Name ______date ______
Algebra 3 Final Exam A Review
Show work on notebook paper.
You may assume that everything on this review will be on the exam.
1.Find the x intercept(s) of the equation: y = x ² - 7x + 10
2.Find the y-intercept(s) of the equation:y = x² - 7x + 10
3.Solve the equation:8(x – 2) = 13 – 2(x + 11)
4.Solve the equation:7 – 3x + 3 = 1 + 2x + 2
5.Two airplanes, one in NY and one in CA, are 3000 miles apart. One leaves NY for CA at a speed of 450 MPH. The other leaves CA for NY at 550 MPH. When will the planes pass each other (express your answer in hours).
6.Simplify:(1 - 3i)(12 + 4i)
7.Simplify:6i(2 - 5i)
8.Solve:x² + 36 = 0
9.Solve:3x² - 2x – 7 = 0
10.Solve:x² - 5x – 6 = 0
11.What is the slope of the line?
12.Write an equation of a lines that passes through (-3, 1) and has a slope of 1/3.
13.Write an equation of a line that passes through (6, -1) and (3, 5)
14.Determine the domain of the function:
15.Determine the domain of the function:
16.Given that f(x) = x + 14 and g(x) = 1 + x + 3x², find h(x) = (f - g)(x)
17.Given that f(x) = 3x + 5 and g(x) = -2x + 1, find h(x) = g(f(x))
18.Given that f(x) = 2x and g(x) = x – 1, find h(x) = (fg)(x)
19.Find the inverse of the function, f-1(x), if it exists:f(x) = 2 – x²
20.Find the inverse of the function f-1(x), if it exists:
21.Describe the end behavior of the graph of the function: f(x) = 4x4 + 2x – 5
22.Describe the end behavior of the graph of the function: f(x) = -x5 – 3x³ + 2x – 25
23.Divide the polynomial using synthetic division:(2x³ + 5x² - 6x – 7) ÷ (x + 2)
24.Divide the polynomial using synthetic division(x³ + 4x² + 1) ÷ (x + 3)
25.Use synthetic substitution to find f(-3), given that f(x) = 12x³ - 6x² + 5
26.Use synthetic substitution to find f(4), given that f(x) = 3x5 – 4x3 + x² - 6
27.Factor completely, given that (x +2) is a factor: f(x) = x³ - 5x² - 2x + 24
28.Factor completely, given that (x + 1) and (x – 1) are factors:
f(x) = x4 - x³ - 7x² + x + 6
29.Find all the roots of the function:f(x) = x³ + 3x² + 25x + 75
30.Find all the roots of the function:f(x) = 2x4 – 7x³ – 27x² + 63x + 81
31.Identify any asymptotes of the graph of the function:
32.Identify any asymptotes of the graph of the function:
33.Write the equation of the graph:34.Write the equation of the graph:
35.Identify the type of conic section: 3x² - 2x + 3y² - 5 = 0
36.Identify the type of conic section:2x² - 8x + 6y² - 8y = 0
37.Graph. Name the center:
38.Graph. Name the center and vertices:
39.Graph. Name the center: (x +7)² + (y – 1)² = 16
40.Graph. Name the vertex and axis of symmetry. x = (y – 4)² + 2
41.If f(x) = 2x, describe the graph of g(x) = -2x-1 -4
42.Evaluate: log364
43.Solve for x:4x + 1 = 15
44.Solve for x:log 2 (x - 1) + 3 = 9
45.Solve for x:3 ln(4x) = 18
46.Anthony borrows $12,000 to purchase a boat. How much will he pay back, considering that he took out the loan for 6 years at 5.25% interest, compounded continuously? Use A = Pert
47.The population of Winnemucca, Nevada, can be modeled by the equation:
P = 6191(1.04)t, where t = 0 was the year 1980. What is the population in 2005?
48.Junius has $2000 to save for college. He has a choice of two accounts. One pays 5% compounded weekly, and one pays 5.25% compounded quarterly. If he leaves the money for 5 years, which will earn him more interest? Use
49. Morris has $2000 to invest. into an account paying 5% interest compounded continuously. How long will it take for Morris to have $6000? Use A = Pert
50.Biologists can estimate the age of an African elephant using the length of its footprint and the equation: l = 45 – 25.7e-0.09a, where l is the length of the footprint (in cm) and a is the age (in years). Estimate the age of an elephant whose footprint measures 36 cm.
STUDY, STUDY, STUDY……, then, study some more.