Multiple Choice Identify the
choice that best completes the statement or answers the question.



Find the opposite and the reciprocal of the number.


1.

500
a.  –500,  c.  500,  b.  –500,  d.  500, 


2.

Simplify .



Evaluate the expression for the given value of the variable(s).


3.



4.

; x = –3



Simplify by combining like terms.


5.



6.



7.

If a = b, then a – c ____ equals b –
c.
a.  always  b.  sometimes  c.  never 



Solve the equation.


8.



9.

a.  14, 4  c.  14, –14  b.  –4, –14  d.  –4, 4 



Solve the equation or formula for the indicated variable.


10.

, for U



Solve for x. State any restrictions on the variables.


11.



12.

A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the
dimensions of the rectangle. Round to the nearest tenth if necessary.
a.  7.5 cm by 22.5 cm  c.  20 cm by 60 cm  b.  7.5 cm by 52.5 cm  d.  15 cm by 22.5
cm 


13.

Two cars leave Denver at the same time and travel in opposite directions. One
car travels 10 mi/h faster than the other car. The cars are 500 mi apart in 5 h. How fast is each car
traveling?
a.  35 mi/h and 45 mi/h  c.  45 mi/h and 55 mi/h  b.  55 mi/h and 35 mi/h  d.  55 mi/h and 65
mi/h 


14.

Michael has $12,500 to invest. He invests part in an account which earns 4.2%
annual interest and the rest in an account which earns 6.2% annual interest. He earns $669.50 in
interest at the end of the year. How much was invested at each rate?
a.  $5,000 at 4.2%, $7,500 at 6.2%  c.  $7,500 at 4.2%, $5,000 at
6.2%  b.  $7,225 at 4.2%, $5,275 at 6.2%  d.  $5,275 at 4.2%, $7,225 at
6.2% 


15.

An inequality ____ has a real number solution.
a.  always  b.  sometimes  c.  never 



Solve the inequality. Graph the solution set.


16.

–4k + 5 £ 21
a.  k ³ –4
 c.  k £ –4
 b.  k ³
 d.  k £



17.

2(2m – 5) – 6 >
–36
a.  m <
 c.  m < –5
 b.  m >
–5
 d.  m >



18.

4(3b – 5) < –31 + 12b
a.  no solutions
 c.  b >
 b.  b <
 d.  all real numbers



19.

26 + 6b ³ 2(3b + 4)
a.  all real numbers
 c.  b ³
 b.  b £
 d.  no solutions




Solve the compound inequality. Graph the solution set.


20.

5x + 10 ³ 10 and 7x – 7
£ 14


21.

4x – 5 < –17 or 5x + 6 > 31


22.




Solve the inequality. Graph the solution.


23.

a.  –18 > x > 8
 c.  –36 < x <
16
 b.  –18 < x < 8
 d. 



24.

Write the ordered pairs for the relation. Find the domain and range.
a.  {(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {–2, –1,
0, 1, 2}; range: {1, 2, 5}  b.  {(5, –2), (2, –1), (1, 0), (2, 1),
(5, 2)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}  c.  {(–2, 5),
(–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {1, 2, 5}; range: {–2, –1, 0, 1,
2}  d.  {(5, –2), (2, –1), (1, 0), (2, 1), (5, 2)}; domain: {1, 2, 5}; range:
{–2, –1, 0, 1, 2} 


25.

Use the verticalline test to determine which graph represents a
function.


26.

Suppose and . Find the value of .


27.

Graph the equation .


28.

Graph the equation by finding the intercepts.


29.

Graph the equation –3x – y = 6.



Find the slope of the line through the pair of points.


30.




Write in standard form an equation of the line passing through the given
point with the given slope.


31.

slope = –8; (–2, –2)
a.  8x + y = –18  b.  –8x + y =
–18  c.  8x – y = –18  d.  8x + y =
18 


32.

slope = ; (5, –3)



Find the slope of the line.


33.



34.



35.




Find an equation for the line:


36.

through (2, 6) and perpendicular to y = x + 1.



Determine whether y varies directly with x. If so, find the
constant of variation k and write the equation.


37.

a.  yes; k = 4; y =4x  c.  yes; k = 6; y
=6x  b.  yes; k = 3; y =3x  d.  no 


38.

a.  yes; k = 1.2; y = 1.2x  c.  yes; k =
6  b.  yes; k = 5  d.  no 


39.

A new candle is 8 inches tall and burns at a rate of 2 inches per hour. a.  Write an equation that
models the height h after t hours.  b.  Sketch the graph of the equation.   


40.

A 3mi cab ride costs $3.00. A 6mi cab ride costs $4.80. Find a linear equation
that models cost c as a function of distance d.
a.  c = 0.80d + 1.20  c.  d = 0.60c +
1.80  b.  c = 1.00d + 1.80  d.  c = 0.60d +
1.20 


41.

Graph the set of data. Decide whether a linear model is reasonable. If so, draw
a trend line and write its equation. {(1, 7), (–2, 1), (3, 13), (–4, –3), (0,
5)}



Graph the absolute value equation.


