Algebra 1
1st Semester Exam Review
Name _______________________________
I. Number Sense
1. Which of the following is equivalent to the expression x(y – z) for real numbers x, y, and z?
a. xy – z
b. xy – xz
c. x + y –x + z
d. x – y + x – z
2. For all real numbers x, y, and z, which of the following expression is equivalent to x + y if z = 0?
a. x + y – z
b. z ● (x – y)
c. xz + y
d. x ● ( y + z)
3. If a = 0, which of the following expressions has a value of 0?
a. a ● (1 – 3 + 2)
b. (a + 2) ● (4 – 3)
c. a + (2 ● 3 + 4)
4. If a is a real number greater than 2, and b is greater than a, which of these expressions has the GREATEST value?
a. ab
b. a – b
c. a + b
d. ab
5. What is the result when 4x + 9 is subtracted from 2x – 7?
6. Which number is not irrational?
a.
15
b.
23.7
c.
4
d. 23.542718…
7. Which number is an integer?
a.
43
87
b.
2
7
c. 
d. 0
8. What number property does the following example show? 35 + 0 = 35
a. Additive Inverse
b. Additive Identity
c. Associative property
d. Commutative prop
9. Which of the following shows the distributive property?
a. 5(9+8) = (59) + (58)
b. 1623 = 2316
d. 296  1 = 296
c. (12+7)+3=12+(7+3)
10. Peter Rose ended his career with 67 more hits than Ty Cobb. Through the 2004 season, former Mississippi State
Bulldog, Rafael Palmeiro, had 1267 fewer hits than Ty Cobb had. How many more hits does Pete Rose have than Rafael
Palmeiro?
II. Matrices
11. An Internet store sells music CDs and music DVDs. The prices are shown in the chart below. Which matrices can be
used to organize the prices and then show an increase of $0.50 for each CD and $1.00 for each DVD?
12. A pair of hardware stores keeps track of the number of items sold in matrix form as shown below.
What is the total number of tools sold at Store 2 for May and June?
13. Matrix B is a result of multiplying matrix A by some scalar. What is the value of y in matrix B?
 3  9
A

 5 8 
y 
 12.6
B
 33.6
 21
1 2
5
and N  

3 4 
7
14. If M  
6
find M + N and M – N.
8
III. Equations and Inequalities
15. What is the solution of the following equation?
3(a – 10) = 2(6 – 2a)
16. What is the solution of the following equation?
1
2 3
x 
2
3 4
17. Sheryl solved the equation below by using the steps shown.
Given: 5(2a – 4) +2 = 8
Step 1: 10a – 20 + 2 = 8
Step 2:
10a – 18 = 8
Step 3:
10a = 10
Step 4:
a=1
Which step contains Sheryl’s first mistake?
a. step 1
b. step 2
c. step 3
18. Solve and graph the following inequality.
–(x + 5) < –1
19. Solve the following equation for x.
x  5 3x  1

3
5
20. What is the SUM of the solutions to the equation x  2  6  4 ?
21. What is the product of the solutions to the equation x  5  1  2 ?
22. Solve a graph the open sentence below.
x  2 1
d. step 4
23. In Miss Mann’s class, you need a score, s, of at least 80 in order to pass a test. Which inequality shows the correct
translation of a passing score?
a. s > 80
b. s  80
c. s < 80
d. s ≤ 80
24. What are the solutions to the following inequality?
b  6  10  15
25. The product of -6 and a number, x, decreased by 9, is greater than -33. What is the number?
a. x > -4
b. x < -4
c. x > 4
d. x < 4
IV. Relations and Functions
26. Which of the following sets represent functions?
F = {(0, 1), (0, 2), (0, 3)}
G = {(2, 1), (3, 1), (4, 1)}
H= {(–1, 2), (0, 4), (2, –1), (–1, 3)}
27. The population of a certain bacteria after t hours can be approximated using the exponential function
p(t) = 22t – t. What is the approximate population of the bacteria after 2 hours?
