Algebra 1 Enriched- Midterm Review
Know all vocabulary, pay attention to the highlighted words in the text, and understand the various types of directions in each of the sections of the textbook. Practice with old homework problems, worksheets, and quiz and test problems. DO NOT ONLY study this review packet. DO NOT WAIT until the last night to review. Be prepared to work with integers, fractions and decimals. Prepare: Get pencils, erasers, calculator!
Chapter 1
Variables
Exponents and Order of Operations
Types of Real Numbers
Operations on real numbers: addition, subtraction, multiplication, division, matrices
Properties of real numbers:
- Distributive
- Commutative
- Associative
- Identity
- Inverse
- Multiplication of Zero
- Multiplication of
Graphing points on a coordinate plane (and the vocabulary associated with it)
Review exercises start on page 67
Chapter 2
Solving one-step, two-step, and multi-step equations, equations with variables on both sides and associated word problems (area, consecutive integer, rate-time-distance)
Formulas and literal equations- be able to solve an equation for one of the letters in it
Measures of central tendency- mean, median, mode, range
Stem-and-leaf plots
Review exercises start on page 125
Chapter 3
Solve and graph inequalities in one variable [remember to flip the arrow when multiplying/dividing by a negative number]
Solve word problems involving inequalities
Solve and graph compound inequalities (and-sandwich/ or-oars of a boat)
Solve and graph absolute value inequalities
Review exercises start on page 175
Chapter 4
Find ratios and rates, including unit rate
Convert rates (dimensional analysis)
Work with proportions
Find parts of similar figures
Use proportions with percent problems
Use
Change from percent to fraction to decimal and back again
Find percent of change (increase or decrease)
Review exercises start on page 227
Chapter 5
Relate graphs to events
Identify relations and know what makes it a function
Find domain and range from a set of ordered pairs, a graph, a mapping, a chart
Use function notation []
Employ the vertical line test for a function
Model functions using rules, tables and graphs
Graph linear, quadratic (parabolas) and absolute value (v) functions
Direct variation
Describe patterns
Know when a pattern is arithmetic vs. geometric
Use the formulasand
Review exercises start on page 275
Chapter 6 (6.1-6.5)
Find rate of change
Find slope from a graph or two ordered pairs
Know about positive, negative, zero and undefined slopes
Find and use the slope-intercept form of a linear equation
Use the x- and y-intercepts to graph a line
Write equations in standard form
Find the equation of a line given: two points, one point and a slope, a graph
Know that parallel lines have the same slope and perpendicular lines have slopes that are opposite reciprocals of each other
Review exercises start on page 331
Chapter 7 (1-3)
Solve a system of equations by graphing
Solve a system of equations by substitution
Solve a system of equations by elimination
Review exercises page 387-388 #6-17,20-23
Chapter 1
1. Simplify the expression:
2. Simplify the expression:
3. Name the set(s) of numbers to which -3 belongs.
4. Are whole numbers, integers, or rational numbers the most reasonable for the situation?
The number of desks in a classroom
5. Order the numbers from least to greatest:
6. Simplify the expression:
7. Evaluate the expression for .
8. Simplify the expression:
9. Evaluate the expression for
10. Write an expression for the phrase: -3 times the quantity 9 times a minus 4
11. Simplify the expression:
12. Give a reason to justify each step.
13. Complete the statement.
If the x-coordinate of an ordered pair is negative, and the y-coordinate is negative, the
ordered pair is in Quadrant ______.
14. Describe the trend in the scatter plot.
Chapter 2
15. Solve and check:
16. Define a variable and write an equation for the situation. Then solve.
A customer went to a garden shop and bought some potting soil for $12.50 and 6 shrubs. If
the total bill was $71.00, what did the shrubs cost?
17. In the triangle, the measure of angle A = measure of angle B. Find the value of x.
18. Find the value of x. (Hint: The sum of the measures of the angles in a triangle is )
19. Solve the equation and check:
20. Solve the equation and check:
21. Solve the equation and check:
22. Solve the equation & check your answer: 3m – 4 = -9 + m
23. Write and solve an equation for the situation:
A buyer for a clothing store is interested in ordering a certain sweater. Company A charges $15.00 per sweater plus a $30.00 shipping and handling fee per order. Company B charges $12.75 per sweater plus a $75.00 shipping and handling fee per order. How many sweaters must the buyer purchase to justify using Company B?
24. Determine whether the equation is an identity or whether it has no solution:
8x + 4x – 15 = -11 + 3(4x – 1)
25. Solve the equation. If the equation is an identity, write identity. If it has no solution, write no solution:
4(x – 4) = -16 + 4x
26. The sum of four consecutive odd integers is -56.
a. If n is the first odd integer, write an expression for the second odd integer.
b. Write the expressions for the third and fourth odd integers.
c. Use these expressions to write and solve an equation to find the four integers.