42.



43.

The graph models a train’s distance from a river as the train travels at a
constant speed. Which equation best represents the relation?


44.

Write the equation for the translation of .


45.

Graph the equation of y = x translated 4 units up.


46.

Write the equation that is the translation of left 1 unit and up 2
units.


47.

Graph the function .


48.

A doctor’s office schedules 15minute appointments and halfhour
appointments for weekdays. The doctor limits these appointments to, at most, 30 hours per week. Write
an inequality to represent the number of 15minute appointments x and the number of halfhour
appointments y the doctor may have in a week.



Graph the absolute value inequality.


49.

y < x + 2 – 2


50.

Graph the function .


51.

An independent system of two linear equations ____ has an infinite number of
solutions.
a.  always  b.  sometimes  c.  never 


52.

The length of a rectangle is 7.8 cm more than 4 times the width. If the
perimeter of the rectangle is 94.6 cm, what are its dimensions?
a.  length = 7.9 cm; width = 39.4 cm  c.  length = 39.4 cm; width = 15.7
cm  b.  length = 23.8 cm; width = 15.7 cm  d.  length = 39.4 cm; width = 7.9
cm 



Use the elimination method to solve the system.


53.

a.  (0, –2)  b.  (–2, 0)  c.  (–2, 2)  d.  (2,
–2) 


54.

a.  f = –7, g = 5  c.  f = 5, g =
7  b.  f = –5, g = –7  d.  f = 5, g =
–7 


55.

a.  (5, –6)  c.  (–5, 6)  b.  no solutions  d.  infinite
solutions 



Solve the system of inequalities by graphing.


56.



57.



58.

Equivalent systems of two linear equations ____ have the same solutions.
a.  always  b.  sometimes  c.  never 


59.

A system of two linear inequalities ____ has a solution.
a.  always  b.  sometimes  c.  never 


60.

Find the values of x and y that maximize the objective function
P = 3 x + 2 y for the graph. What is the maximum value?
a.  maximum value at (5, 4); 32  c.  maximum value at (9, 0);
27  b.  maximum value at (0, 8); 16  d.  maximum value at (0, 0); 0 


61.

Given the system of constraints, name all vertices. Then find the maximum value
of the given objective function. Maximum for
a.  (0, 2), (2, 0), (4, 6); maximum value of –6  b.  (0, 2), (2, 0), (6,
4); maximum value of 12  c.  (0, 2), (2, 0), (4, 2); maximum value of
10  d.  (0, 2), (2, 0), (4, 6); maximum value of 8 


62.

The maximum value of a linear objective function ____ occurs at exactly one
vertex of the feasible region.
a.  always  b.  sometimes  c.  never 


63.

Your computer supply store sells two types of inkjet printers. The first, type
A, costs $137 and you make a $50 profit on each one. The second, type B, costs $100 and you make a
$40 profit on each one. You can order no more than 100 printers this month, and you need to make at
least $4400 profit on them. If you must order at least one of each type of printer, how many of each
type of printer should you order if you want to minimize your cost?
a.  40 of type A 60 of type B  c.  60 of type A 40 of type
B  b.  30 of type A 70 of type B  d.  70 of type A 30 of type
B 



Identify the given matrix element.


64.



65.

In May, Bradley bought 48 styrofoam balls and decorated them as toy figurines.
In June, he sold 19 figurines. In May, Lupe bought 44 styrofoam balls to decorate, and in June, she
sold 21 figurines. Which matrix represents all of their May purchases and their June sales?



Find the sum or difference.


66.



67.



68.



69.



70.

Suppose A and B are 2 × 5
matrices. Which of the following are the dimensions of the matrix A + B?
a.  2 × 5  b.  10 × 10  c.  7 × 1  d.  7 × 7 



Use matrices A, B, and C. Find the sum or difference if
you can.


71.

B + A


72.



73.




Find the values of the variables.


74.

a.  x = 2, y = 4  c.  x = 4, y =
2  b.  x = –1, y = 3  d.  x = 3, y =
–1 


75.

a.  t = –8, y = 4  c.  t = –2, y =
6  b.  t = 6, y = –8  d.  t = –8, y =
6 



Solve the matrix equation.


76.



77.



78.



79.



80.




Find the product.


81.



82.

Find .



Determine whether the product is defined or undefined. If defined, give the
dimensions of the product matrix.


83.

a.  defined; 2 × 2  c.  defined; 1 × 2  b.  defined; 2 ×
1  d.  undefined 



Evaluate the determinant of the matrix.


84.



85.



86.

Write the system as a matrix equation. Then identify the coefficient matrix,
the variable matrix, and the constant matrix.



Solve the system.


87.

a.  (–3, –2, –4)  c.  (3, –2,
–4)  b.  (11, 17, 0)  d.  (–3, 2, 4) 


88.

a.  (5, –4, 1)  c.  (5, 4, –1)  b.  (–5, –36,
–13)  d.  (–5,
–4, 1) 


89.

a.  no unique solution  c.  (2, 1, 5)  b.  (2, 0, –5)  d.  (–2, 0,
–5) 



Write the coefficient matrix for the system. Use it to determine whether the
system has a unique solution.


