Semester 1 Review
Name ____________________
1. Evaluate the expression for the given value of the variable.
; x = –3
a. –27
b. 26
c. –10
d. –28
c.
d.
2. Simplify by combining like terms.
a.
b.
3. Solve the inequality.
–8 + 2k  2
a. k  3
c. k  3
b. k  5
d. k  5
4.An absolute value equation ____ has an extraneous solution.
a. always
b. sometimes
c. never
5. A furniture maker uses the specification
specification as an inequality.
a.
b.
for the width w in inches of a desk drawer. Write the
c.
d.
6. Which of the following is not a function? (ordered pairs, graph, table, graph)
a. {(3, 4), (-1, 6), (5, -10)}
b. {(1, -3), (0, -3), (5, 1)}
c.
d.
x
y
-2
3
1
4
-2
2
7. Find an equation for the line:
through (8, 5) and parallel to y = 2 x – 2.
a.
1
2
y=  x 9
b. y = 2 x  21
c.
y=
1
x+1
2
d. y = 2 x  11
8. Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
x
y
6
30
24
120
96
480
384
1920
a. yes; k = 5; y =5x
b. yes; k = 4; y =4x
c. yes; k = 6; y =6x
d. no
9. Determine whether y varies directly with x. If so, find the constant of variation k.
–3y + 6x = – 8
b. yes; –3
a. yes; 2
c. no
d. yes; 6
10. Find the value of y for a given value of x, if y varies directly with x.
If y = 0.6 when x = 0.48, what is y when x = 1.2?
a. –0.96
b. 1.5
d. –1.5
c. 0.96
11. The graph models a train’s distance from a river as the train travels at a constant speed. Which equation best represents
the relation?
y
100
Miles From River
80
60
40
20
–4
–2
Hours Before River
a.

4
x
b.
y  x  60
c.

5
x  2 ; 8 units up
6
5
y   x  10
6
5
y  x 8
6
y
b.

y  x  60
2
Hours After River
12. Write an equation for the vertical translation.
a.

River
y  60x
d.
y
1
x
60


c.
d.

5
x  10
6
5
y  x 6
6
y
13. The length of a rectangle is 7.8 cm more than 3 times the width. If the perimeter of the rectangle is 48.4 cm, what are its
dimensions?

a. length = 4.5 cm; width = 11.9 cm
c. length = 4.1 cm; width = 20.1 cm
b. length = 20.1 cm; width = 11.9 cm
d. length = 20.1 cm; width = 4.1 cm
14. A group of 40 people attended a ball game. There were three times as many children as adults in the group. Set up a
system of equations that represents the numbers of adults and children who attended the game and solve the system to find
the number of children who were in the group.
a. a  c  50
c. a  c  50
; 10 adults, 30 children
; 30 adults, 10 children
b.
c  3a
a  c  50
a 3c
d.
; 30 adults; 19 children
a  3c
a  c  50
c  3 a

15. Use the elimination method to solve the
 system.

3x  y  4z  0
; 19 adults; 30 children
4 x  4 y  2z  8

2x  2y  3z  4
a. (1, –7, –2)
b. (–3, 0, 5)
c. (–3, –7, –4)
16. A system of two linear inequalities ____ has a solution.
a. always
b. sometimes
d. (3, 5, –4)
c. never
17. The maximum value of a linear objective function ____ occurs at exactly one vertex of the feasible region.
a. always
b. sometimes
c. never
18. The solution to a system of three equations in three variables is ____ one point.
a. always
b. sometimes
c. never
19. Which area represents the solutions of the graphed system of inequalities?
y  3x  12
y
3
x3
2

a. 1
c. 3
b. 2
d. 4
20. Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
a. linear function
linear term:
constant term: –6
b. quadratic function
quadratic term:
linear term:
constant term: –6
c. quadratic function
quadratic term:
linear term:
constant term: –30
d. linear function
linear term:
constant term: –30
21. 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
665
677
759
911
1,133 1,425 1,787
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.
; 2,721 waterfowl
b.
c.
; 2,219 waterfowl
; 2,736 waterfowl
d.
; 3,359 waterfowl
22.
a.
Which is the graph of
?
c.
y
8
6
4
2
–8 –6 –4 –2 O
–2
2
4
6
8
x
–4
–6
–8
b
.
d.
23. Identify the vertex and the y-intercept of the graph of the function
a. vertex: (2, –5);
c. vertex: (–2, –5);
y-intercept: –12
y-intercept: 9
b. vertex: (–2, 5);
d. vertex: (2, 5);
y-intercept: –7
y-intercept: –7
24. Use a graphing calculator to solve the equation
a. 1, 1.33
c. 2, 2.67
b. –1.33, –1
d. –0.17, 0.17
25. Simplify
a.
using the imaginary number i.
b.
c.
.
. If necessary, round to the nearest hundredth.
d.
26. Simplify the expression.
a.
b.
c.
d.
27.
a. –25
b. 25
d. –25i
c. 25i
28. Solve the quadratic equation by completing the square.
7  157
6
7  157
3
a.
b.


