Math for College Algebra

​Math 1111 - College Algebra

Test 1 Review​

by Teresa Fuston

Multiple Choice

Solve for y:

$$4\left(y+9\right)=-5\left(y-9\right)-y$$  

• $$\frac{1}{2}$$  

• $$-\frac{1}{2}$$  

• $$-\frac{9}{10}$$  

• $$\frac{9}{10}$$  

​Solution:

Multiple Choice

Solve:

$$4\left(3+y\right)-y=6+3\left(y+2\right)$$  

• $$y=0$$  

• $$y=-6$$  

• no solution

• all real numbers are solutions

​Solution:

Multiple Choice

A local hamburger shop sold a combined total of 771 hamburgers and cheeseburgers on Monday. There were 71 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Monday?

• 350

• 421

• 700

• 71

​Solution:

Multiple Choice

The length of a rectangle is 6 feet longer than its width.

If the perimeter of the rectangle is 48 feet, find its area.

• $$15\ ft$$  

• $$9\ ft$$  

• $$135\ ft^2$$  

• $$9\ ft\ x\ 15\ ft$$  

​Solution:

Multiple Choice

Write an inequality for the graph shown below.

• $$x<3$$  

• $$x>3$$  

• $$x\le3$$  

• $$x\ge3$$  

​Solution:

Multiple Choice

Write the interval notation for the given graph.

• $$\left[-6,\ -1\right]$$  

• $$\left(-6,\ -1\right]$$  

• $$\left[-6,\ -1\right)$$  

• $$\left(-6,\ -1\right)$$  

​Solution:

Multiple Choice

Solve the inequality.

$$3−5y>−17$$  

• $$y<4$$  

• $$y>4$$  

• $$y<-4$$  

• $$y>-4$$  

​Solution:

Multiple Choice

Solve the inequality:

$$5w−39\le−2\left(6−7w\right)$$  

• $$w\ge3$$  

• $$w\ge-3$$  

• $$w\le3$$  

• $$w\le-3$$  

​Solution:

Multiple Choice

Graph the line:

$$2x+y=3$$  

​Solution:

Multiple Choice

Graph the line:

$$x=3$$  

​Solution:

Multiple Choice

Find the slope of the line graphed.

• $$m=\frac{6}{5}$$  

• $$m=\frac{5}{6}$$  

• $$m=-\frac{5}{6}$$  

• $$m=-\frac{6}{5}$$  

​Solution:

Multiple Choice

Find the slope and the y-intercept of the line:

$$−6x+3y=−9$$  

• $$m=2$$   $$y-int:\ \left(0,\ 3\right)$$  

• $$m=-2$$  

  $$y-int:\ \left(0,\ -3\right)$$

• $$m=2$$  

  $$y-int:\ \left(0,\ -3\right)$$  

• $$m=-2$$  

  $$y-int:\ \left(0,\ 3\right)$$  

​Solution:

Multiple Choice

Find an equation for the line passing

through the points (-1, 3) and (1, -1).

• $$y=-2x+1$$  

• $$y=2x-1$$  

• $$y=-2x-1$$  

• $$y=2x+1$$  

​Solution:

Multiple Choice

What is the slope of a line perpendicular to this line?

$$-2x-5y=10$$  

• $$-\frac{2}{5}$$  

• $$\frac{2}{5}$$  

• $$\frac{5}{2}$$  

• $$-\frac{5}{2}$$  

​Solution:

Multiple Choice

Use substitution to solve the system.

$$x=3y−4$$  

$$5x+4y=37$$  

• $$\left(3,\ 5\right)$$  

• infinitely mant solutions

• no solution

• $$\left(5,\ 3\right)$$  

​Solution:

Multiple Choice

Solve the following system of equations using elimination.

$$4x+5y=10$$  

$$8x+5y=30$$  

• $$\left(5,\ -2\right)$$  

• infinitely many solutions

• no solution

• $$\left(-2,\ 5\right)$$  

​Solution:

Multiple Choice

Factor completely:

$$16w^2-12w^3$$  

• $$w^2\left(16-12w\right)$$  

• $$4w\left(4w-3w^2\right)$$  

• $$2w^2\left(8-6w\right)$$  

• $$4w^2\left(4-3w\right)$$  

​Solution:

Multiple Choice

Factor:

$$4x^2-49$$  

• $$(2x−3)(2x+3)$$  

• $$(2x−7)(2x+7)$$  

• $$\pm\frac{7}{2}$$  

• $$\pm\frac{3}{2}$$  

Multiple Choice

Factor:

$$12v^3+8v^2-21v-14$$  

• $$(3v+2)(4v−7)$$  

• $$(3v+2)(4v^2−7)$$  

• $$\left(3v+2\right)^2\left(4v-7\right)$$  

• $$(3v+2)^2(4v^2−7)$$  

​Solution:

Multiple Select

Factor:

$$2x^2+17x+15$$  

Select the two correct factors:

• $$\left(x+1\right)$$  

• $$\left(2x+3\right)$$  

• $$\left(x+5\right)$$  

• $$\left(2x+15\right)$$  

​Solution:

