Algebra 2 – 300
Midterm Review
NAME: ______________________________________ DATE: _____________
1) Which of the following is a quartic monomial?
A. 43x2y + 2
B. 56x4y – 3
C. 23x2y – x2
D. 6x2y2
E. 4x5 – 6x7
2) Find the value of 3 – [5x + 2(4 – x)] if x = 2
3) If m = -5, find the value of m3 – 2m + 10
4) Solve:
3 – 4x > x + 15
5) Solve: |2x + 9| ≤ -20
6) Graph the following compound inequality: -9 ≤ 3x + 1 < 13
7) Which is an example of a positive rational number that is an integer?
A.
−12
6
B.
1
4
C. −7
D. 2
E.
8) Graph the solution: |-3x + 2| > 13
9) Transform y +3 =
−5
(x + 6) into slope-intercept form.
2
10) Which graph represents the inequality: 3x + 2y ≤ 6?
A.
B.
C.
D.
E.
−1
3
11) If 7x – 4y = 28, find the y-intercept.
A. 28
B. –4
C. 7
D. –7
E. 4
12 and 13) Identify the domain and range of the following graph:
14) Given y = | x – 5 |, what is the range of the function?
15) What is the linear equation that has an x-intercept of -3 and a y-intercept of 4?
A. –3x + 4y = 12
B. –4x + 3y = 12
C. 3x – 4y = 12
D. 3x + 4y = 0
E. 4x – 3y = 12
16) What is the linear equation for a graph that is horizontal and contains (10, 2)?
A. x = 10
B. y = 2
C. x + y = -6
D. y = 10
E. x = 2
17) Find the equation of the line in point slope form that passes through (8, -12) and is perpendicular to 2x
– 4y = 6.
18) Solve the system of equations:
y = -x + 7
-3x +3y = - 9
19) If 4/3 x + 2/3y = 32/3 and 5/2x – y = -5/2, what is the value of y?
20) Find the slope of a line perpendicular to the line whose equation is
y = 2/3x + 7.
21) Identify the equation of the graph below:
22) Convert the equation x = 5/3 y – 2/3 into standard form
23) Which system of equations has no solution?
A. 3x + y = 3
x+y=1
B. 2x + y = 1
4x + 2y =15
C. 2x + y =14
2x – y = 28
D. x – y = 21
x + y = 31
E. x + y = 17
x – y = 12
24) What is the equation of a horizontal line passing through the point (2, 3)?
A. x = 3
25) Simplify:
B. y = 3
− 6 ⋅ − 15
C. x = 2
D. y = 5x
E. y = |x|
26) Which system of inequalities has the graph shown?
27) What is the slope of a vertical line?
A. 0
B. 1
C. -1
D. No Slope
E. Undefined Slope
28) State the quadratic formula.
29) Find the value of the discriminant in the equation:
2x2 + 7x = - 6
30) Use the discriminant to describe the nature of the roots for the equation: 2x2 + 7x – 15 = 0.
A. 2 Imaginary Roots
B. 2 Real, Irrational Roots
D. 2 Real, Rational Roots
31) Solve 2x² = - 6x - 7
(No decimals-simplify the radicals)
C. 1 Real, Rational Root
E. 1 Irrational Root
32) Solve: (3x + 1)2 = 12
(No decimals-simplify the radicals)
33) If g(x) = 5x2 + 8x – 2, find g(2).
34) If f(x) = 5x2 - 6x , find x when f(x) = 8.
(No decimals-simplify the radicals)
35) Find the vertex of the parabola: y = 2x2 – 3x - 1.
36) Find the x-intercepts of the parabola: y = x² +5x – 24.
37a.) Find the equation of the parabola given.
37b.) Find the equation of a parabola with vertex (1, 5) and passing through (2, 11).
38) What is the axis of symmetry of the parabola for the following equation: y = 2x² -4x – 2?
39) Simplify: (- 2 + 3i) + (16 + 2i) – (27 + 7i)
40) Multiply: (8 - 2i)(12 +5i)
41) Simplify:
3
5i
42) Simplify:
2
6 + 5i
43) Simplify:
(7 + 2i)³
44) Solve: 3x2 – 2x +7 = 0
45) Solve: 2x² + 6x – 12 = 0
46) Transform y = 2x² - 12x + 5 into vertex form by completing the square.
47) The x-values of a set of order pairs is called the _______________.
