Mid-Term Exam Review For Math 1
Friday, December 18, 2015
Math Study Strategies
 Use your notes to study vocabulary terms, formulas, and mathematical properties.
Be sure to include example problems and solutions.
 Stay neat and organized when working through problems. The steps of a problem
should be clear and easy to read.
 Review old homework assignments, paying extra attention to problems that were
answered incorrectly. You don't want to make the same mistakes on the exam.
 Think about the possible test questions. Most math textbooks have a review at the
end of each chapter. Practice solving problems from each section of the review,
including word problems.
 Learn and understand how to use the formulas in a chapter. Applying a formula to
a variety of problems is a good way to memorize it.
 Understand any new definitions or vocabulary words from the lesson.
 Become familiar with the calculator used in class. Use a similar one for homework
assignments and on exams. Understanding how to use the calculator can make a
difficult problem simpler and easier to solve.
 Draw diagrams to help visualize new concepts or complex problems.
 Study with a partner. Explain the steps needed to solve each type of problem.
Discuss how the problems in a chapter are similar and different.
 Review the objectives at the beginning of a chapter or lesson. Practice solving the
types of problems that meet the objectives.
 Review visuals, such as graphs, tables, and diagrams. Be able to identify important
pieces of information and practice creating these visuals.
 Use repetition. Repeat steps and rewrite formulas. Using the same steps or
formulas again and again will make problem solving easier to remember.
 Always read math problems completely before beginning any calculations. If you
"glance" too quickly at a problem, you may misunderstand what really needs to be
done to complete the problem.
 If you know that your answer to a question is incorrect, and you cannot find your
mistake, start over on a clean piece of paper. Oftentimes when you try to correct
a problem, you continually overlook the mistake. Starting over on a clean piece of
paper will let you focus on the question, not on trying to find the error.
Foundations of Algebra
 1.1 Variables and Expressions
 1.2 Order of operations & Evaluating Expressions
 1.3 Real numbers and the Number Line
 1.4 Algebraic Properties
 1.5 Adding and Subtracting Real Numbers
 1.6 Multiplying and Dividing Real Numbers
 1.7 Distributive Property
Solving Equations
 3-2 Solving Equations by Using Addition and Subtract
 3.3 Solving Equations by Using Multiplication and Division
 3-4 Solving Multi- Step Equations
 3-5 Solving Equations with Variables on both Sides
 3-6 Ratios and Proportions
 3-7 Percent of Change
 3-8 Solving Literal Equations
Solving Inequalities
 2.1 Solving Inequalities by Addition and Sub
 2.2 Solving Inequalities by Multiplication and Division
 2.3 Solving Multi-Step Inequalities
 2.4 Solving Compound Inequalities
 2.5 Solving open Sentences Involving Absolute Value
Systems of Equations
 4-1 Solving Systems of Equations -- (Substitution)
 4-2 Solve Systems of Equations by Elimination
 4-3 Elimination Using Multiplication
Linear Functions
 5-1 Graphing Linear Equations
 5-2 Solve Linear Equations by Graphing
 5-3 Slope and Rate of Change
 5-4 Slope and Direct Variation
 5-5 Arithmetic Sequence
1. Graph 3x – y = 1.
1.
2. Solve 4x + 9 = 4x + 13.
2. _________________________
1
3. Find the value of r so that the line through (2, –3) and (–4, r) has a slope of − 2.
3. _________________________
4. A giraffe can travel 800 feet in 20 seconds. Write a direct variation equation for
the distance traveled in any time.
4. _________________________
5. Find the 25th term of the arithmetic sequence with first term 7 and common
difference –2.
5. _________________________
6. Write an equation of the line whose slope is 2 and whose y-intercept is 9.
6. _________________________
7. Write an equation of the line that passes through (–1, –7) and (1, 3).
7. _________________________
3
8. _________________________
8. Write y – 4 = – 2 (x + 6) in standard form.
9. Write the slope-intercept form of an equation of the line that passes through
(–2, 0) and is parallel to the graph of y = –3x – 2.
9. _________________________
10. The table below shows the distance driven during four different trips and the
duration of each trip. Draw a scatter plot and determine what relationship
exists, if any, in the data. Write an equation for a line of fit for the data.
