Download Midterm Practice Test

Midterm Practice Test
1. For the function G( x)  80 x  6 x 2 , which gives the maximum value of G?
a. G(40/3)
b. G(6/80)
c. G(20/3)
d. G(10/3)
2. What is the axis of symmetry for the following equation:
2x2 + 2x – 8 = -10x
3. Which quadratic function is equivalent to f ( x)  x 2  6 x  4 ?
a.
f ( x)  ( x  3) 2  5
b.
f ( x)  ( x  6) 2  4
c.
f ( x)  ( x  3) 2  3
d.
f ( x)  ( x  4) 2  12
4. The graph of f(x) = x2 will be translated 5 units up and 2 units to the right. Which function
describes the graph produced by the translation?
a. g(x) = x2 – 4x + 9
c. g(x) = x2 +4x – 1
2
b. g(x) = x – 10x + 27
d. g(x) = x2 + 10x + 23
5. A profit function for a new business follows the function P ( x) 
1 2
x  6 x , where x represents
3
the number of months. After how many months will the company begin to make a profit?
a. 2
b. 9
c. 12
d. 18
6. A suspension bridge has two towers that rise 200 ft above the surface of the road. The towers
are 1000 ft apart and the cable that connects the two towers is in the shape of a parabola,
where it is 5 ft above the surface of the road at its lowest point.
What is the approximate height of the cable above the road at a point that is 150 feet from
either tower?
Midterm Practice Test
7. The heights of two different projectiles after they are launched are modeled by f(x) and g(x). The
function f(x) is defined as f(x) = -16x2 + 42x + 12. The table contains the values for the quadratic
function g.
What is the approximate difference in the
maximum heights achieved by the two
projectiles?
x
g(x)
0
9
1
33
2
25
8. What is the maximum y-value in the solution set to the system of equations below?
y  2 x 2  3x  20
y  3x
a. -15
b. -2
c. 5
d. 6
9. The sum of two numbers is 24. The sum of the squares of the two numbers is 306. What is the
product of the two numbers?
10. The number of bacteria in a culture can be modeled by the function N(t) = 28t2 – 30t + 160,
where t is the temperature, in degrees Celsius, the culture is being kept. A scientist wants to
have fewer than 200 bacteria in a culture in order to test a medicine effectively. What is the
approximate domain of temperatures that will keep the number of bacteria under 200?
a. -1.01°C < t < 2.03°C
c. -0.77°C < t < 1.85°C
b. -0.90°C < t < 1.97°C
d. -0.8°C < t < 1.93°C
1
3
11. If x 2  16 4 , what is the value of x?
a.
b.
c.
d.
128
64
8
4
1

 16 x 6 y 2
12. Which expression is equivalent to  1

6 6
 x y
9
a.
b.
1
64 x 2
y 12
3
c.
d.
9
24 x 2 y 2
24 x 4
y9
64
1
x 2y8
3
2




Midterm Practice Test
2
3
13. A function f ( x)  kx with a non-zero constant k, is transformed to form the new function
2
g ( x)  kx 3 . Which transformation mapped f (x) onto g (x ) ?
a.
b.
c.
d.
Shifted 3 units down
Rotations of 90° counterclockwise
Reflection over the x-axis
Reflection over the y-axis
14. Which of the following functions represents a reflection over the y-axis, followed by a
1
translation of 3 units down from its parent graph f ( x )  x 2
1
a.
f (x)  x 2  3
1
3( x ) 2
b.
f (x) 
c.
f ( x )  (3  x ) 2
1
d.
f ( x) 
1
( x ) 2
3
15. The volume, V, of a certain gas varies inversely with the amount of pressure, P, placed on it. The
volume of this gas is 175 cm3 when 3.2 kg/cm2 of pressure is placed on it. What amount of
pressure must be placed on 400 cm3 of this gas?
a. 1.31 kg/cm2
b. 1.40 kg/cm2
c. 2.86 kg/cm2
d. 7.31 kg/cm2
16. The length of a violin string varies inversely as the frequency of its vibrations. A violin string 15
inches long vibrates at a frequency of 450 cycles per second. Which equation can be used to
calculate the frequency, F, of a violin string with length l?
6750
l
30
b. F 
l
c. F  6750l
d. F  30l
a.
F
17. y varies inversely as the square of x. If y = 12 when x = 16, what is the value of x when y = 48?
a. 1024
b. 8
c. 64
d. 32
18. At a constant speed, the distance traveled is directly related to the length of time traveled. If a
20 mile drive takes 30 minutes, how much longer will a 24 mile drive take?
a. 4 minutes
b. 6 minutes
c. 20 minutes
d. 36 minutes
Midterm Practice Test
19. At a constant temperature of 70 degrees Fahrenheit, the volume of a balloon can be found using
the following equation V 
70
, where x represents the amount of pressure, in pounds per
x
square inch. What is the most appropriate domain for the function V?
a. 0  x  70
b. All real numbers
c. x  0
d. x  70
20. Which is an example of an even function?
a. f ( x )  x 4  2x 2  7
b.
f ( x )  2x  4 x 2
c.
f ( x )  2( x  4) 2  2
d.
f ( x )  2x 3
21. Which is an example of an odd function?
a. f ( x )  3x 3  5
b.
f ( x )  3x 3  5x  2
c.
f ( x )  3x 3  x
d.
f ( x )  3x 3  x  1
22. The equation s = 2 5x can be used to estimate the speed, s, of a car in miles per hour, given the
length in feet, x, of the tire marks it leaves on the ground. A car traveling 90 miles per hour came
to a sudden stop. According to the equation, how long would the tire marks be for this car?
a. 405 feet
b. 380 feet
c. 355 feet
d. 430 feet
23. The value, V, of a car can be modeled by the function V(t) = 13,000(0.82)t, where t is the number
of years since the car was purchased. To the nearest tenth of a percent, what is the monthly
rate of depreciation? After about how many years will the car be worth $5000.