PAP Algebra 2
Spring Cumulative Test/ Semester Exam Review
Name__________________________ You must show work in your spiral!!
Chapter 5
1) Solve using the Quadratic formula:
Period. ______ Seat # _____
18) Simplify
4 x 2  11x  3
2) Complete the square to solve:
x 2  4x  6
3) Find the vertex of: y  2 x 2  2 x  9
x  3 2  3x  7 4
1
19) Solve for x:
Find the discriminant of y  2 x 2  2 x  9 and
5)
explain what it tells you about the solution(s)
Factor the following and solve for x:
21) Multiply
2 )(9 –
A. 2 x 2  6 x  0
22) Multiply (9 +
B. 4 x  9  0
23) Solve the equation.
2
C. x 2  6 x  8  0
E. 6 x 2  8 x  9 x  12  0
Factor x 3  27
25) Find the inverse of f ( x)  2 x  7  4
3
x  3x  x  3 by
2
x 1
9) Write in factored form. 2𝑥 3 + 6𝑥 2 + 4𝑥
10) Write a polynomial function in standard form
with zeros at 1,2 and 3.
11) Volume of a box= (12  2h)(8  2h)( h) . Which
could be the height (h) 2, 5, or 9 ? Why?
12) Explain why (x-2) cannot be a factor of
4𝑥 3 + 3𝑥 2 − 𝑥 − 3 without having to divide.
Chapter 7
13) Simplify the expression. (7𝑔5 ℎ6 )2 (𝑔4 ℎ2 )4
3
4 x10  3 10 x 3
15) Rationalize the denominator of
16) Simplify the expression.
27) Let f ( x)  x 2  3x and
g ( x)  2 x  5
Find f(g(x)).
28) Let h( x)  x 2  3x  1 and
k ( x)  3x  2
Find 3h( x)  2k ( x)
Chapter 8
29) The population of a town is 4,700 and is
growing 4% each year.
a. Write an equation to model the situation.
b. Predict the population after 12 years.
30) A boat costs $15,500 and decreases in value
by 10% per year. How much will the boat be
worth after 5 years?
31) Suppose you invest $300 at an annual
3
11  10
1
of 3 7
5
17) Write as the sum of 2 simplified fractions :
3  20 6
2
2
26) Simplify 16 2  125 3
Chapter 6
7) Classify the polynomial by degree and number
of terms. 𝑥 3 − 4𝑥 2 + 3
8) Use synthetic division to find the quotient:
14) Multiply and simplify:
2)
24) Find the inverse of f ( x)  ( x  2) 2  4
D. 7 x 2  27 x  4
3
1
20) Add if possible.
4)
6)
2015
interest rate of 2.7% compounded
continuously. How much will you have in the
account after 25 years?
32) Evaluate the logarithm
33) Evaluate the logarithm
PAP Algebra 2
Spring Cumulative Test/ Semester Exam Review
34) The half-life of a certain radioactive
material is 39 hours. An initial amount of the
material has a mass of 47 kg. Write an
exponential function that models the decay of
this material. Find how much radioactive
material remains after 14 hours. Round your
answer to the nearest thousandth.
35) Write the equation in logarithmic form.
57 = 78125.
36) Write the expression as a single logarithm.
log 3 18 − log 3 3
37) Write the expression as a single logarithm.
3 log b v  2 log b x  3 log b w
38) Expand the logarithmic expression.
39) Expand the logarithmic expression. log 3 7𝑏 5
40) Solve
by converting and using
change of base formula. Round to the nearest
ten-thousandth.
48) Write an equation for the translation of
1
y  that has the asymptotes x = –3, y = 7
x
and a vertical stretch of 6.
49) Write an equation for the translation of
y
1
a = 2, c = – 3, and d = 5.
x
50) Describe the asymptote(s) and hole(s) for
the graph of
. State
which point of discontinuity is removeable.
51) Describe the vertical asymptote(s) and
hole(s) for the graph of
of
.
53) Find the horizontal asymptote of the graph of
.
43) Simplify
54) Simplify the rational expression.
1
ln( e)10
2
55) Simplify the rational expression.
Chapter 9 (ch.11 new book)
44) Suppose that x and y vary inversely, and x = 8
when y = 12. Write the function that models
the inverse variation.
45) Describe the variation of:
y
x
3w 2
46) Suppose that m and r vary inversely and
when m = 8. Write a function that
models the inverse variation and
find r when m = 3.
47) The number of days d, it takes a movie crew
to set up a stage for a scene varies inversely
as the number of workers, w. If the stage can
be set up in 3 days by 20 workers, how many
days would it take if only 12 workers were
available?
.
52) Find the horizontal asymptote of the graph
41) Solve
42) Evaluate 2 log 2 8  4 log 3 81
2015
4
56) Simplify:
2 x

x 3
3
57) Simplify: x  3
9
2x  6
58) Divide.
59) Add
60) Subtract:
2x
x4

x  36 x  6
2
61) Solve the equation.
PAP Algebra 2
Spring Cumulative Test/ Semester Exam Review
2015
Graph #72-80 on graph paper.
72) y  2 x  3
62) Solve the equation.
63) If Janet can paint a house in 8 days and
Jenny can paint the same house in 5 days. How
long will it take them to paint the house if
they work together?
Chapter 10
64) Find the Domain and Range of the shape in
interval notation.
y
73) y  x  2  4
74) y 
1
 x  2 2  5
2
75) y   x  5  2
76) y 
5
1
x  23  1
2
4
77) y  23 x  1  3
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
78) y 
–2
–3
1 x 1
2  2
2
79) y  log 2 ( x  4)  2
–4
–5
65) Identify the focus and the directrix of the
graph of y 
1
 x  2 2  3
8
66) The filament of a flashlight bulb is located at
the focus, which is 0.75 centimeters from the
vertex of the flashlight’s parabolic reflector.
Write an equation for the cross section of the
parabolic reflector if the vertex is at the
origin and the reflector is pointing down.
67) Identify the vertex of the parabola:
y 2  x  8 y  26 .
68) Identify the vertex, focus, and directrix of
the graph of (𝑦 − 6)2 = 4(𝑥 − 1). Make a
sketch if necessary.
69) Find the center and the radius of the circle:
𝒙𝟐 + 𝟔𝒙 + 𝒚𝟐 − 𝟐𝒚 = 𝟔
70) Write an equation of a circle with center
(–4, –7) and radius 8.
71) Write an equation of a circle with
center (8,–7) and diameter 8.
80) y 
x2  x  2
1
x 2  4x  3
81) Given f ( x)  a  f ( x  h)  k , how do “a” ,
“h” and “k “ impact the graph of f(x) ?
Graph the following OPTIONAL – more practice
1
1
x2
y  2 x  5  4
y
1
y  x  12  3
2
1
y 
2
1
y  x 1  4
3
2
y  x3
3
y  ln(x  4)  1
x2
3
y  3 x  2 1