Name________________________________
Date________________ Period_____
Algebra 2 Pre-AP Fall Semester Exam REVIEW
The semester exam will have 50 multiple choice questions, similar to those below.
1.
Solve S 
2.
Solve
4.
5.
6.
1
PL  B for L .
2
3x  7  11.
3. Solve |4x – 3| = -12
Sally has determined that she would like to have a garden length that satisfies
{6 ft < length ≤ 14 ft}, if she wants the length to be three less than double the
width, what are the possible widths?
Consider the graphs below. What function best represents the graph of f(x)? g(x)?
The graphs of the function g and h were
obtained from the graph of the function f
using a transformation as shown above.
Based on the graph, what equation can be
used to describe g(x) in terms of f(x)?
and h(x) in terms of f(x)?
7.
8.
Graph the solution set (number line) for
1 2
5
 x
2 5
10
Karen has taken 3 science quizzes. Her scores were 80, 84, and 92. What
minimum score must she get on her next quiz to have an average score of
at least 88?
9. Which of the following relations is a function? (may have more than one)
I. {(-1,
II. {(-1,
III.{(-1,
IV. {(-1,
0),
0),
2),
0),
(0,
(0,
(1,
(1,
1), (2, 2)}
1), (-1, 4)}
2), (2, 2)}
-6), (1, 6)}
10.Southern Phone Company is promoting a new cell phone service plan; a customer can
make up to 600 minutes of calls each month for $49.99. If the number of minutes used
in a month exceeds 600, then the function
c = 0.35(m – 600) + 49.99
describes the monthly charge, c, in dollars in terms of m, the total number of minutes
used. Which of the following statements best describes this function?
A The first 600 minutes used costs 35 cents each, after which there is an additional
charge of $49.99.
B If the total number of minutes used is more than 600, then every minute beyond
600 costs 35 cents.
C If the total number of minutes used is more than 600, then every minute used
costs 35 cents.
D Every minute used costs 35 cents, regardless of the total number of minutes used.
11.What is the domain of the function graphed below?
12. Which of the following is not a correct description of the graph of the function
y = -4x + 9?
A The graph of the function contains the point (2, 1), and when the value of x
increases by 1 unit, the value of y decreases by 4 units.
B The graph of the function contains the points (-1, 13), (3, -3), and (4, -7).
C The graph of the functions contains the points (0, 9), (-2, 17), and (3, 21).
D The graph of the function is a line that passes through the point (0, 9) with a slope
of -4.
13. If (5k, 8k) and (3k, 14k) are two points on the graph of a line and
k is not equal to 0, what is the slope of the line?
14. The amount an appliance repairman charges for each job is represented by the function
t = 80h + 15, where h represents the number of hours he spent on the job and t
represents the total amount he charges in dollars for the job. The repairman plans to
change the amount he charges for each job. The amount he plans to charge is
represented by the function t = 80h + 45. What will be the effect of this change on the
amount he charges for each job?
15. Graph 3x – 2y < 8?
16.The sum of the perimeters of two different equilateral triangles is 72 centimeters, and
the difference between their perimeters is 18 centimeters. If x represents the side
length of the larger triangle and y represents the side length of the smaller triangle,
write the system of equations that could be used to find the dimensions of the
triangles?
17. Consider the system of inequalities below.
1
x3
2
y  3 x  9
y
Graph this system below.
18. At an FCCLA bake sale the brownies cost $0.75 and the cookies are $1.00. If at the
end of the day 85 items were sold and $73.25 was collected, how many brownies and
cookies were sold?
19.What is the y- value of the solution to the matrix equation below?
 3 2   x  7 
 2 1   y   6 

   
20. What is the value of t in the solution of this system?
-6r + 4s = -19 - t
s - 2t = -5r + 17
6r - 6t - 24 = 5s
21. If (x + 3i) + (5 + yi) = (1 + 12i) What are the appropriate values of x and y?
22. In an AC circuit, the voltage E (in volts), current I (in amps), and impedance Z (in
ohms) are related by the formula E= I  Z. Find the voltage of a circuit, with a
current of 8 + 2i amps, and an impedance of 3 – 7i ohms.
