Download p− 72 10p−90 ÷ p2 − p− 72 p2 − 7p−18

CP Algebra II Exam Review
Name: ______________________
1. Simplify each expression.
a.
6a − 12 a + 5
÷
6
10a 2
p 2 − p − 72 p 2 − p − 72
÷
c.
10 p − 90 p 2 − 7 p −18
e.
5b
2
−
3b 20b − 8
b.
6x 5 y 3
24 y
÷
2
7xy
35x 4 y 3
d.
6n 2 − 18n 1
⋅
n−3
n −1
f.
2
3x
+
x + 3 x −1
2.
Variable M varies directly with p. If M = 75 when p = 10, find M
when p = 16.
3.
R varies inversely with variable T.
when T = 30.
4.
Variable Y varies jointly with P and Q. If Y = 144 when P = 12 and
Q = 8, find Y when P = 15 and Q = 25.
5.
In science, one theory of life expectancy states that the lifespan of mammals
varies inversely to the number of heartbeats per minute of the animal. If a
gerbil's heart beats 360 times per minute and lives an average of 3.5 years,
what would be the life expectancy of a human with an average of 72 beats
per minute? Does this theory appear to hold for humans?
If R is 168 when T = 24, find R
6.
Sketch the graph of each.
7.
a. y =
5
x−3
b. y =
−2
−3
x +1
Determine the equation of each graph.
8
a.
b.
6
4
2
–5
5
–2
–4
–6
c.
6
4
2
–5
5
–2
–4
–6
10
10
8.
Solve the triangle.
9.
The point (–4, 6) lies on the terminal side of an angle. Find the values of
sin θ , cosθ , and tan θ .
10.
In triangle ABC, a = 5, b = 7, and c = 10 Find angle C.
11.
In triangle ABC, b = 10, c = 12, and <C = 120˚. Solve the triangle.
12.
Convert 206˚ into radians.
13.
Find the area of a triangle with side lengths 8, 12, and an included angle of 102˚.
14.
Graph
15.
⎛
π ⎞
y = 2cos 3⎜ θ −
+4
12 ⎟⎠
⎝
Match the equation to the appropriate graph.
i. y = sin2x
ii. y = cos2x
iii.y = 3sinx
iv. y = sinx + 3
16.
Find
a1 in the arithmetic sequence where d = −7 and a4 = 5 .
17.
Find
a14 in the arithmetic sequence where a1 = 4 and d = 3.
18.
Find the arithmetic means in the sequence 35,______,______,______,19 .
19.
Find the geometric means in the sequence 4000,______,______,______,______,125 .
20.
Find the sum of 7 +19 + 31+ ...+199 .
21.
Find a5 for the geometric sequence where a1 = 120, and a3 = 30.
22.
Write a recursive formula for the sequence 3, 6, 12,...
23.
24.
Super Bounce, a manufacturer of handballs, added a chemical to its product to give
the ball a better bounce. To test the bounce, a ball is dropped from a height of 64 ft.
The height of each successive bounce is 77.5% of the previous bounce. If this pattern
continues, how far will the ball travel in total in a downward vertical direction?
∞
∑12(.5)
n −1
n =1
25.
9
∑1.5
k
k =1
26.
11
∑ (2k −1)
k =4
27.
Express as a single logarithm.
a. log5 25 + log5 25
b. log5 40 − log5 8
c. 3log 4 4 4
d. log 2 36 − 2 log 2 3
28.
a.
Simplify.
log6 216
29.
a.
b. log 1000
a.
d. ln e
−
1
2
Solve for the given variable. Express answers to 3 decimals when appropriate.
b.
log x 81 = 4
d.
30.
c. log125 5
log16 x =
3
4
log x e391 = 391
c.
e.
log 27 x =
b.
log 5
5
3
Solve each equation.
log 4 x 2 = log 4 169
100
= log 5 20
w
ln eπ = k
31.
Use logarithms to solve. Express your answers correct to 3 decimal places when
appropriate.
a.
32.
343 = 7 x
b.
3⋅ 2 x = 1
The California state lottery is called “6/53”, meaning a winner must select six
different correct numbers from the integers 1 through 53.
a.
How many different ways can six numbers be selected?
b.
Suppose you had to select the numbers in a specific order. What would be the
number of possibilities?
c.
Describe each situation as a permutation or a combination. Provide an
explanation for your decision.
33.
How many distinct 10-letter arrangements exist, chosen from the word bookkeeper?
34.
The C Club is awarding door prizes for CHS Baseball game attendance. They display
the items in the commons during lunch to entice fans. How many ways can 5
identical CHS caps, 6 identical CHS T-shirts, and 4 identical CHS water bottles can
be displayed?
35.
The CHS math club sold pies, deep dish or regular crust, for a fundraiser. Customers
may choose from apple, peach, pecan, and pumpkin pies. The pies may be made to
order in 8inch or 10 inch pans. How many different pie options are possible?
36.
In how many ways can 4 different calculus and 4 different statistics books be arranged
on a shelf if the calc and stat books must alternate on the shelf?
37.
How many different seven-digit telephone numbers are possible if the first digit cannot
be a zero or a one? Assume no other restrictions and that repetitions are allowed.
38.
Suppose you toss a fair coin 3 times. What is the probability that…
a)
…it lands on heads exactly once.
b)
…it lands on heads exactly twice.
c)
…it lands on heads at least twice.
39.
a) What number of different quartets can be selected from six boys and five girls?
b) How many of these quartets consist of two boys and two girls?
40.
If the digits 1, 2, 3, 4, 5, 6, and 7 are used without repetitions,
a) how many numbers each of five figures can be formed?
b) How many end in 25?
41.
A building has five entrances. In what number of ways can one enter the building and
leave by a different entrance?
42.
One card is chosen at random from a deck of 52 playing. Calculate the following
probabilities.
a. P(8 or a heart)
b. P(Queen or a King)
c. P(Ace or a red card)