Multiple Choice

Solve:

$$\left(3y+5\right)\left(8-y\right)=0$$  

• $$-8,\frac{5}{3}$$  

• $$-\frac{5}{3},8$$  

• $$-8,-\frac{5}{3}$$  

• $$-\frac{3}{5},8$$  

​Solution:

Multiple Choice

Solve:

$$y^2=-13y$$  

• $$-13$$  

• $$0,\ 13$$  

• $$-13,\ 0$$  

• no real solution

​Solution:

Multiple Choice

Solve:

$$a^2+3a=28$$  

• $$-4,7$$  

• $$-7,4$$  

• $$-7,-4$$  

• $$4,7$$  

​Solution:

Multiple Choice

Solve:

$$\left(v-4\right)^2-72=0$$  

• $$-4+6\sqrt[]{2}$$  

• $$-4\pm6\sqrt[]{2}$$  

• $$4+6\sqrt[]{2}$$  

• $$4\pm6\sqrt[]{2}$$  

​Solution:

Multiple Choice

Fill in the blank with a number to make the expression a perfect square trinomial.

$$x^2-16x+$$  ____.

• 64

• -64

• 256

• -8

​Solution:

Multiple Choice

Solve the quadratic equation by completing the square.

$$x^2+12x+33=0$$  

• $$6\pm\sqrt[]{69}$$  

• $$6\pm\sqrt[]{3}$$  

• $$-6\pm\sqrt[]{3}$$  

• $$-6\pm\sqrt[]{69}$$  

​Solution:

Multiple Choice

Use the quadratic formula to solve for x. Simplify!

$$3x^2-8x+1=0$$  

• $$\frac{4\pm\sqrt[]{13}}{3}$$  

• $$\frac{4\pm\sqrt[]{52}}{3}$$  

• $$\frac{-4\pm\sqrt[]{13}}{3}$$  

• $$\frac{-4\pm\sqrt[]{52}}{3}$$  

​Solution:

Multiple Choice

Is the relation shown in the graph a function?

• yes

• no

• not enough information

​Solution:

Multiple Choice

Is the relation shown in the graph a function?

• yes

• no

• not enough information

​Solution:

Multiple Choice

The function  $$g$$   is defined as follows.

$$g\left(x\right)=−2x^3−5$$  

Find  $$g\left(-3\right)$$  .

• -59

• -59

• 211

• 49

​Solution:

Multiple Choice

The function  $$h$$   is defined as follows.

$$h\left(x\right)=\left|\frac{1}{3}x-11\right|$$  

Find  $$h\left(9\right)$$  .

• -2

• 2

• 8

• -8

​Solution:

Multiple Choice

A construction crew needs to pave a road that is 207 miles long. The crew paves 7 miles of the road each day. The length, L (in miles), that is left to be paved after d days is given by following function L(d) = 207 - 7d

How many miles of the road does the crew have left to pave after 12 days?

• 123 miles

• 207 miles

• 195 days

• 27.9 days

​Solution:

Multiple Choice

The function  $$g$$   is defined as follows.

$$g\left(x\right)=\frac{x-2}{x-5}$$  

Find the domain.

Write your answer as an interval or union of intervals.

• $$\left(-\infty,\ -5\right)\cup\left(-5,\ \infty\right)$$  

• $$\left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$$  

• $$\left(-\infty,\ 5\right)\cup\left(5,\ \infty\right)$$  

• $$\left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$$  

​Solution

Multiple Choice

Find the domain of the function.

$$h\left(x\right)=\sqrt[]{−8x+40}$$  

Write your answer using interval notation.

• $$\left(-\infty,\ 5\right)$$  

• $$\left(5,\ \infty\right)$$  

• $$\left(-\infty,\ 5\right]$$  

• $$\left[5,\ \infty\right)$$  

​Solution:

Multiple Choice

The graph of function  $$f$$   is shown.

Find two values of $$x$$  for which  $$f\left(x\right)=3.$$  

• -1

• 2

• -1 and 2

• 0 and -3

​Solution:

Multiple Choice

The graph of function  $$f$$   is shown.

Find   $$f\left(1\right).$$  

• -1

• 0

• 1

• 2.5

​Solution:

Multiple Choice

Write the domain and range of using interval notation.

• domain: (-3, 5]

  range: (-5, 3]

• domain: (-3, 5)

  range: (-5, 3)

• domain: (-5, 3)

  range: (-3, 5)

• domain: (-5, 3]

  range: (-3, 5]

​Solution:

Multiple Choice

Use the graph to determine which statement is true about f(-3).

• f(-3)>0

• f(-3)=0

• f(-3)<0

• none of these

​Solution:

Multiple Choice

The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that W = 25T + 500 gives W as a function of T during the next 80 minutes.

Identify the correct description of the values in the domain.

• amount of water in the pond (in liters)

• number of minutes water has been added

​Solution:

Multiple Choice

The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that W = 25T + 500 gives W as a function of T during the next 80 minutes.

Coose the most appropriate set of values for the domain.

• the set of real numbers from 0 to 80

• the set of all real numbers from 500 to 2500

• the set of all real numbers from 25 to 500

• {80, 81, 82, 83, ...}

• {0, 1, 2, 3, ..., 500}

​Solution: