Name __________________________Alg 2 Sem 1 Finals Review
Date
________Period:_______
Unit 1 Finals Review
1. Consider the arithmetic sequence: 1.5,1.0, 0.5, 0.5,... NC
a. Find the common difference.
b. Write a recursive formula to generate the sequence if u1  1.5 .
c. Write an explicit formula to generate the sequence.
d. Find the 20th term.
e. Find n when un  12 .
2. Consider the arithmetic sequence: 11,16, 21, 26,31,...
a. Find the common difference.
NC
b. Write a recursive formula to generate the sequence if u1  11 .
c. Write an explicit formula to generate the sequence.
d. Find the 10th term.
e. Find n when un  91 .
3. Issac has just received job offers from both Spoons, Inc. and Forks.com. Spoons, Inc. tells Issac they will
start his salary at $55,000 ( u0  55, 000 ) and increase his salary by $1,200 each year. Forks.com says they
will start his salary at $38,000 ( u0  38, 000 ) and increase his salary by $2,500 each year. C
a. For each company, write recursive and explicit formulas for calculating Issac’s salary in the nth year.
(i) Spoons, Inc.
(ii) Forks.com
b. Which job offer would you recommend him to accept? Support your answer.
1
4. Match each recursive formula with the graph of the same sequence. NC
A.
B.
C.
u0  5
un  un 1  1 where n  1
i.
ii.
iii.
u0  5
un  un 1  1 where n  1
u0  12
un  un 1 -4 where n  1
Unit 3 Finals Review – Linear Models and Systems
1. Write an explicit formula for the recursively defined arithmetic sequence given below: NC
u1  4
un  un 1  8 where n  2
2. Refer to the graph of the sequence to the right.
a. Write a recursive formula for the sequence. How is the common difference
represented on the graph? What is the value of u0 ?
b. What is the slope of the line through the points?
c. Write an equation for the line that contains these points.
3. A graph contains the points  0,10 and  3,19  . NC
a. Write the recursive arithmetic formula that generates these points.
b. Write an explicit formula for this sequence.
c. Determine the value of u27.
d. Find the value of n for which un  229 .
2
4. Write an equation for the line that passes through the points  5,3 and  5, 3 . Write your answer in both
point-slope form and slope-intercept form. NC
5. Write an equation in point-slope form for the line parallel to y  7  4 x and passing through the point
 2, 5 . NC
6. Let A and B be points such that A 13, 2 and B  2,8 . NC
a. Write an equation in point-slope form for a line parallel to segment AB and passing through the point
 2,   .
b. Write an equation for the perpendicular bisector of segment AB .
7. Solve the system using elimination or substitution.
Confirm your answer by graphing at right.
y  3  2x
y  5  2x
8. Solve each system by elimination or substitution. NC
a.
b.
c.
d.
3
9. IHS’ senior class is trying to decide which of two catering companies to hire for Prom. Marvelous Meals
charges $2000 plus $55 per person. Posh Parties charges $2500 plus $45 per person. Both companies are
known for their good food and excellent service, so they want to choose the caterer that will cost less.
Which company should they hire? Represent the dilemma with a system of equations and use the solution to
the system to explain your choice. NC
10. White Christmas was a great success! Exactly 300 tickets were sold. Students were charged $7 each, and
$12 for adults. In total, the play raised $2790. Let s = the # of student tickets sold and let a = the # of adult
tickets sold. Write a system of equations and solve it to find out how many students and adults attended the
play.
11. The table below shows the height, in inches, and weight, in pounds, of members of the basketball team.
Height (in) Weight (lbs)
71
170
68
160
70
175
73
180
74
190
a. Find an equation in point-slope form for
the line of best fit for the data. NC
b. Interpret the slope of the line of best fit in
the context of this situation. NC
c. Use your line to predict (extrapolate) the
weight of a 6’6” player. C
4
Unit 4 Finals Review
For problems 1-8, use the following information for f ( x) , g ( x ) , and h( x) to find the following: NC
1. f  2   _______
y  f  x
x
2
2. f  g  3   _______
5
3. h  g  35   _______
x
3
5
5
4. f  h  5   _______
2
2
5. g f  h  6    _______
0
6. Find all x when f  x   1 ; x = _________
g  x  4  x 1
2
7. Find all x when g  x 1  1 ; x = ________
6
8. Find the domain and range of f ( x) .


h  x
1
-4
6
5
2
0
9. Given j ( x)  x 2 , k ( x)  2 x  3 , and m( x)  3x , find the following: NC
a.