Time (hours)
1
2
2.5
4
Distance (miles)
50
85
120
180
10. ______________________
11. The table below shows the cost to ride the New York City
subway in various years.
11. _________________________
Year
1985
1987
1990
1994
2000
2007
Subway
Fare
$0.90
$1.00
$1.15
$1.25
$1.50
$2.00
Source: Metropolitan Transportation Authority (MTA)
Use a regression line to estimate the cost of a subway
ride in 2014.
Solve each inequality.
12. 4x – 5 < 7x + 10
12. _________________________
13. 2(5a – 4) – 3(6 + 2a) ≤ 6
13. _________________________
Solve each compound inequality.
14. 5 < 2t + 7 < 11
15. 13 < 4 – 3v or 2v – 14 > 8
14. _________________________
15. _________________________
For Questions 16 and 17, solve each open sentence.
Then graph the solution set.
16. |3b – 5| ≤ 7
17. |w + 5| > 1
18. Use a graph to determine whether the system
x – y = 4 and y = x has no solution, one solution,
or infinitely many solutions.
For Questions 19-22, determine the best method
to solve each system of equations. Then solve the
system.
16. _________________________
17. _________________________
18. _________________________
19. _________________________
19. x + y = 2
y = 2x –1
20. –x – 5y = 7
x+y=1
20. _________________________
21. 3x + y = 26
3x + 3y = 18
22. 4x – 8y = 52
7x + 4y = 1
21. _________________________
22. _________________________
23. Write a verbal expression for 4r + 9.
23. _______________________
24. Write an algebraic expression for the difference of 5 and n cubed.
24. _______________________
25. Evaluate 2x + 5𝑦 2 – 3z if x = 6, y = 4, and z = 7.
25. _______________________
26. Name the property used in the equation 1 = 6n. Then find the value of n.
26. _______________________
For Questions 27-28, simplify each expression.
27. 2𝑡 2 + 5𝑡 2 + 3t
27. _______________________
28. 7(r + 2t) – 5t
28. _______________________
29. 5(4a + b) + 3a + b
29. _______________________
30. Find the solution set for 3b – 4 = 8 if the replacement set is {1, 2, 3, 4, 5}.
30. _______________________
For Questions 31-32, determine whether each relation is a function.
31. _______________________
31. {(1, 5), (2, 4), (3, 5), (4, 9)}
32. x = –2
32. ______________________
33. If f (n) = 6 – 2n, find f (–1).
33. ______________________
34. True or False: A linear graph can have a maximum or a minimum.
34. ______________________
35. Draw a reasonable graph showing the relationship between the temperature
of a pizza as it is removed from an oven and placed on a counter at room
temperature, and time.
35.
36. The sides of an equilateral triangle measure (2x + 4) units.
What is the perimeter?
36. ______________________
37. Translate 𝑚2 – 4 = 2r + 1 into a sentence.
37. ______________________
38. Write a problem based on the given information.
h = the height of a math textbook;
h + 2 = the height of a science textbook
4h + 2 (h + 2)
38. ______________________
Solve each equation.
39. m – 5 = –23
39. ______________________
40. –4 = 8 + k
40. ______________________
𝑎
41. 2 + 9 = 30
41. ______________________
2
42. – 7 x = –16
42. ______________________
43. 5(c + 3) = 15 + 2(2c – 1)
43. ______________________
44. 10(a + 1) – 14a = 9 – (4a – 1)
7
44. ______________________
3
45. 10 = 𝑥 + 1
45. ______________________
For Questions 24 and 25, evaluate each expression if
a = 3, b = 4, and c = 9.
46. 2⎪a – b⎥ + ⎪c⎥
46. ______________________
47. c – b⎪1 – a⎥
47. ______________________
48. Solve ⎪2x – 1⎥ = 5. Then graph the solution set.
48. ______________________
4
20
49. Determine whether and are equivalent ratios.
9
45
Write yes or no.
50. A magazine is on sale for 15% off the original
price. If the original price of the magazine is $4.60,
what is the discounted price?
49. ______________________
50. ______________________
51. ______________________
51. Solve
𝑡−𝑣
𝑟
= k, for v.
52. How many pounds of peanuts costing $3.00 a
pound should be mixed with 4 pounds of cashews
costing $4.50 a pound to obtain a mixture costing
$3.50 a pound?
52. ____________________