-5\right|>5$$  , the sign is $$>$$  .  Which word should we use?

• AND

• OR

Here are the 2 cases we write out:

Multiple Choice

                      Step 3:   We'll solve each of them.                What is the solution to the first:      $$x-5>5$$  

• x > 25

• x > 0

• x > 10

Multiple Choice

                           Now solve the second one.                What is the solution to:   $$x-5<-5$$  

• x < 16

• x < 0

• x < -8

Let's try another!

Multiple Choice

First, isolate:      $$5\left|x+2\right|-1<14$$   The new inequality will be:                      (Hint:  'move' two things!) 

• $$\left|x+2\right|<10$$  

• $$\left|x+2\right|<\frac{13}{5}$$  

• $$\left|x+2\right|<9$$  

• $$\left|x+2\right|<3$$  

Multiple Choice

What is the inequality case for:         $$\left|x+2\right|<3$$  ?  

• $$x+2<3$$   OR   $$x+2>-3$$  

•     $$-3<x+2<3$$  

Multiple Choice

How do we write the final solution?  (everything between -5 and 1)? 

• $$-5<x<1$$  

• $$-5>x>1$$  

Multiple Choice

What is step one in using the quadratic formula to solve a problem?

• Find the discriminant ( $$b^2-4ac$$ )

• Identify A, B, and C

• Simplify the radical ( $$\sqrt{b^2-4ac}$$ )

• Plug A, B, and C into the formula

Multiple Choice

What number added would make a perfect square trinomial?

x² - 8x + ______

• -4

• -64

• 12

• 16

Multiple Choice

Solve by factoring: x² + 3x - 18 = 0

• x = -3 and x = 6
• x = 3 and x = -6
• x = -9 and x = 2
• x = 9 and x = -2

• set up equation in standard form

• substitute a, b and c values into the formula

• solve for x

Open Ended

Solve using the Quadratic Formula: $$2x^2-4x=-7$$  

Multiple Choice

Solve using the Quadratic Formula.

• A
• B
• C
• D

Multiple Choice

Solve for X

2|X+3|+3=1

• X= -4 and X= -2

• X=2 and X= -2

• X=0

• No Solution

Multiple Choice

Solve for x
l 4x−3 l = 17

• x = 5 and x =-3.5
• x = 0 and x = -5
• x = 10 and x = -10
• No Solution