Download Semester 1 Exam Review

Algebra 2
Semester 1 Review
Name: _____________________________
Date: _______________ Per: _______
1. For f ( x )  ( x  6)2 , evaluate each of the following.
a. a. f (12)
b. f (6)
c. f (0)
d. Find the value of x for which f ( x )  9 .
2. Consider the sequence 1, 3, 5…
a. Write the next four terms of the sequence.
b. What is the generator?
c. What kind of sequence is it? How can you tell?
d. Complete the table and the graph then write a rule for the sequence.
x
y
0
1
2
3
4
5
6
Rule: t(n)=_________________
3. Solve each equation below for x.
a.
3x  39
b. 25 x  1252
c. 2(x2)  128
4. Using your knowledge of shifts and parent graphs, write the equation of the graph to the below.
a. y =______________________________
b. Domain: ________________________
c. Range: _________________________
5. For the equation: y  x 2  2 x  8
a. Complete the table and graph
x
-5
-4
-3
-2
-1
0
1
2
3
y
b. Write the x- intercepts, y-intercept, and vertex as ordered pairs (x, y).
c. Find the domain and range.
6.
Solve the following equation for x: 4 x  5  4(2 x  7)
7. Given the function f ( x)  8 x 2  7 find f ( 5)
8. Graph y 
1
( x  1)2  4 .
2
9. Randi’s Rent-a-Wreck charges $15.00 a rental car, and $0.20 per mile driven.
a. Write an equation to model this data.
b. How much would it cost someone to drive 321 miles?
10. Write an equation to model the data in the following table:
x
0
1
2
y
23
14
5
1
2
11. Write a rule for the geometric sequence 4, 2,1, ,...
12. Find n when t  n   12 for the arithmetic sequence t  n  
13. Simplify (find the equivalent expression) the following:
1
n3
3
x4 y6
x2 y3
14. Find an equivalent expression by factoring: 3x 2  11x  20
15. Multiply the following binomials: (2 x  3)( x  4)
16. Solve the system of equations algebraically
y  13 x  5
2x  y  9
17. Tomas’ grandfather put $1000 in the bank for him when he was born. The account has been earning
5.25% interest compounded continuously. Tomas is now 18 years old and wants to take out the money
so he can go to college. How much money does he have now? Show how you got your answer.
18. Simplify each expression. Be sure that your answer has only positive exponents.
a.
4 x 7 y3z 9
x 5 y 5z 2
b.
(6x 4 y 7 )(2x 2 y5 )
19. Find the x-intercepts by factoring or the quadratic formula and the y-intercept of each equation.
f  x   x2  2x  8
f  x   x2  25
f  x   x2  7 x  12
X:________________________
X:______________________
X:_____________________
Y:________________________
Y:______________________
Y:_____________________
20. Find the exponential function for an
A. initial value (0, 4) that passes through the point (1, 24)


B. initial value (0, 1/2) that passes through the point  2,
1

8
C. initial value (0, 7) that passes through the point (4, 112)
21. Find the equation of each of the following quadratic equations.
A. Moved 3 units up and 4 units right
B. The function opening down, moving 7 units down and 5 units right
C. Has a stretch factor of 0.6, and moves 3 units up
22. Write the equation in graphing form of the graph below.
23. Write the equation of the line that passes through (2, 6) and (8, -16)
24. Find the slope of the line that passes through the points (20, 7) and (–12, –9).
25. Change the equation y  x 2  4 x  12 into graphing (vertex) form.
26. Solve the following system of equations: y  3 x  2
y  2x  2
27. Solve:
3
5

2 x  4 3x
28. Solve for y:
5 x  2 y  30
29. Rewrite each of the following radicals as expressions with rational exponents:
4
1
a. 𝑥 7
b. 𝑦 4
30. Rewrite each of the following expressions with rational exponents as radicals:
5
a. √𝑧
2
b.√𝑎
31. Solve using the quadratic formula: 𝑥 2 − 7𝑥 − 9 = 0
32. Solve using the zero product property: (𝑥 − 5)(2𝑥 + 3) = 0
33. Expand and simplify the following: (𝑥 − 5)2 + 9
34. Write the equation of the line through (2, 7) and a slope of -3
35. Name the 6 parent functions we have learned and give their parent equation and general equation.
Name
Parent
General
a. ______________________
______________________
______________________
b. ______________________
______________________
______________________
c. ______________________
______________________
______________________
d. ______________________
______________________
______________________
e. ______________________
______________________
______________________
f. ______________________
______________________
______________________