b. k  m(2) 
j  k (1) 
c. m  k ( x) 
10. If k ( x)  f  g ( x)  , give possible equations for f ( x) and g ( x ) . NC
a. k ( x)   x  4   3
2
c. k ( x)  ( x  4)  2
b. k ( x)  (2 x  8) 3
11. Let h( x)  3 x  11 14 . NC
a. Write the equation of the parent function, f ( x) .
b. Describe the transformations of h( x) from its parent function. *Remember order matters*
c. For h( x) find the following:
Domain:
Range:
Line of symmetry equation:
Vertex:
d. Write a new equation for the same parent function that has been dilated horizontally with a scale factor of
½ and has a horizontal translation of 7 units and a vertical translation of 𝜋 units.
5
12. Sketch a graph of each equation and then state the domain, range, (and when applicable) line of symmetry
and vertex coordinates. NC
2
 x2
a. y   
b. y     x  3
c. y  3 x 1  2
 1
 2 
Domain:
Domain:
Domain:
Range:
Range:
Range:
Vertex:
Vertex:
Line of Symmetry:
Line of Symmetry:
13. For each graph, find the function’s domain and range and write an equation: NC
a.
b.
Domain:
Domain:
Range:
Range:
Equation:
Equation:
14. Given the following graphs, state the parent function or relation and write the equation of the given graph.
a.
b.
c.
Parent Function:
Parent Function:
Parent Relation:
Equation:
Equation:
Equation:
6
For problems 15 and 16, consider the unit circle x2 + y2 = 1. NC
15. a. Write the equation of the image of the unit circle after a horizontal dilation by a factor of 2 and a vertical
dilation by a factor of 3.
b. Write the equation of a circle with center  2, 5 and radius 10.
c. What two equations would you use to graph the circle in part b in your calculator? (Hint: Solve for y.)
16. a. Write the equation of the image of the unit circle after a horizontal dilation by a factor of 5 and a vertical
dilation by a factor of 3.
b. Graph the image.
c. Translate the ellipse from part a horizontally 2 units and vertically -3 units.
Write the equation of the second image.
 x  7   y 8 
17. Given the equation 
 
  1 , NC
 5   10 
a. Describe the transformations from the parent relation.
2
2
b. Is this equation a circle or an ellipse?
c. Where is the center located?
18. Solve for x:
a. x 2  12  52
b.
 x  4
2
 5  31
c. 2 x 1  4
7
Unit 5 Finals Review – Exponential Functions
1. Simplify as much as possible; write your answer without negative exponents. NC
a.
6 x 2 y 7
y (3x) 2
 5u v   2u v 
2 3 2
d.
b.
 2 x  8x 
e.
4 x 3b 7
b7 x 2 (2 xb) 3
5 2
40u 3v15
3
 3z 4 y 7 
c.  4 2 
 5x y 
2
3
2. Solve for x. NC
a. 2 x5  128
e. 8x
2
3
 32
b. 4 x
f.
5
3
2
 108
x  23  15
3
c.
6
x 2
g. x  27
3
d. 32( x 3)  278 x
1
h. 27   
 81 
2
x
3. Are the following equations exponential functions? If it is an exponential, find f  1.2  . If it isn’t explain
why not. C
a. f ( x)  2 x 2
b. f ( x)  22 x
4. Make an accurate sketch of the given equation, and then find the domain, range, and asymptote. NC
x
a. y  2  2   1
b. y  3x  1
Domain:
Domain:
Range:
Range:
Asymptote:
Asymptote:
8
5. Find the inverse function of each function. If the inverse is not a function, explain why not. C
5
a. f ( x) 
b. f ( x)  x  2
( x  3)
4
1
c. f ( x)  ( x  1) 3  3
6. Write the equation for an exponential function in the form f  x   ab x that passes through the points 1,12 
and  4,55 . C
7. Brian invested money in an account with a fixed interest rate at the start of his 6th grade year, 2005. The
interest is compounded annually. At the start of his freshman year (2008) his balance was $1,313.52 and
after 10 years his balance will be $4,252.13. C
a. Find an exponential equation in the form f  t   abt that models these data. (Round the growth rate to
thousandths.)
b. How much did Brian originally invest (gift from grandma)?
c. What is the interest rate for the account?