27. Solve the equation for x: dx + fy = g
28. The formula for converting degrees Fahrenheit (F) to degrees Celsius (C) is .
a. Transform the formula to find Fahrenheit temperature in terms of Celsius.
b. Find the Fahrenheit temperature when the Celsius temperature is .
29. Find the mean, median, mode, and range of: 3, 30, 30, 27, 13, 30, 21, 30.
30. The data below show the average daily high temperature for Fargo, North Dakota for each month of the year. Use a stem-and-leaf plot to organize the set of data: 65, 61, 56, 67, 77, 74, 53, 84, 70, 59, 63, 81
31. Determine whether each number is a solution of the given inequality: x(7 – x) > 8
a. 8b. -1c. 2
32. Write an inequality for the graph:
33. Tina can type at least 60 words per minute. Write and graph an inequality to describe this statement.
34. Rewrite the inequality so that the variable is on the left. Then, graph the solution.
35. Graph the inequality from the given description: x is at most -1
36. Tell what you must do to the first inequality in order to get the second.
37. Solve the inequality: x – 2 – 2(x – 8) > 0
38. Write an inequality that represents the situation & graph the solution: all real numbers between -5 and 5
39. Solve the inequality & graph the solution:
40. Write a compound inequality that the graph could represent:
41. Solve the equation. If there is no solution, write no solution.
42. Write an absolute value equation that has the given values as solutions: 7 and 11
43. Solve & graph the solution:
Chapter 4
44. Complete the statement: 47 ft/hr = _____ mi/wk
45. A worker on an assembly line takes 6 hours to produce 21 parts. At this rate, how many
parts can she produce in 12 hours?
46. Solve the proportion
47. Find the missing side, x, of the similar figures.
48. Use a percent equation to solve: What percent of 24 is 6?
49. Use a percent proportion to solve: What is 42% of 800?
50. Write and solve a percent proportion to find the whole, if 12 is 20% of it.
51. A ski club planned a trip to Squaw Valley, and 6 of the members are going. If this is 10%
of the club, how many members are in the ski club?
52. Rose earns 6.7% commission on her camera sales. In January, she earned $217.08 in
commissions. What were her sales for the month?
53. Use the formula for simple interest, I = prt. Find the missing value.
t = _____, I = $318.33, p = $535, r = 8.5%
54. Find the percent of change and describe it as an increase or decrease. Round to the nearest
percent. 5.35 lb to 6.6 lb
55. The circulation of a newsletter decreased from 7,900 to 6,162. Find the percent of decrease
in circulation to the nearest percent.
Chapter 5
56. Label each section of the graph.
57. Find the domain and range of the relation
58. Plot the points Use the vertical-line test to determine whether
the relation is a function.
59. Use the vertical line test to determine whether the graph represents a function.
60. Use a mapping diagram to determine whether the relation is a function.
{(– 8, 3), (– 5, 3), (0, 3), (2, 3)}
61. Determine whether the relation is a function. If the relation is a function, state the domain and range.
x / y– 2 / 1
– 8 / 4
1 / 5
– 2 / 2
62. Evaluate the function for x = – 30.
f(x) = x + 2
63. Find the range of the function rule y = 2x + 8 for the domain.
{ – 5, – 4, – 2, 1, 5}
64. Graph the function. y = –
65. Graph the function. f(x) = 2 – x2
66. An employee receives a weekly salary of $250 and an 8% commission on all sales.
a. Write a rule to describe the function.
b. Find her earning for a week with $1556 total sales.
67. Is the equation a direct variation? If it is, find the constant of variation.
68. Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.
9, 13, 17, 21, . . .
69. Is the given sequence arithmetic or geometric? Justify your answer.
3, 9, 27, 81, . . .
70. Find the third, sixth, and eighth terms of the sequence.
A(n) = 12.2 + (n – 1)(–3.4)
71.Write a rule for the given sequence: 3, -12, 48, …
72. The rate of change is constant in the graph. Find the rate of change. Explain what the rate of change means for the situation.
Chapter 6
73. Find the slope of the line that passes through the pair of points.
,
For questions 74 and 75: State whether the slope is zero or undefined.
74.
75. (– 8, – 7), (– 2, – 7)
76. Tell whether each statement is true or false. If false, give a counterexample. Justify your answer.
a. All vertical lines have the same slope.
b. The slope of a line that passes through Quadrant IV must be positive.
c. A line with slope zero must pass through the origin.
