Final Exam Review
You must turn this in on the day of your exam.
Name _________________________________
1. Solve each of the following equations for the given variable. a. 𝐴 = 𝜋𝑟
2
for 𝑟 b. 𝑆𝐴 = 2𝜋𝑟
2
+ 2𝜋𝑟ℎ for ℎ
2. Simplify the expressions given below. a. 5 − 2(𝑥 − 3) + 7 b. 9(𝑥 − 3) − 𝑥(2𝑥 + 1)
3. Find the solution(s) to each of the quadratic equations below. a. 3𝑥
2
− 20𝑥 = 7 b. 2𝑥
2
+ 3 = −13 c. 5𝑥 2 = 75 d. 3𝑥 2 − 𝑥 + 1 =0
4. Factor completely. a. 𝑥
2
+ 12𝑥 + 35 c. 𝑥
2
+ 3𝑥 − 40 b. d.
3𝑥
7𝑥
2
2
− 6𝑥
+ 27𝑥 − 4

e. 5𝑥 2 − 14𝑥 + 9
5. Solve the equations. a. (4𝑥 − 3)(2𝑥 + 7) = 0 c. 𝑥 2 + 9𝑥 − 22 = 0 b. f.
(𝑥 − 1)
10𝑥
2
Increasing = ______________ Decreasing = ______________
Positive = _______________ Negative = _______________
Max or Min (circle one) Axis of Symmetry = __________
3 − 25𝑥
+ 12 = 0 d. 𝑥 2 + 10𝑥 = −1 e. 6𝑥 2 + 4𝑥 + 2 = 0 f. 8𝑥 2 − 12𝑥 = 0
6. Vertex = ( _____ , _____ ) 𝑥 − int(s) = ______________ 𝑦 − int = _________
As 𝑥 → +∞ , 𝑓(𝑥) → ________ Domain = ______________
As 𝑥 → −∞ , 𝑓(𝑥) → ________ Range = _______________

7. Determine the following characteristics each function. a. 𝑦 = 𝑥 2 − 2𝑥 − 8
Vertex = ( _____ , _____ ) 𝑥 − int(s) = ______________ 𝑦 − int = _________
Max or Min (circle one) Axis of Symmetry = __________ b. 𝑦 = 𝑥 2 − 4𝑥 + 5
Vertex = ( _____ , _____ ) 𝑥 − int(s) = ______________ 𝑦 − int = _________
Max or Min (circle one) Axis of Symmetry = __________
8. Determine the average rate of change over each interval using the function 𝑦 = 𝑥
2
− 3𝑥 + 5 . a. −3 ≤ 𝑥 ≤ −1 b. 2 ≤ 𝑥 ≤ 6
9. Determine the vertex and the transformations that are present in each of the functions below.
Compare them to the parent function 𝑓(𝑥) = 𝑥 2
. a. 𝑓(𝑥) = (𝑥 − 5)
2
+ 8 vertex = ( _____ , _____ )
________________________________ b. 𝑓(𝑥) = 3𝑥
2
− 7 vertex = ( _____ , _____ )
________________________________
________________________________ ________________________________

c. 𝑓(𝑥) = −
4
5 𝑥
2 vertex = ( _____ , _____ )
________________________________
________________________________ d. 𝑓(𝑥) = −(𝑥 + 9)
2 vertex = ( _____ , _____ )
________________________________
________________________________
10. Convert each of the vertex form quadratic functions into standard form. a. 𝑦 = (𝑥 − 3)
2
− 2 b. 𝑦 = −3(𝑥 + 4)
2
− 1
11. Convert each of the standard form quadratic functions into vertex form. a. 𝑦 = 𝑥 2 − 12𝑥 + 40 b. 𝑦 = 2𝑥 2 − 4𝑥 + 1
12. Use the rectangle to the right to answer the following questions. a. What are the coordinate of the point in the top right corner?
( _____ , _____ ) b. What is the length of the diagonal of the rectangle (corner to opposite corner)?
Diagonal = _________ c. What is the area of the rectangle?
Area = _________

13. Use the given characteristics to determine if the parabola opens up, down, left, or right. a. Focus: (−3, 2) b. 𝑥 + 5 = 4𝑦 2 c. 𝑦 − 3 = −1(𝑥 + 1) 2
Directrix: 𝑦 = 6
_____________ _____________ _____________
14. What are the coordinates of the vertex of the parabola with equation 𝑦 =
1
8 𝑥
2
− 8𝑥 + 15 ?
Vertex = ( _____ , _____ )
15. Given a circle centered at (−3, 1) with a radius of 5, determine if each of the following points on inside, on, or outside the circle. a. (0, 5)
______________ b. (−7, −3)
______________ c. (−1, 4)
______________
16. Rewrite each circle equation below into standard form or center-radius form then determine its center and radius. a. 𝑥
2
+ 𝑦
2
− 4𝑥 + 10𝑦 + 25 = 0 b. 𝑥
2
+ 𝑦
2
+ 6𝑥 − 27 = 0 center: ( _____ , _____ ) radius = _________ center: ( _____ , _____ ) radius = _________
17. What is the probability of randomly selecting a number between 1 and 20 that is even and a multiple of 3?
18. What is the probability of randomly selecting a number between 1 and 20 that is even or a multiple of 3?

20. Jimmy is a football wide receiver. This season the ball has been thrown to Jimmy 50 times and he has caught 34 of them. What is the probability that Jimmy does NOT catch the next ball thrown to him?
21. What is the probability of rolling a six-sided number cube 3 times such that a 1 is rolled each time?
22. In a bag of candy there are 5 snickers and 3 twix bars. What is the probability of randomly choosing two without replacement such that they are both snickers?
23. If 𝑃(𝐴) = 0.55
, 𝑃(𝐵) = 0.33, and 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0.19
what is… a. 𝑃(𝐴|𝐵) b. 𝑃(𝐵|𝐴) c. 𝑃(𝐴 𝑜𝑟 𝐵)
24. 21 students were asked about what they do most with their phones.
Social Media (S)
Music (M)
Boys (B)
7
3
Girls (G)
9
2
Total 10 11
One student is selected at random from this group. What is… a. 𝑃(𝐵) b. 𝑃(𝑀 𝑜𝑟 𝐺) c. 𝑃(𝑆 𝑎𝑛𝑑 𝐵) e. 𝑃(𝐵|𝑀) d. f.
𝑃(𝑀|𝐺)
𝑃(𝐵 ∪ 𝑆)
Total
16
5
21