Mr Ebert – 0304 – Fall 2016Test 1 Review

The answers to this review (and all other notes we’ve done in class) are available at Mr Ebert’s website: <ebertdavid.wordpress.com/math-0303>. Happy studying!

1) If a state’s income tax is 4.3% of taxable income, how much will you owe in tax if your taxable income is $51,000?

2) Evaluate the expression x2+4 x if x=3.

3) Solve the following equations:a. 5 x+7=52b. −7 x+3=11c. 2 ( x+1 )=8d. 2 x=7e. −16+5n=−7 (8n−6 )+3f. −11+10 ( p+10 )=4−5 (2 p+11)

g.x2+10=7

4) Evaluate the following, given f ( x )=2x−1, g ( x )= x3+1, and h ( x )=√ x.

a. f (10 )b. g (−21 )c. h( )d. a if f (a )=−11e. b if h (b )=7f. c if g (c )=12g. For what value of x does f ( x )=g (x)?h. True or False: f (1 )=h(1)?i. True or False: f (2 )=h(2)?

5) If f ( x )=3−7 x, find the solution to f ( x )=19.

6) Fill in the following table for f ( x )=x2+2 and g ( x )=x+4:x f ( x ) g ( x )

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a. For what x value(s) does f ( x )=g ( x )b. Are f (x) and g(x ) equivalent? How do you know?

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7) Fill in the following table for f ( x )= (x−2 )2 and g ( x )=x2−4 x+4:x f ( x ) g ( x )

a. For what x value(s) does f ( x )=g ( x )b. Are f (x) and g(x ) equivalent? How do you know?

8) Use the graph of y=f ( x ) to answer the following questions:

a. Find f (4 )

b. Find f (5)

c. Find f (0)

d. Find f (−3)

e. Find x if f ( x )=−2

f. Find x if f ( x )=2

g. Find x if f ( x )=−8

9) Use the table below to answer the following questions:

a. Find f (−1)

b. Find g(0)

c. Find x if f ( x )=−3

d. Find x if g ( x )=0

e. Find x if g ( x )=2

f. For what x does f ( x )=g (x)?

g. What is f (g (−2 ))?

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x f (x) g(x )−2 −2 2−1 0 10 2 01 0 02 −3 1

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10) Write an equation for the following straight lines. Use y=mx+b form:a. b.

c. The line with a y-intercept of 100 and a slope of −3.

d. Mario’s plumbing service charges $40 to make a house call, plus $25 per hour.

e. 3 x−12 y=24

f. The line passing through the points (0,7) and (2 ,−1).

g. The line passing through the points (4,9) and (11,12).

h. The table at right:

i. The graph below:

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x y−2 −10−1 −120 −141 −162 −18

11) A cell phone company offers a plan for $39.95 that charges $0.20 for each minute of use that exceeds the included 400 minutes. Write an expression for the total charge that uses m for the number of excess minutes.

12) Andrei has a glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. This is the formula for the volume of water Andrei should use W (measured in liters) as a function of the number of marbles used n:

W (n)=32−0.05n

a. What is the volume of the tank?b. What is the volume of each marble?

13) A big cruise ship drops anchor off the Caribbean island of Antigua. The heavy anchor drops into the water at a constant rate. This is the formula for the anchor's height above the water's surface E (measured in meters) as a function of time t (measured in seconds):

E (t )=−2.4 t+75

a. Evaluate E(10) and determine its meaningb. At t=0, how high is the anchor above the water?c. When does the anchor reach the surface of the water?

14) Jada has a stand in the marketplace where she sells ground paprika. The graph at right describes her weekly profit (in dollars) as a function of the amount of paprika she sold that week (in kilograms).

a. How many kilograms of paprika does Jada need to sell to cover her costs exactly?

b. Fill in the blank: Jada makes $ ________ for every 5 kilograms of paprika she sells.

c. Write an equation for the line.d. How much profit would Jada make if

she sold 150 kilograms of paprika?

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15) Solve the following systems of equations:

a. { 2x− y=04 x+3 y=−20

b. {2a−3b=223a+4 b=−1

c. { 9x−3 y=24−6 x+2 y=−16

d. { 2 x+8 y=6−5 x−20 y=−15

e. {2x+5 y=31y=3 x+13

f. {−3 x+3 y=4−x+ y=3

16) An amusement park collected $15522.30 in revenue from ticket sales one day. They charge $27.99 for adults and $8.99 for children. If there were 970 people in attendance that day, then how many were adults and how many were children?

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