23. In the quadratic equation x2 – x + c = 0, c represents an unknown constant.
If x = 5 is one of the solutions to this equation, what is the value of c?
24.The base of a triangle is 4 inches less than triple its height. If the area of the triangle
is 226 square inches, write the equation that can be used to find h, the height of the
triangle in inches?
25.The graph of a quadratic function is shown below.
Where
Where
Where
Where
is the y-intercept?
is the maximum?
are the x-intercepts?
is the axis of symmetry?
26. The graph of a quadratic function is shown below.
Name________________________________
Date________________ Period_____
What is the best estimate of the positive
value of x for which this function
equals 1?
27. The table below shows ordered pairs that satisfy the quadratic function f.
x
f(x)
-2
-14
-1
-14
0
-12
1
-8
2
-2
3
6
4
16
5
28
Based on the table, a solution to the
equation f(x) = 0 is found in which
interval?
28. Which of the following quadratic functions does not have zeros of -20 and 4?
f ( x)   x 2  16 x  80
2
B f ( x)   x  16 x  80
1 2
C f ( x)  x  4 x  20
4
3 2
D f ( x)   x  24 x  120
2
29. Graph the given relation or equation and find the domain and range. Then determine whether the
relation or equation is a function.
(3.7, 5.7), (–1.3, 5.7), (–4.3, 3.7), (–4.3, –2.3)
a. Domain: {–4.3, 5.7, 3.7} Range: {–2.3, 3.7, –1.3}
c. Domain: {–2.3, 3.7, 5.7} Range: {–4.3, –1.3, 3.7}
The equation is not a function.
The equation is a function.
b. Domain: {–4.3, –1.3, 3.7} Range: {–2.3, 3.7, 5.7}
d. Domain: {–4.3, –1.3, 3.7} Range: {–2.3, 3.7, 5.7}
The equation is a function.
The equation is not a function.
A
30. Find the value of f(–5) and g(6) if
and
.
a. f(–5) = 30; g(6) = –44.12
b. f(–5) = 11; g(6) = 76.03
c. f(–5) = –19; g(6) = 54.61
d. f(–5) = –31; g(6) = 53.39
31. Write the equation 2y = 20x + 0.5 in standard form. Identify A, B, and C.
a
where
,
, and
.
.
b
where
,
, and
.
.
c
where
,
, and
.
.
d
where
,
, and
.
.
____ 32.
Write the equation 7y = 22x + 0.4 in standard form. Identify A, B, and C.
a.
where
,
, and
.
b.
where
,
, and
.
c.
where
,
, and
.
d.
where
,
, and
.
____ 33.
Find the x-intercept and the y-intercept of the graph of the equation 7x + 4y = 10. Then
graph the equation.
a. The x-intercept is – 5 . The y-intercept is – 10 .
c. The x-intercept is 7 . The y-intercept is 10 .
2
7
10
5
b. The x-intercept is . The y-intercept is .
7
2
____ 34.
a. – 1
b. 15
4
7
4
d. The x-intercept is – . The y-intercept is – 5 .
7
2
Find the slope of the line that passes through the pair of points (6, 11) and (9, 8).
c. 2
d. – 3
19
____ 35.
a. – 1
b. – 11
9
____ 36.
Find the slope of the line that passes through the pair of points (2, 11) and (9, 4).
c. 2
7
d. 11
15
Graph the line that passes through (–5, 5), parallel to a line whose slope is –0.2.
a.
c.
y
(–5, 5)
–5
–4
5
–3
–2
4
3
3
2
2
1
1
–1
–1
–5
–4
1
2
3
4
x
5
–3
–2
–5
–4
–3
–2
–1
–1
–2
y
d.
–3
5
–4
4
–5
3
(–5, 5)
5
4
–2
b.
y
(–5, 5)
(–5, 5)
2
1
1
1
2
3
4
5
–5
x
–4
2
3
4
5
x
y
–3
5
–4
4
–5
3
2
–1
–1
1
–3
–2
–1
–1
1
2
3
4
5
x
–2 that satisfies the following condition.
