1. Ingeniería

Name: ______________________ Class: _________________ Date: _________
Math Analysis Chapter 7 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Solve the system of equations algebraically.
4x − 3y = 3
3. What is one of the solutions of
2sin 2 x + 3sin x + 1 = 0 ?
a. π
6x − 6y = 6
a. many solutions
b. ÁÊË −1, 0 ˜ˆ¯
c. ÁÊË 0, − 1 ˜ˆ¯
d. no solution
b.
c.
d.
2. In the accompanying diagram, m∠A = 28°
π
3
7π
6
5π
3
4. Solve the system of equations.
and AC = 13. Which equation could be used to
find x in ABC ?
4x + 3y + z = 5
2x + 6y + z = 8
7x + 4y + 2z = 8
a.
b.
c.
d.
y=1
no solution
z=3
x=1
5. Solve the system of equations.
a.
b.
c.
d.
ÏÔ
ÔÔ x y
Ô + =5
ÌÔ 5 3
ÔÔ
ÔÓ x − y = −1
13
sin 28°
x = 13 sin 28°
13
x=
cos 28°
x = 13 cos 28°
x=
a.
b.
c.
d.
1
(35 / 4, 39 / 4)
(35 / 4, 6)
(10, 39 / 4)
(5, 6)
ID: P
Name: ______________________
ID: P
8. Solve the system of equations.
2
and secθ < 0, find cosθ and tanθ.
5
21
secθ = 2 5 , tanθ =
5
6. Given sinθ =
a.
b.
cosθ = −
21
5
, tanθ = −
5
21
c.
cosθ =
21
2 21
, tanθ =
5
21
d.
cosθ = −
21
2 21
, tanθ = −
5
21
7. If sinu =
π
2
a.
b.
c.
d.
ÏÔ
ÔÔ x + y = −2
ÌÔ
ÔÔ 2
Ó x − 5y = 24
a. (2,− 4) and (−7, 5)
b. (−2, 0) and (7,− 9)
c. (−5, 3) and (−7, 5)
d. (−2, 0) and (5,− 7)
9. Identify one of the factors of
24x3 – 42x2 + 4x – 7
4
5
π
with 0 < u <
and cos v = −
with
2
5
13
a.
b.
c.
d.
< v < π , what is cos(u − v)?
8
13
56
221
56
−
221
(4x 2 + 1)
(6x 2 + 1)
(6x 2 – 7)
(4x 2 – 7)
10. At a local electronics store, CDs were on sale.
Some were priced at $14.00 and some at $12.00.
Sabrina bought 9 CDs and spent a total of $114.00.
How many $12.00 CDs did she purchase?
a. 9
b. 6
c. 5
d. 3
33
65
11. Cara wants to invest $16,000 in certificates of deposit (CDs). For tax purposes, she wants her total interest per
year to be $900. She wants to put $1000 more in a 2-year CD than in a 1-year CD and invest the rest in a 3-year
CD. How much money should she invest in each type of CD?
Number of Years
Rate of Interest
a.
b.
c.
d.
1
3.0%
2
5.0%
1-year: $250, 2-year: $1250, 3-year: $12,500
1-year: $1250, 2-year: $2250, 3-year: $14,750
1-year: $1250, 2-year: $1250, 3-year: $12,500
1-year: $1250, 2-year: $2250, 3-year: $12,500
2
3
6.0%
Name: ______________________
12. If secθ =
a.
cotθ
b.
cotθ
c.
cotθ
d.
cotθ
ID: P
13. Find the exact value of sin15°
25
, find cotθ .
24
25
=
23
24
=
7
10
=
7
23
=
25
a.
b.
c.
d.
−
1
2
2−
4
6−
4
2
4
6
2
The following carryout combinations are available at Mike’s carryout joint.
One pizza, one coke, one bag of chips
One pizza, two cokes
Two pizzas, two bags of chips
$9.00
$10.00
$12.00
17. Choco pies are cookies made from chocolate (c),
sugar (s), and flour (f). Chocolate costs $5 per
pound, sugar costs $3 per pound, and flour costs
$2 per pound. You spend $50 on 18 pounds of food
and buy twice as much flour as sugar.
14. Assume that the price of a combo meal is the same
price as purchasing each item separately. Find the
price of a pizza, a coke, and a bag of chips.
a. pizza: $2, coke: $4, bag of chips: $3
b. pizza: $2, coke: $3, bag of chips: $4
c. pizza: $3, coke: $2, bag of chips: $4
d. pizza: $4, coke: $3, bag of chips: $2
Write a system of three equations that represents
how much food you should purchase.
a. c + s + f = 50
5c + 3s + 2f = 18
f = 2s
b. 5c + 3s + 2f = 50
c + s + f = 18
f = 2s
c. 5c + 3s + 2f = 50
c + s + f = 18
s = 2f
d. 5c + 3s + f = 50
c + s + f = 18
f = 2s
15. If Samantha wants two bags of chips and a coke,
how much should she plan to spend?
a. $6
b. $7
c. $8
d. $9
16. Mrs. Davis went to a produce market to buy
bananas and strawberries. She spent $8.00. If the
bananas were $0.50 per pound, and the strawberries
were 4 times that much, how many pounds of
bananas did she buy if she bought 7 pounds of fruit
altogether?
a. 16 pounds
b. 5 pounds
c. 4 pounds
d. 3 pounds
3
Name: ______________________
ID: P
19. Sketch the graph of the system of inequalities.
ÏÔÔ
ÔÔÔ x ≥ 0
ÔÔ
ÔÔ y ≥ 0
Ô
ÌÔÔ
ÔÔ x + 2y ≤ 6
ÔÔ
ÔÔÔ
ÔÓ 3x − y ≥ 4
18. Which point lies in the solution set for the system:
¸Ô
ÏÔÔ
ÔÔ 3x + 5y < −3 ÔÔÔ
˝Ô
ÌÔÔ
ÔÓ −6x + 5y > −5 ÔÔ˛
a.
b.
c.
d.
(8, –3)
(9, –8)
(–7, 1)
(7, 9)
a.
b.
c.
d.
4
Name: ______________________
ID: P
20. Graph y = 2 + 3sin x
21. Convert 54 0 to radian.
a.
b.
a.
c.
d.
20
π
3
10
π
3
3
π
10
3
π
20
22. Find all the solutions of
interval [0,2π )
a.
b.
b.
c.
d.
3 sec x + 2 = 0 in the
π 2π
3
,
3
π 5π
,
6 6
5π 7π
,
6 6
4π 5π
,
3 3
23. In the figure below, sinC = 0.59 and tanC = 0.73.
What is the length of BC ?
c.
d.
a.
b.
c.
d.
5
8.7
5.7
4.1
7.8
Name: ______________________
ID: P
24. Use the figure below to determine the exact value
of sin2x =
a.
b.
c.
d.
10
29
25
29
20
29
4
29
2
sin x
25. Simplify
2
sec x − 1
cos 2 x
2
b. sin x
2
c. sec x
2
d. tan x
a.
6