MATD 0390 – Intermediate Algebra – Review Sheet for Exam #2
Show your work on your own paper – you will not receive credit for answers only Do not write on this sheet Remember, each problem represents a concept to review. 1) Graph the linear function:
2) A satellite television company charges $33.99 per month for a 100-channel package, plus
$3.50 for each pay-per-view movie watched that month.
a) Find a linear function that expresses the total monthly bill B as a function of x, the
number of pay-per-view movies watched that month.
b) What is the monthly bill if 5 pay-per-view movies are watched that month?
c) How many pay-per-view movies were watched if the bill was $58.49?
3) Let
a)
b)
c)
d)
e)
What is the slope?
What is the y-intercept?
Find the zero of f.
Find the solution of
Solve f (x) > 8 .
4) Find a linear function f (x) such that f (1) = 5 and f (5) = 17 .
2x 2 − 5
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5) For the function h(x) =
, find h(−3)
x +1
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4€
x −8
6) Find the domain of the function: g(x) =
3x + 6
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7) Solve €
and graph the solution set: x < 4 and x + 3 > 2
8) Solve and graph the solution set: 7 < 5 − 2x < 15
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9) Solve and graph the solution
set:
or
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10) Solve and graph the solution set:
or
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11) Solve:
12) Solve:
13) Solve: 2x −1 + 7 = 10
For problems 13 – 17, solve the system of equations.
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14)
15)
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2x − y = 1
−4 x + 2y = 3
16)
17)
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3x = y + 4
−6x + 2y = −8
18) Jerome’s piggy bank contains a total of 40 nickels and quarters. The value of the coins in
the bank is $4.40. How many nickels and how many quarters are in the bank?
19) A boat traveled 30 miles upstream in 1.5 hours. The return trip downstream took only
1 hour. Find the speed of the boat and the speed of the current.
20) A coffee shop makes a blend of Arabica beans that sell for $9 a pound and Robusta beans
that sell for $11.50 a pound. How many pounds of Arabica and Robusta beans are
required to make 100 pounds of the blend that sells for $10.00 a pound?
21) Ms. Monroe wants to create 30 ounces of vitamin C solution of strength 9%. She has
vitamin C solutions of strengths 8% and 12%. How many ounces of each solution should
she use?
22) Graph the system of linear inequalities:
23) Graph the system of linear inequalities:
24) Simplify:
25) Simplify:
26) For
, find
27) Subtract:
28) Multiply:
29) Multiply:
30) Multiply:
For problems 31 – 36, let
and let
31)
32)
33)
34)
35)
36)
3
Find the following:
⎛ f ⎞
⎟(x) .
⎝ g ⎠
2
37) Let f (x) = 4 x − 8x +12x and let g(x) = 4 x . Find ⎜
38) Divide using long division: (3x 2 +19x − 40) ÷ (x + 8)
€ 39) Divide using long division:€
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40) Divide using long division: (2x −10x +17) ÷ (x − 2)
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3
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