–2 equation in slope-intercept form for the line
____ 37.
Write an
–3
–3
slope 8 and passes through (5, 21)
–4
–4
a. y =
c. y =
–5
–5
b. y =
d. y =
____ 38.
Write an equation in slope-intercept form for the line that satisfies the following condition.
slope 9 and passes through (10, 20)
a. y =
c. y =
b. y =
d. y =
____ 39.
Write an equation in slope-intercept form for the line that satisfies the following condition.
passes through (1, 10), parallel to the line that passes through (16, 12) and (37, 5)
a. y =  1 x 1
c. y = 31 x 31
3
b. y = –7x – 1
3
____ 40.
3
d. y =  1 x
3
3
31
3
Write an equation in slope-intercept form for the line that satisfies the following condition.
3
passes through (5, –8), perpendicular to the graph of y = 10 x + 15
a. y =  10 x + (  10 )
c. y = 3 x + 26
3
3
10
26
b. y =  x +
3
3
10
3
26
d. y = x + 3
3
10
Solve each system of equations by using substitution.
41.
3x + 2y = 15; 4x – 6y = 20
a. (0, 5)
b. (5, 2)
c. (5, 0)
d. (4, 0)
Solve each system of equations by using elimination.
____ 42.
;
a. (8, 2.5)
c. (8, 1)
b. (9, 1)
d. (6.75, 7)
Given below are some inequalities. Plot the feasible region graphically.
.
43.
;
;
;
y
y
a.
c.
–5
–4
–3
–2
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–2
–1
–1
–3
–3
–4
–4
–5
–5
d.
5
4
4
3
3
2
2
1
1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
vertex: (3.5, –2.5)
max: none
min: f(3.5, –2.5) = 6
2
3
4
5
x
1
2
3
4
5
x
y
5
–1
–1
1
vertices: (3.5, 1.3)
max: f(3.5, 1.3) = 2.2
min: f(3.5, 1.3) = 2.2
y
–3
–2
–2
b.
–4
–3
–2
vertices: (2.09, 1.3), (3.5, –2.5)
max: f(3.5, –2.5) = 6
min: f(2.09, 1.3) = 0.79
–5
–4
vertex: (1.3, 3.42)
max: f(1.3, 3.42) = –2.12
min: none
44.
Consider the quadratic function
. Find the y-intercept and the equation of the axis
of symmetry.
a. The y-intercept is  3 . The equation of the axis of symmetry is x = 2.
2
b. The y-intercept is – 2. The equation of the axis of symmetry is x = 3 .
2
c. The y-intercept is 3 . The equation of the axis of symmetry is x = –2.
2
d. The y-intercept is 2. The equation of the axis of symmetry is x =  3 .
2
Determine whether the given function has a maximum or a minimum value. Then, find the maximum or
minimum value of the function.
____ 45.
a. The function has a maximum value. The maximum value of the function is 30.
b. The function has a minimum value. The minimum value of the function is 30.
c. The function has a maximum value. The maximum value of the function is –2.
d. The function has a minimum value. The minimum value of the function is –2.
46.
Simplify
a.
c.
b.
d.
____ 47.
Simplify
a.
c.
b.
d.
____ 48.
a.
b.
Simplify
____ 49.
a.
b.
Simplify
c.
d.
c.
d.
____ 50.
a.
b.
Simplify
____ 51.
a.
b.
Simplify
____ 52.
a.
b.
Simplify
____ 53.
a.
b.
Simplify
____ 54.
Simplify
c.
d.
c.
d.
c.
d.
c.
d.
a.
c.
b.
d.
____ 55.
Simplify
a.
c.
b.
d.
____ 56.
a.
b.
Simplify
____ 57.
a.
b.
Simplify
____ 58.
a.
b. 33
Simplify
c.
d.
c.
d.
c.
d.
____ 59.
a.
b. 24
Simplify
____ 60.
a.
b.
Simplify
____ 61.
a.
b.
Simplify
____ 62.
a. 3, -3
b. 3
Solve for x.
____ 63.
a. 4, -4
b. 2
Solve for x.
c.
d.
c.
d.
c.
d.
c. 3i, -3i
d. 3i
c. 4i
d. 4i, -4i