Name: ________________________ Class: ___________________ Date: __________
Algebra II Honors Test Review 7-4 to 7-6
Short Answer
Simplify.
1
1
1. 20 2 ⋅ 20 2
4
2. 8 3
3. 9 −2.5
4. Write (8a −6 )
−
2
3
in simplest form.
3
5. Write the exponential expression 3x 8 in radical form.
6. Write the radical expression
7
8
in exponential form.
x 15
Solve the equation.
7.
x + 10 − 7 = −5
4
8. 4(3 − x) 3 − 5 = 59
Solve. Check for extraneous solutions.
9. 6x =
24 + 12x
1
ID: A
Name: ________________________
ID: A
10. The area of a circular trampoline is 112.07 square feet. What is the radius of the trampoline? Round to the nearest
hundredth.
11. Let f(x) = −3x − 6 and g(x) = 5x + 2. Find f(x) + g(x).
12. Let f(x) = x 2 + 2x − 1 and g(x) = 2x − 4. Find 2f(x) – 3g(x).
13. Let f(x) = 3x + 2 and g(x) = 7x + 6. Find f ⋅ g and its domain.
14. Let f(x) = 3x − 6 and g(x) = x − 2. Find
f
and its domain.
g
15. Let f(x) = −2x − 7 and g(x) = −4x + 3. Find (f û g)(−5).
16. Let f(x) = x 2 + 6 and g(x) =
x+8
. Find ÁÊË g û f ˜ˆ¯ (−7) .
x
17. Let f(x) = 4 + 5x and g(x) = 2x − 1. Find f(g(x)) and g(f(x)).
2
Name: ________________________
ID: A
x−2
and g(x) = 2x 2 + 4.
4
a. Find f(g(x)).
18. Let f(x) =
b. Find g(f(x)).
19. The velocity of sound in air is given by the equation v = 20 273 + t , where v is the velocity in meters per
second and t is the temperature in degrees Celsius.
a. Find the temperature when the velocity of sound in air is 318 meters per second. Round the answer to the
nearest degree.
b. Find the velocity of sound in meters per second when the temperature is 20°C. Round the answer to the nearest
meter per second.
20. An airplane travels at a constant speed of 375 miles per hour in still air. During a particular portion of the flight,
the wind speed is 40 miles per hour in the same direction the plane is flying.
a. Write a function f(x) for the distance traveled by the airplane in still air for x hours.
b. Write a function g(x) for the effect of the wind on the airplane for x hours.
c. Write an expression for the total speed of the airplane flying with the wind.
3
Name: ________________________
ID: A
Essay
21. Spheres are being packed into a square box as shown in the diagram.
a. Express the radius r of each sphere as a function of the length x of the sides of the square.
b. Express the volume V of a sphere as a function of the radius r.
c. Find (V û r)(x).
d. Find and interpret (V û r)(6).
Other
22. Michael is shopping for a new CD player with a built-in alarm clock. Electronics City has a special coupon for
$30 off any CD player and is also having a sale with a 25% discount on any alarm clock.
a. Write a function rule to model a 25%-off sale, and a function rule to model a $30-off coupon.
b. Use composition of functions to model how much Michael would pay for a CD alarm clock if the clerk applies
the discount first and then the coupon.
c. Use composition of functions to model how much Michael would pay for a CD alarm clock if the clerk applies
the coupon first and then the discount.
d. Michael selects a CD alarm clock with a regular price of $150. How much more will the item cost if the clerk
applies the coupon first?
e. Why does the CD alarm clock cost less if the discount is applied after the coupon?
4
ID: A
Algebra II Honors Test Review 7-4 to 7-6
Answer Section
SHORT ANSWER
1. 20
2. 16
1
3.
243
a4
4.
4
5. 3 8 x 3
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
−
15
8x 7
–6
–5, 11
1
5.97 feet
2x – 4
2x 2 − 2x + 10
21x 2 + 32x + 12; all real numbers
3; all real numbers except x = 2
–53
63
55
f(g(x)) = 10x – 1; g(f(x)) = 10x + 7
x2 + 1
a. f(g(x)) =
2
x 2 − 4x + 36
b. g(f(x)) =
8
a. –20°C
b. 342 meters per second
a. f(x) = 375x
b. g(x) = 40x
c. f(x) + g(x) = 375x + 40x or 415x
1
ID: A
ESSAY
x
6
4
b. V(r) = π r 3
3
21. [4] a. r(x) =
x3
π
162
d. (V û r)(6) = 4.189
This is the volume of one sphere when the length of each side of the box is 6.
[3] only three parts correct
[2] only two parts correct
[1] only one parts correct
c. (V û r)(x) =
OTHER
22. a. Let x = the original price
Cost with 25% discount: f(x) = x – 0.25x = 0.75x
Cost with a coupon for $30: g(x) = x – 30
Ê
b. ÁË g û f ˆ˜¯ (x) = g(f(x))
= g(0.75x)
= 0.75x − 30
c. (f û g)(x) = f(g(x))
= f(x − 30)
= 0.75(x − 30)
= 0.75x − 22.5
d. (f û g)(x) − (g û f)(x) = (0.75x − 22.5) − (0.75x − 30)
= 7.5
It will cost $7.50 more.
e. If the coupon is applied first, then the cost of the item is less. Therefore, the discount is smaller than it would be
on the higher original price.
2