77. Find the slope and y-intercept of the equation.
y =
78. Write the slope-intercept form of the equation for the line.
79. Use the slope and y-intercept to graph the equation.
y =
80. Is the ordered pair on the graph of the given equation?
(2, – 4); y =
81. Find the x- and y- intercepts of the equation.
3x – 6y = 24
82. Graph the equation using x- and y- intercepts.
– 3x – 8y = 24
83. For each equation, tell whether its graph is a horizontal or a vertical line.
a.
b.
84. Write the equation in standard form.
85. Graph the equation.
86. A line passes through the given points. Write an equation for the line in slope-intercept form.
Then rewrite the equation in standard form.
(2, -4), (5, -6)
87. Find the slope of a line parallel to the graph of the equation.
88. Are the graphs of the pair of lines parallel, perpendicular, or neither? Explain
89. Write an equation for the line that is parallel to the given line and passes through the given point.
90. Find the slope of a line perpendicular to the graph of the equation.
91. Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.
92. Tell whether each statement is true or false. Explain your choice.
a. Two lines with negative slopes can be perpendicular.
b. Two lines are perpendicular if the product of their slopes is 1.
Chapter 7
93. Is (-1, 2) a solution of the system? Explain
94. Is (-4, 3) a solution of the system? Explain.
95. Solve by graphing. Check your solution.
Graph the system. Tell whether the system has no solution or infinitely many solutions.
96.
97.
98. Without graphing, decide whether the system has one solution, no solution, or
infinitely many solutions. Explain.
Solve the system using substitution.
99.
100.
Solve the system using elimination.
101.
1.5400
2.429
3. Integers, rational numbers
4.Whole Numbers
5.
6.27
7.-8
8.16
9.
10.
11.
12.a. Commutative Prop. Of Mult.
b. Associative Prop. Of Mult.
c. Multiply w/ parentheses first
d. Simplify
13.III
14.Negative correlation
15.72
16.p = price of shrubs
17.46.5
18.
19.
20.3
21.
22.
23.21
24.No Solution
25.Identity
26.a.
b. and
c.
the integers are −11, −13, −15, & −17
27.
28.a.
b.
29.range = 27, mean = 23
Median = 28.5, and mode = 30
30.
31.a. no
b. no
c. yes
32.m < −3
33.x ≥ 60
34.x ≥ 3
35.
36.Both sides of the first inequality mustbe multiplied by −6 to get the second.
37.x < 14
38.−5 < x < 5
39.0 ≤ x < 20
40.x ≤ −7 or x > 5
41.r = −7 or r = 21
42.Sample answer:
43.x −2 or x > 1
44.1.5
45. 42
46.40
47.
48.25%
49.336
50.60
51.60 members
52.$3240
53.7 years
54.23%, increase
55.22%
56.Answer may vary
A – speed is about to slow for some time, as if skating uphill
B – gaining speed quickly, as if beginning a downhill descent
C – high speed briefly, as if just skating down a hill
D – constant speed for some time, as if skating on an even surface
57.
58.the relation is not a function
59.Function
60.
It is a function
61.The relation is not a function
62.−23
63.{−2, 0, 4, 10, 18}
64.
65.
66.a. f(p) = 0.08s + 250
b. $374.48
67.
68.Add 4 to the previous term; 25, 29
69.Geometric; common ratio = 3
70.5.4, −4.8, −11.6
71.
72.the balloon ascends 100 ft/sec
73.10
74.Undefined
75.0
76.a. True, the slope of any vertical line is undefined
Continuation of #76
b. False, the slope of y = −x passes through Quadrant IV and it has a negative slope
c. False, unless the line is y = 0, it will pass above or below the origin
77.
78.y = 2x + 5
79.
80.yes
81.x-intercept:8
y-intercept: −4
82.
83.a. horizontal
b. vertical
84.4x – 3y = −8 or −4x + 3y = 8
85.
86.; 2x + 3y = 8 or -2x – 3y = -8
87.3
88.parallel; the slopes are equal
89.x
90.
91.Neither
92.a. False, for two lines to be perpendicular one slope must be the opposite reciprocal of the other. Therefore, one line must have a positive slope.
b. False, two lines are perpendicular if the product of their slopes is −1.
93.Yes, (−1, 2) makes both equations true.
94.No, (−4, 3) is not a solution to the system. It is not on y = -3
95.(8, 1)
96.No Solution
97.Infinitely Many solutions
98.The system has one solution., A system of linear equations has no solution when the equations are of parallel lines and infinitely many solutions when the equations are of the same line. The slopes of the lines are not equal, so neither case applies.
99.(−6, −24)
100.(2, -2)
101.(15,-10)