28. Given the function g(x) = 2x and the domain is {0, 2, 4}, what is the range?
29. Given the function f(x) = x – 1 and the range {–1, 1, 2}, what is the domain?
30. Given the table of values below, find the rule of the function it represents.
x
-1
0
1
2
f(x)
2
1
0
-1
a. f(x) = x + 1
b. f(x) = –x + 1
c. f(x) = –x2 + 1
31. Given the table of values below, find the rule that could represent the nth term.
n
f(n)
1
4
2
7
3
10
a. f(n) = 3n + 1
4
13
b. f(n) = 4n
c. f(n) = 5n – 1
32. Which of the following graphs does not represent a function?
a.
b.
33. Find the domain, range, and inverse of the relation below.
{(0, 1), (4, 5), (-8, 7), (3, 9)}
domain =
range =
inverse=
c.
d. f(x) = x2 – 1
34. A commercial printer uses the following function to calculate customer cost for p, the number of pieces printed?
f(p) = 75 + .02p
What would be the customer cost for 2,000 pieces printed?
35. What is the domain and range of the following graph?
V. Graphing Linear Equations
36. Which of the following equations is a linear equation?
a. y = │x + 2│
c. y 
b. y = 2x2 + 1
1
x 3
2
d. y = 3xy
37. If the point (b, 3b) lies on the line represented by 3x + 2y = 6, what is the value of b?
38. What is the slope and y-intercept of the linear equation x – 4y = –12?
39. Sketch the graph of the following equations below.
x+3=5
y – 5 = –3
x  2y  8
40. What is the slope of the line containing the two points (4, –7) and (–4, 7)?
41. Which of the following ordered pairs is a solution to the equation 4x – 3y = 13?
a. (–3, 4)
b. (4, 1)
c. (–3, 5)
d. (–5, 3)
42. Find the slope and the y intercept of the linear equation 3x – 4y = 12.
43. Find the slope of the wire formed by the line segment AB.
A
15
5
B
10
44. Coach Baughman is taking his wife on a date to Old Venice. Unfortunately, his car is broken down so he will have to
take a cab. The cab fare has a service charge of $3.15 plus $.15 per mile. Write an equation to help Coach Baughman
calculate his total cab fare cost.
45. Use the graph below to answer the following questions:
a.) For which ten-year period was the rate of change of the population of Green Bay the greatest?
b.) For which ten-year period was the rate of change of the population of Green Bay the least?
VI. Graphing Linear Inequalities
46. Graph the inequality 2x – 3y < 9.
48. What inequality is represented by the graph shown below?
47. Graph the inequality x – 2y ≥ 2
VII. Formulas
49. Solve the following equation for y.
ay + b = c
50. The formula for finding the area of a rectangle is A = bh. Solve the formula for b in terms of the area and height.
51. The formula for finding the perimeter of a rectangle is P = 2L + 2w. Solve the formula for w in terms of the
perimeter and length.
52. On a map, the library is located at (5, –1), the school is located at (7, 8), and your house is located at (3, 4). You
walked from your house to the school. After school, you walked to the library to complete a project. Then, you walked
back home from the library. If one grid unit on the map represents 0.5 miles, how far did you walk?
53. Find the midpoint of the line segment with endpoints (–17, 22) and (13, 40).
54. Line segment AB has a midpoint at (5, –3). If endpoint A is located at (–2, 8), where is B located?
55. A missing hiker is located at point B(6, 2) on the coordinate plane. A rescue helicopter at point A(-6, 7) is sent to
pick the hiker up and transport him to the hospital at point C(-4, -6). The helicopter then returns to the helicopter
station at point A.
(a) If the helicopter stops for fuel exactly halfway between the hospital and the helicopter station, at what
coordinates does it stop?
(b) Once the hiker is rescued, how far does the helicopter have to travel to get to the hospital? (1 unit = 2 miles)
VIII. Writing Equations of Lines
56. A line passes through the point (2, –5) and has a slope of 2. What is the equation of the line?
57. What is the equation for the line that passes through (4, 9) and (5, 6)?
58. A line passes through the points (2, –5) and (–1, 4). What is the value of x when y = 7?
59. The speed of a car is given in the chart below as it applies its brakes. If the deceleration is linear, write an equation
that could represent the car’s speed, x, at y seconds.