90.

a.  ; yes  c.  ; no  b.  ;
no  d.  ;
yes 



Determine whether the function is linear or quadratic. Identify the
quadratic, linear, and constant terms.


91.

a.  linear function linear term: constant term: –6  c.  quadratic
function quadratic term: linear term: constant term:
–6  b.  quadratic function quadratic term: linear term: constant
term: –6  d.  linear
function linear term: constant term: –6 



Identify the vertex and the axis of symmetry of the parabola. Identify points
corresponding to P and Q.


92.

a.  (–1, –2), x = –1 P'(0, –1),
Q'(–3, 2)  c.  (–1, –2), x =
–1 P'(–2, –1), Q'(–1, 2)  b.  (–2,
–1), x = –2 P'(–2, –1), Q'(–1,
2)  d.  (–2, –1),
x = –2 P'(0, –1), Q'(–3,
2) 


93.

A biologist took a count of the number of migrating waterfowl at a particular
lake, and recounted the lake’s population of waterfowl on each of the next six weeks. Week  0  1  2  3  4  5  6  Population  585  582  629  726  873  1,070  1,317         
a.  Find a quadratic
function that models the data as a function of x, the number of weeks.  b.  Use the model to
estimate the number of waterfowl at the lake on week 8.   
a.  ; 1,614 waterfowl  b.  ; 2,679
waterfowl  c.  ; 1,961 waterfowl  d.  ; 2,201
waterfowl 


94.

A manufacturer determines that the number of drills it can sell is given by the
formula , where p is the price of the drills in dollars. a.  At what price will the
manufacturer sell the maximum number of drills?  b.  What is the maximum number of drills that can be
sold?   
a.  $60; 285 drills  c.  $31; 2,418 drills  b.  $30; 2,415 drills  d.  $90; 8,385
drills 


95.

Which is the graph of ?


96.

Write in vertex form.



Factor the expression.


97.



98.



99.



100.



101.



102.

The function models the height y in feet of a stone t
seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit
the ground? Round to the nearest hundredth of a second.
a.  7.79 seconds  c.  0.25 seconds  b.  11.02 seconds  d.  5.51 seconds 


103.

Simplify using the imaginary number i.


104.

Find the missing value to complete the square.



Solve the quadratic equation by completing the square.


105.




Rewrite the equation in vertex form.


106.



107.




Use the Quadratic Formula to solve the equation.


108.



109.



110.


Short Answer


111.



112.

Is the relation {(3, 5), (–4, 5),
(–5, 0), (1, 1), (4, 0)} a function? Explain.


113.

Find the slope of the line. Show your work.
Rx + Sy =
T


114.

Graph .


115.

Graph . What is the minimum value of the function?


116.

Graph . Does the function have a maximum or minimum value? What is
this value?


117.

Graph .

Essay


118.

Write the equation of the line that contains the point (8, –3) and is
perpendicular to . Graph the equation. Write the equation in standard form.
Show your work.


119.

Use the following data: . a.  Make a scatter
plot.  b.  Draw
a trend line for your scatter plot.  c.  Write a linear equation for your trend line. Show
your work.   


120.

A fish market buys tuna for $.50 per pound and spends $1.50 per pound to clean
and package it. Salmon costs $2.00 per pound to buy and $2.00 per pound to clean and package. The
market makes $2.50 per pound profit on tuna and $2.80 per pound profit for salmon. The market can
spend only $106 per day to buy fish and $134 per day to clean it. How much of each type of fish
should the market buy to maximize profit? a.  Write an objective function P and constraints for a linear program to
model the problem.  b.  Graph the constraint and find the coordinates of each vertex.  c.  Evaluate P at each vertex to find
the maximum profit.   


121.

Maribel is going to build a rectangular pen for her two dogs. She has 180 feet
of fencing. To keep the dogs separate, she plans to put fencing down the middle of the pen to split
the large rectangle into two smaller rectangles. What are the dimensions and area of the largest pen
area she can use to accommodate both dogs? Show and explain your work.


122.

Show that is equal to . Then use this to explain how you know
that 5 is the minimum value of the function.


123.


Other


124.

Describe the verticalline test for a graph and tell how it can determine
whether a graph represents a function.


125.

Do the values in the table represent a direct variation? Explain your
answer.


126.

Explain how to determine whether a system is independent, dependent, or
inconsistent without graphing.


127.

Explain how to solve a system of equations by substitution.


128.

What does the expression represent if A is a matrix? If
exists, what can you say about the dimensions of A? Explain.


129.

A baseball player hits a fly ball that is caught about 4 seconds later by an
outfielder. The path of the ball is a parabola. The ball is at its highest point as it passes the
second baseman, who is 127 feet from home plate. About how far from home plate is the outfielder at
the moment he catches the ball? Explain your reasoning.


130.

A data processing consultant charges clients by the hour. His weekly earnings
E are modeled by the function , where x is his hourly rate in dollars. Can he earn
$2500 in a single week? Explain.
