Midterm Review (Algebra 2)
Name_______________________________
Chapter 1& 2: Equations Inequalities, and Linear Functions
1. The graph of function f(x) is shown below find f(3)
2.
Evaluate the expression f ( x)  2 x 2  5x  1 , when f(-2) =
3. Solve the inequality 2( x  4)  5 x  14 . Then graph its solution on a number line.
4. Solve the compound inequality. Then graph its solution on a number line.
a. 2x  5  7 or 3x  9  12  2x
b. 8  2x  6  15
5. A bag of lawn fertilizer claims that it will cover 5000 square feet of grass. Your yard is 27,500 square feet.
If one bag of lawn fertilizer costs $18.96, then how much will it cost to fertilize your yard?
6. Solve the inequality 2 x  1  5 . Graph your results on a number line.
7. Graph. Identify the slope and y-intercept of the line whose equation is: 2 x  3 y  12
8.
What is the equation of the line that passes through the point (2, 1) and has a slope of -2?
9.
What is the vertex of the graph of y  12 x  2  4
10. The graph shows the temperature change between 5am and 8pm. Find the temperature change from 5 am to
11:00 am.
Chapter 4—Quadratic Functions
11. What is the vertex of the graph of y = 2x2 –12x + 19
12. What is the correct factorization of 3x2 + 17x + 10?
13. What is the correct factorization of 5x2 – 7x + 2?
14. What are the solutions of -x2 – 12 = -87?
15. Write the expression as a complex number in standard form: (-1 + 2i)(11 - i)
16. Solve the equation:  6(u  5) 2  120
17. If x2 + 5x + c is a perfect square trinomial, what is the value of c?
18. What are the solutions of x2 + 20x + 104 = 0?
19. With the quadratic formula, find the solutions of 5x2 + 9x = - x2 + 5x + 1
20. Consider the quadratic function f(x) = -3x + 7x -2. Find the y intercept and the equation of the axis of
symmetry.
21. A rocket is launched with an initial velocity of 94 feet per second from the top of a cliff 52 feet high. Its
height is described by h(t) = -15t2 + 94t + 52. How long will the rocket take to hit the ground?
22. Johnson Manufacturing estimates that its profit P(in hundreds of dollars)after producing x thousand units
can be expressed as P(x) = -2x2 + 104x + 16. How many units must be produced to obtain the maximum
profit?
23. Multiple Choice: Solve 𝑥 2 + 6x = –6 by graphing. If exact roots cannot be found, state the consecutive
integers between which the roots are located.
A) –2, –3
B) between –4 and –3; between –2 and –1
C) –3
D) between –5 and –4; between –2 and –1
24. Multiple Choice: What quadratic inequality is graphed?
A) y ≥(x+4)(x-3)
B) y ≤ x2 - x -12
C) y ≤ x2 + x + 12
D) y ≥ x2 - x -12
Chapter 5: Polynomials and Polynomial Functions
 2x2 y 
25. What is the simplified form of 
1 
 6 xy 
2
26. Subtract: (3x3 + 10x + 5) - (x3 – 4x + 6)
27. Add: (10x – 3 + 7x2) + (x3 - 2x + 17)
28. Find (3x-5)3
29. Factor completely: 3x4 + 9x3 + x2 + 3x
30. Factor completely: 10x3 + 20x7
31. Divide: (10x4 + 5x3+ 4x2 - 9 ) by (x + 1)
32. Determine the end behavior of the function: f(x) = -4x4 – 3x2 – x + 5
33. Multiple Choice: Which cubic equation is graphed?
A) y = 4(x + 4)(x + 1)(x – 2)
1
B) y = 4(x + 4)(x + 1)(x – 2)
1
C) y = 4(x - 4)(x - 1)(x + 2)
D) y = - 4(x + 4)(x + 1)(x – 2)
1
34. Find all the roots of x4 – 18x2 + 12x + 80
35. State the number of real zeros for the function whose graph is shown below:
Chapter 8 – Rational Functions
35. Simplify and reduce the rational expression.
2 x3 y 2 3x 2 z 2

9 x4 z3
4 y 3
36. Identify all horizontal and vertical asymptotes of the graph of the following function:
f ( x) 
8
x2  4
37. Multiple Choice: What function matches the graph to the right?
A) 𝑓(𝑥) =
C) 𝑓(𝑥) =
1
𝑥−3
+1
1
𝑥+3
B) 𝑓(𝑥) =
D)
1
𝑥+3
−1
1
𝑓(𝑥) = 𝑥−3 − 1
38. What are the domain and range of the function
f ( x) 
8
+2
x2  4
39. Graph the rational function f(x) 
2x 2  3x  1
.
x 2  5x  4
40. Simplify the rational expression.
x 2 - 3x  2
x 2  5x - 6
41. Simplify the rational expression.
x 2  8 x  16 x 2  6 x  8

x2
x2  4
42. Simplify the rational expression.
4x
3

x 1 x 1
43. Perform the operations and simplify:
44. Solve.
6 x1
4

2
x  9 x 3
x2  3 x  3

x 2
2
45. Perform the operations and simplify:
2x 3 1
 
15 x 9
46. Laurie can paint a fence in 7 hours and her friend Beth can paint a fence in 4 hours. How long will if take
them if they paint the fence together.