8. Lucy bought a car that depreciates in value 17% per year. After owning a car for 3 years, it is now worth
$13,722.89. How much did she originally buy her car for? C
Unit 5 Finals Review – Logarithmic Functions
1. Rewrite the following in either log or exponential form. Do not solve. NC
1
a. log m 23  3
b. log t  3
c. t 4  123
3
d. 3x  90
9
2. Solve the following equations: (NC abc only)
1
a. log3 81  x
b. log 6
x
36
e. log14 563  x
f. 23 x  21
c. log3 1  x
d. log7 10  x
g. 3x  14
h. 52 x1  81
3. What are the relationships that two functions will share if they are inverses with each other? There are a
few!
4. Graph the following logarithmic functions. Then state their domain, range, and asymptote. NC
a. y  log3  x  3  5
b. y  log2  ( x  2)   1
Domain:
Domain:
Range:
Range:
Asymptote:
Asymptote:
5. The Richter scale is used for measuring the magnitude of an earthquake. The Richter magnitude is given by
R  0.67 log(0.37 E )  1.46 where E is the energy (in kilowatt-hours) released by the earthquake. C
a. An earthquake releases 15,500,000,000 kilowatt-hours of energy. What is the earthquake’s magnitude?
b. How many kilowatt-hours of energy would an earthquake have to release in order to be an 8.5 on the
Richter scale?
6. The wind speed s (in miles per hour) near the center of a tornado is related to the distance d (in miles) the
tornado travels by the equation s  93log d  65 . On March 18, 1925, a tornado whose wind speed was
about 280 miles per hour struck the Midwest. How far did the tornado travel? C
7. Cameron bought a flat-screen television for $1,850. The value decreases by about 22% each year. How long
before the TV will be worth half its value? (i.e. What is the half-life?) C
10
Unit 7 (Part 1) Finals Review – Quadratic Functions
1. Solve for x (Hint: Use both the zero-product property and the quadratic formula). NC
a. x 2  5 x  1
b. 2 x 2  5 x  3  0
c. x 2  4 x
d. 3x 2  300  0
e. 2 x 2  3 x  4
2. Given the following quadratic equation: y  3x 2  12 x  17 . Locate the vertex algebraically. Show all work.
Is the vertex a max or min? NC
3. a. Write an equation for a parabola that has its vertex at  1, 2  and passes through the point 1,1 . NC
b. Find the following:
Domain:
Range:
Line of Symmetry:
1 2
x  6 x  10 . NC
2
Vertex:
Line of Symmetry:
4. Find the domain, range, vertex, and line of symmetry for h( x) 
Domain:
Range:
11
5. Use the parabola at right to do the following: NC
a. Write the equation of the parabola in vertex form.
b. Write the equation of the parabola in factored form.
c. Show the equations in part a and b are the same by putting them both in general form.
6. Bob competes in the pole vault. A stopwatch records when he begins running. You record when he leaves
the ground, at 2.4 s, and lands, at 4.1s. C
a. Write an equation representing Bob’s height as a function of time. (Hint: Let a = -16 ft/s2).
b. When did Bob reach his maximum height?
c. What was Bob’s maximum height?
7. Ethan wants to build a 5’ trough out of a piece of plywood that is 3’ by 5’. Find the dimensions for the
trough with the largest volume. C
3 feet
5 feet
8. Find the zeros/roots of the following quadratics: NC
a. f ( x)   x 2  10 x  24
b. g ( x)  3x 2  10 x  3
9. a. Tell whether each equation is written in general form, vertex form, or factored form. NC
i. f ( x)  2( x  2)( x  2)
ii. g ( x)  3( x  0.5)2  2
iii. h( x)  x 2  6 x  8
b. Write equation iii in the other two forms.
12