48) Factor completely: 5 x 5 − 125 x
49) Solve the following system and check your answers:
4x - 2y = 14
12x - 6y = 40
( _____, _____ )
50) In a telephone survey of 150 households, 75 respondents answered “Yes” to a particular question, 50
answered “No,” and 25 were “Not sure.” Find each experimental probability.
a) P(answer was “yes”)
b) P(answer was “no”)
c) P(answer was “not sure”)
d) P(answer was not “not sure”)
Part II – Free Response (10 points each)
This is what the directions will look like: Choose 3 of 6 problems. Show ALL work
to receive credit. If you do more than 3 problems, be sure to indicate which problems
are to be graded or the first 3 will be corrected.
1. Dan sells one-gallon (4 quarts) cartons of milk for $3.09 and half-gallon cartons for $1.65 each.
Assume that the price you pay and the # of quarts in the carton vary linearly.
a. Write the particular equation expressing price in terms of quarts.
b. If Dan sold 3-gallon cartons of milk, what would your model predict the price to be?
c. Suppose that you found a carton of milk marked at $3.45, but there was nothing on the carton to say
what size it is. What would your model predict as the size of the carton?
d) What is the cost per quart for milk?
2. A local BMW dealership is offering a lease on a new 323i for $2500 down and $379 per month.
(a) Write an equation representing the price of the car if it is leased for x months and let y be the price.
(b) How much would the car cost if you leased it for 2 years?
A BMW dealership 25 miles away is offering the same car for $2000 down and $419 per month.
(c) Write an equation representing the price of the car if it is leased for x months and let y be the price.
(d) How much would the car cost if it were leased for 2 years?
(e) At what point do the two cars cost the same?
3. The DHS Bowling club has arranged to earn some extra money by cleaning up Woodland Park. The
Parks & Rec. Department has agreed to pay each old member of the club $10 and each new member $8 for
their services. (The old members have more experience at cleaning parks.)
a. Define the variables, then write the objective function expressing the dollars the club earns in terms of
the number of old and new members who work.
b. The following factors restrict the numbers of students who can work:
i. Both the numbers of old and new members are non-negative.
ii. The club has at most 9 old members and at most 8 new members who can work.
iii. The department will hire at least 6 students, but no more than 15.
iv. There must be at least 3 new members.
v. The number of new members must be at least half the number of old members.
vi. The number of new members must be less than or equal to 3 times the number of old members.
c. Graph the system of inequalities.
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
d. Based on your graph, is it feasible to have no old members at all? Explain.
e. What numbers of old and new members would earn the maximum feasible amount? What is that
amount?
f. What numbers of old and new members would earn the minimum feasible amount? What is that
amount?
4. Mr. Sullivan is using a water balloon launcher to target unsuspecting seniors in the parking lot. The
height in feet of the water balloon above the ground varies quadratically with the time in seconds since Mr.
Sullivan has launched it. The balloon was 6 ft. above the ground when Mr. Sullivan launched it. One
second later it was 23.75 ft. above ground, while 4 seconds after launch it was 74 ft. above ground.
a. Write the particular equation expressing distance above ground in terms of time in seconds.
b. A bird is flying 300 ft. above ground. Is it in danger of being struck by Mr. Sullivan’s balloon?
c. How long will it take before the balloon hits the ground?
d. How high will the balloon be 10 seconds after launch?
5. Answer all parts.
a) Solve the following system:
⎧3w − 6 x + 5 y = −6
⎪
⎨2 y − w + 4 x = −8
⎪8 x − 7 y + 9 w = 61
⎩
b) Solve for X.
⎡5 1 ⎤
⎡5 − 3 ⎤
⎢0 − 3⎥ ⎡ 2 0⎤ − 5 X = 6 ⎢0 1 ⎥
⎢
⎥ ⎢ − 1 5⎥
⎢
⎥
⎦
⎢⎣1 2 ⎥⎦ ⎣
⎢⎣3 − 2⎥⎦
c) f ( x) = x 2 − 7 x + 13, and g (x ) = 2 x − 4
g (3) = __________ __
f ( g (1)) = _________
6.
The table below shows by year the number of Internet users ( in Millions). The number of users
depends on the year.
YEAR
USERS
1997
60
1998
83
1999
104
2000
122
2001
138
2002
153
a) Use your calculator to find the Line of Best Fit
WRITE THE EQUATION HERE:
__________________________
b) Predict the number of Internet users in 2005
_________________
c) The current World population is 6.02 Billion. According to your model, in what year will
50% of the World population be using the Internet?
________________