Math 2 Honors Midterm Review
Name ________________________
1. The graph below shows the height (in meters) of a baseball in flight as time (in seconds) passes and
y = h(x).
a.
Identify the theoretical domain and range of h(x).
b.
What does the equation h(.55) = 10 tell about the flight of the ball?
c.
What is the value of h(4) and what does it tell about the flight of the ball?
d.
Estimate the values of x that satisfy the equation 5 = h(x)?
e.
Identify the practical domain and range of h(x). (Use proper notation)
f.
The maximum value of the graph is 20 and the x-intercepts are (0, 0) and (4, 0). Find a
function rule for h(x).
2. The graph below shows the height (in meters) of a baseball in flight as time (in seconds) passes and
y = h(x).
a. What is the value of h(3) and what does it tell about the flight of the ball?
b. Identify the practical domain and range of h(x). Use proper notation
Domain =
Range =
c. The maximum value of the graph is 20 and the x-intercepts are (0, 0) and (4, 0). Find a
function rule for h(x).
d. Use your equation from part c. to find the values of x that satisfy the equation 10 = h(x).
Indicate units.
e. Identify the theoretical domain and range of h(x). Use proper notation
Domain =
Range =
3. A student kicks a soccer ball off the ground towards another player and it traveled 60 feet before
landing. If it cleared an opposing player’s head that is 6 feet off the ground that is 40 feet away by
15 feet, write an equation that would model the height of the ball given a distance traveled. Draw a
picture!!!
4. A student from another class was asked to graph the function f ( x)   x( x  6). The graph below
was created by the student. Is the graph correct? Explain how you know.
5. The graph of a particular quadratic function has one of its x-intercepts at (4, 0) and a minimum point
of (0, -16).
a.
What is the other x-intercept of the function?
b.
Find a function rule for this quadratic function.
c.
If possible, find a function rule for another quadratic function that has the same xintercepts as this function but has a different y-intercept. If not possible, explain why
not.
6. The Mayfield High football team is selling coupon books for an athletic fundraiser. The function
that represents this situation is graphed below, where the I ( x ) axis represents the amount of money
the team will collect and the x axis represents the cost of the book.
a. Estimate the value of I (25) .
Write your answer as an ordered pair(s).
b. Interpret the meaning of the solution to part a.
c. Solve I ( x)  3000 . Write your answer as an ordered pair(s).
d. Interpret the meaning of the solution to part c.
e. At what price should the Mayfield High School football team set the cost of the coupon
book? Justify your answer with mathematical reasoning.
2
2
2
2
7. Given the functions f ( x)  6 x , h( x)  x  5 , k ( x)  0.2 x , g ( x)  4 x .
a. Which function(s) result in a vertical stretch when compared to t ( x )  x 2 ? Explain how you
know.
b. Which function(s) will have a maximum? Explain how you know.
c. Write the function rule that will reflect f ( x)  6 x 2 , vertically compressed it by a factor of 3,
and then translate it up 13 units.
3
8. Write a quadratic rule that would have x-intercepts at (-4, 0) and ( 7 , 0) . (No decimals or
fractions.)
9. You must show your work for questions 47-49 in order to receive credit.
Solve the following:
10 x  5  15  0
10. Solve the following: 2 x 2  x  3  0 Sketch the graph to help you visualize it.
11. Solve the following:
3x  2 3x  2