Time
(sec)
0
1
2
Speed
(mph)
60
45
30
60. Line p is defined by the equation 4x + 2y = 18. Which of the following lines is parallel to line p?
a. y  
1
x 1
2
b. y 
1
x 1
2
c. y = 2x –2
d. y = –2x – 1
61. Write an equation for the line that is perpendicular to y = 2x + 3 and passes through the point (2, 1).
62. Write and equation for the line that is parallel to y = 2x + 3 and passes through the point (2, 1).
IX. Scatter Plots
63. Determine what is happening according to the given graph.
People Entering Amusement Park
1000
900
Number of People
800
700
600
500
400
300
200
100
10
20
30
40
50
60
70
80
90 100
Time (minutes)
64. Determine what is happening according to the given graph.
Strawberries Picked
100
90
Quarts Picked
80
70
60
50
40
30
20
10
1
2
3
4
5
6
Time (hours)
7
8
9
10
Use the following scatter plot to answer #65 and #66.
Domestic Traveler Spending in the U.S., 1987-1999
450
425
400
375
350
325
300
275
250
225
1986
1988
1990
1992
1994
1996
1998
2000
Year
Source: The World Almanac, 2003
65. What is the equation for the line-of-best-fit?
66. Predict the amount of spending for domestic travelers in 2010.
Use the following table to answer #67 and #68.
Year
Sales (millions)
Sport Utility Vehicle Sales in the U.S. (1991-2001)
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
0.9
1.2
1.4
1.6
1.8
2.2
2.5
2.8
3
3.4
3.8
67. Let x represent the number of years since 1990. Let y represent the sport utility vehicle sales in millions. Write the
slope-intercept form of the equation for the line of fit using the points representing 1992 and 2000.
68. Predict the number of sport utility vehicle sales in 2005.
X. Systems of Equations
69. What is the solution to the system of equations : x = 4y
4x – y = 75
70. What is the product of the coordinates of the solution to the system represented by 4x + y = 12 and –2x – 3y = 14?
71. What is the solution to the system represented by 2x = y + 6 and 4x – 2y = 12?
72. Monica and Max Gordon each want to buy a scooter. Monica has already saved $25 and plans to save $5 per week
until she can buy the scooter. Max has $16 and plans to save $8 per week. What system can be written to represent
this situation?
Algebra I
Concepts/Definitions for 1st Semester Exam
Define the following terms in your own words.
Expression
Equivalent
Matrix
Corresponding Elements
Scalar
Solution
Equation
Inequality
Absolute Value
Relation
Function
Domain
Range
Vertical Line Test
Slope
Linear Equation
x-intercept
y-intercept
Slope-Intercept form
Rate of Change
Parallel
Perpendicular
Correlation
Line-of-best-fit
Real Number
Rational #
Irrational #
Integer
Whole #
Natural #
Commutative
Associative
Distributive
Zero Property
Additive Identity
Additive Inverse
Multiplicative Inverse
Multiplicative Identity
You should know how to do the following concepts:
 Apply properties of real numbers to simplify algebraic expressions.
 Use matrices to solve mathematical situations and problems.
 Solve, check, and graph multi-step linear equations and inequalities in one variable, in both mathematical and
real-world situations.
 Determine whether a relation is a function
 Identify domain and range
 Analyze the relationship between x and y values
 Graph and analyze linear functions
 Graph and analyze absolute value equations
 Write, graph, and analyze inequalities in two variables.
 Apply slope to determine if lies are parallel or perpendicular
 Solve problems that involve interpreting slope as a rate of change.
 Apply the appropriate formula to determine length, midpoint, and slope of a segment in a coordinate plane
 Draw conclusions and make predictions from scatter plots
 Use linear regression to find the line-of-best-fit from a given set of data.
 Solve systems of equations and be able to set up a system from a word problem.