7  101
3
7  20
6
c.
d.
and by number of terms.
29. Classify –8x5 – 4x4 + 7x2 + 10 by degree
a. quintic polynomial of 4 terms
c. quadratic binomial
b. quartic polynomial of 4 terms
d. cubic binomial

30.Use a graphing calculator to determine which type of model best fits the values in the table.
x
–6
–2
0
2
6
y
1176
56
0
–40
–1032
a. cubic model
b. quadratic model
c. linear model
d. none of these
31. Use a graphing calculator to find a polynomial function to model the data.
x
1
2
3
4
5
6
7
8
9
10
f(x)
12
4
5
13
9
16
19
16
24
43
a.
b.
c.
d.
f(x) = 0.8x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58
f(x) = 0.08x3 – 1.73x2 + 12.67x + 35.58
f(x) = 0.08x4 + 1.73x3 – 12.67x2 + 34.68x – 35.58
f(x) = 0.08x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58
32. Determine which binomial is not a factor of
a. x + 4
c. x – 5
b. x + 3
d. 4x + 3
33. Determine which binomial is a factor of
a. x + 5
b. x – 5
.
.
c. x + 15
d. x + 8
34. The volume of a shipping box in cubic feet can be expressed as the polynomial
. Each dimension
of the box can be expressed as a linear expression with integer coefficients. Which expression could represent one of the
three dimensions of the box?
a. x + 6
c. 2x + 3
b. x + 1
d. 2x + 1
35. Find the solutions of
a. 3
b. –3
.
c. –3, 3
d. no solution
36. Factor the expression.
a.
b. no solution
c.
d.
37. Ian designed a child’s tent in the shape of a cube. The volume of the tent in cubic feet can be modeled by the equation
, where s is the side length. What is the side length of the tent?
a. 3 feet
b. 9 feet
c. 6 feet
d. 27 feet
38. Find a third-degree polynomial equation with rational coefficients that has roots –6 and 3 + i.
a.
c.
b.
d.
39. For the equation
, find the number of complex roots and the possible number of real roots.
a. 4 complex roots; 0, 2 or 4 real roots
b. 5 complex roots; 1, 3, or 5 real roots
c. 4 complex roots; 1, 3, or 5 real roots
d. 5 complex roots; 0, 2 or 4 real roots
40. A manufacturer of shipping boxes has a box shaped like a cube. The side length is
3a – 3b. What is the volume of the box in terms of a and b?
a.
c.
b.
d.
Short Answer:
41. Solve the equation. Check for extraneous solutions.
42. Graph
43. Graph
. Identify the vertex and the axis of symmetry.
. What is the minimum value of the function?
44. A science museum is going to put an outdoor restaurant along one wall of the museum. The restaurant space will be
rectangular. Assume the museum would prefer to maximize the area for the restaurant.
a) Suppose there is 120 feet of fencing available for the three sides that require fencing. How
long will the longest side of the restaurant be?
b) What is the maximum area?
45. Two boats leave from the same point at the same time. One boat travels due east and the other travels due north. One boat
travels 6 kilometers per hour faster than the other. After 4 hours, the boats are 67 kilometers apart. (Hint: Use Pythagorean
Theorem).
a. Let x be the speed of the slower boat. Write a quadratic equation that models the situation.
b. Use a graphing calculator to solve the equation in part (a) graphically. What are the
solutions, to the nearest hundredth?
c. What are the speeds of the boats? Round your answers to the nearest hundredth.
46. Without graphing or using substitution or elimination, determine how many solutions the system has and explain why.
2y  x  5
3x  6y  8
47. 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.
48. 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. What is not a possible amount he could earn in a single
week? Explain.
49. Divide.
2x 4  3x 3  5x  1  2x  1
50. Find the discriminant. How many/what type of solutions are there?
3x 2  5x  2  0
51. Find f(2) – g(-1) if f (x)  x  3 and g(x)  5x  7 .
52. Graph the inequality.
y < -3x + 5


53. Solve the equation.
2(x  2)  3x  5x  4  x
54. Find an equation that represents the situation: At 10:00 am the temperature is 53 degrees. At 2 :00 pm the temperature is
65 degrees.
55. Using the graphed constraints, find the values of x and y that maximize
13. Graph the function y  2 x  3.

.