x
5
12. Use the graph below to answer the following questions:
a. Evaluate g(x) = 30. Write as ordered pair(s).
b. Evaluate g(5). Write as ordered pair(s).
3
13. x  33   23
14. If k is a positive integer between 30 and 55, what is one possible value of k for which
(k  4)  6
is a positive integer?
Use the following information to answer questions 15-19. The film society is planning a special
showing of a recently released film. The number of people who will attend the screening depends on the
ticket price. Based on past experience, they decide to use the rule N( p) = 400 – 20p to predict the
number of people who will attend the screening if the ticket price is p dollars. The rule I(p) = 400p –
20p can be used to estimate the income from ticket sales based on the ticket price.
15. Find the value of N(12).
a. 160
b.
19.4
c.
12
d.
400
16. What value(s) of p satisfies N(p) = 100?
a. -1600
b.
15
c.
-160,000
d.
0.253 and 19.747
17. At what ticket price does the maximum income occur?
a. $2000
b.
$10
c.
$400
d.
$20
c.
$400
d.
$20
18. What is the maximum income?
a. $2000
b.
$10
19. The cost to the film society can be determined using the rule C(p) = 1,700 – 2(400 – 20p). Find the
ticket price(s) that will allow the film society to break even on the screening of this film. (Use the
equation(s) from the previous questions)
a. $15
b.
$3
c.
$1020 and $1500
d.
$3 and $15
Use the following information for questions 20-25. The graph below shows the height (in meters) of a
baseball in flight as time (in seconds) passes and y = h(x).
20. What does the equation h(1.2) = 16.8 tell about the flight of the ball?
a.
b.
c.
d.
After 16.8 seconds, the height is 1.2 meters.
The ball was thrown only 16.8 meters high.
The ball was in the air for 1.2 seconds.
After 1.2 seconds, the ball was 16.8 meters in the air.
21. What is the value of h(3)?
a. .25
b.
15
c.
3.75
d.
.25 and 3.75
22. Estimate the values of x that satisfy the equation 10 = h(x)?
a. 0
b.
.6
c.
3.4
d.
.6 and 3.4
23. Identify the practical domain of h(x).
a. {x : x  ℝ}
b. {x : 0 ≤ x ≤ 4}
c. {x : x ≥ 0}
d. {x : x ≤ 4}
24. Identify the practical range of h(x).
a. {y : 0 ≤ y ≤ 20}
b. {y : y  ℝ}
c. {y : y ≥ 0}
d. {y : y ≤ 4}
25. The maximum value of the graph is 20 and the x-intercepts are (0, 0) and (4, 0). Find the function
rule.
a.
b.
ℎ(𝑥) = −𝑥 2 + 20
ℎ(𝑥) = (𝑥 − 4)2
c.
d.
h(x)= 𝑥(𝑥 − 4)
ℎ(𝑥) = −5𝑥(𝑥 − 4)
26. Which two of the following expressions are equivalent? CIRCLE TWO OF THE FOLLOWING.
a. 36 x 2  45 x
b. 9 x(4 x  5)
d. 9 x(4 x  3 x)
e. 36 x 2  27 x
c. 12 x(3x  4)
27. Rewrite all of the following in simplest form. NO DECIMALS! No negative exponents.
2
 (2 x 3 y 5 ) 2 


4 3 3 
 ( x y ) 

3 4 
 8x y 
  4 xy 3 3 


2
Use the following equation to answer the question below: A  Po (1  r )t Po represents initial amount, r
represents the rate, t represents time and A represents the amount after t years.
28. If you deposit $12,550 and it is grows to a value of $15,300 in 4 years, what was the annual interest
rate? Round to the thousandth.
29. The formula for the area of a circle is A   r 2 , where A represents the area and r represents the
radius. If the area of a circle is 225 in2 , what is the radius?
30. SKIP!!!!
31. Use the properties of exponents and the relationship between exponential and radical expressions to
determine whether the following statements are true or false. If a statement is false, rewrite the right
side of the equation to make a true statement.
2
4
27 x y  3xy i
b. (4 x)  2 x
c.
36t16  6t 8
d.
e.
5 x 2 y 1 3 55 x 4 y 2  25 x 2 3 5 x 2 y
a.
3
3
9
3
4
27 y18
4
3 y 2  3 y16
32. Mr. Mackar is playing forward in his adult soccer league. With the time winding down he kicks the
soccer ball off the ground towards the goal. The path of his shot was in the shape of a quadratic.
The shot went over the goal after 1.4 seconds and was at a height of 9.6 feet. What was the initial
velocity?
33. Solve the following quadratics. Show your work!
4 x 2  15  239
10 x 2  7 x  8 x
6 x 2  11x  6  4
34. Solve the following equations by completing the square. Show your work!
5 x 2  12 x  9  17
35. Ms. Golem is playing angry birds and is trying to hit a target. She released the bird at a height of 1.2
cm. After 0.4 seconds the bird was at a height 6.2 cm. The bird hit its target at 2.6 cm after 1.89
seconds. What rule represents this quadratic situation?
36. Solve: x + 7x + 15 = 3
37. Solve: 16x - 100 = 0
38. Solve: 3x + 5 =
- 6x + 9
39. Write a function rule for the graph below.
40. Rewrite all of the following in simplest form. NO DECIMALS! No negative exponents.
( x 1 )4  (4 x 5 )3 
41. Suppose Mr. Shirey had a sling shot to shoot water balloons back at the seniors. The balloon left the
sling shot at a height of 7.3 feet off the ground and the water balloon reached 80 feet after .8
seconds. Write an equation that would model the height h(t) of the water balloons after a given time
t with the initial upward velocity.
a. If the water balloon misses everything, how long will the balloon have stayed in the air?
b. One of the seniors got hit in the face at a height of 85.5 feet (remember he is on the building), how
long did the balloon take to hit him if it hit him on the way up?