Name ______Date ______Period 1 3 4 5 6 7
Semester 1 Exam Study Guide
Answer Key
1. What is the solution to the inequality 10x – 7 3x + 28?
Add 7 to both sides which equals 10x 3x + 35. Subtract 3x from both sides which equals 7x35. Divide both sides by 5; the solution is x 5.
2. Brianna had 5 rolls of dimes and 3 extra dimes. She used the equation to find n, the number of dimes she had altogether. Rewrite this equation so she can use it to find d, the number of dimes in each roll.
To solve for d, subtract 3 from both sides which equals n – 3 = 5d. Divide both sides by 5 which equals n/5 – 3/5 = d.
3. What is the solution to the equation 4x – 7 – 9x = 13 + 5x?
Combine like terms on the left side of the equal sign equaling -5x – 7 = 13 + 5x. Add 7 to both sides which equals -5x = 20 + 5x. Subtract 5x from both sides which equals -10x = 20. Divide both sides by -10; the solution is x = -2.
4. Gale wants to buy some new clothes, but she cannot afford more than $95 before the sales tax is added. The blouses she wants are priced $16 each and the pants she wants are priced $23 each. Write and solve an inequality to be used to determine b, the number of blouses, and p, the number of pants Gale can afford. After solving, draw a graph to represent the solution.
16b + 23p < 95 is the inequality.
5. Use the expression to answer the questions: 5x2 – 4x + 3
i. Name the term(s) of this expression. 5x2, -4x, 3
ii. Name the coefficient(s) of this expression. 5 and -4
iii. Name the constant(s) of this expression. 3
iv. True or False: 2 is the exponent of the term 5x. True
6. The Cross Country Team is sponsoring a bake sale. If their goal is to raise at least $700, how many cakes must they sell at $4.00 each in order to meet that goal?
i. Write an inequality that represents this situation.
4c 700
ii. How many cakes must they sell in order to meet their goal?
4c 700 is the inequality. Divide both sides by 4 which equals c > 175.
iii. Draw the graph of the solution to this inequality.
Draw a number line with 175 on it. Use a closed point shaded to the right.
7. Julia bought a pair of shoes with a price of $150 from the catalog with 7% sales tax and a $10 shipping fee. Calculate:
i. The amount she paid for sales tax 150 times .07 = $10.50
ii. The total amount, including the sales tax and the shipping fee, that Julia paid for the shoes was $180. What was the shipping fee, in dollars? $19.50. She paid $180, subtract $150 for the shoes and $10.50 for the tax, so the shipping is $19.50.
8. Which number completes the following table? How did you determine your answer? Multiply the input by itself to get the output; it can also be written as x2.
Input (x) / 3 / 6 / 9 / 12Output (y) / 9 / 36 / 81 / 144
9. Raul is buying video games and he wants to spend $200 or less on his purchase. The type of games he likes best, racing games, cost $52 each. Write an inequality that shows how many racing games he can purchase.
52g 200
10. What is the solution to the equation 3x + 5(4x – 6) – 8 = 3x – 14?
Compute distributive property to equal 3x + 20x – 30 – 8 = 3x – 14. Combine like terms on the left side of the equal sign to equal 23x – 38 = 3x – 14. Add 38 to both sides to equal 23x = 3x + 24. Subtract 3x from both sides 20x = 24. Divide both sides by 20 to give the solution x = 1.2
Graph the linear equation: Plot -2 on the y-axis. Move up 7 and right 2 and plot the point. Connect the points.
11.
12. List the coordinates of each point:
Set up proportions to solve #12-15.
13. Convert 175 miles to feet. 924,000 feet
14. Convert 80 feet to inches. 9600 inches
15. Convert 350 seconds to minutes. 5.8 minutes
16. Convert 30 minutes to seconds. 1800 sec
17. Convert 108 inches to yards. 3 yds
Write the correct algebraic expression for each phrase.
18. 11 divided by x 11/x
19. triple a quantity decreased by 9 3x - 9
20. ten less a number 10 - x
21. twelve less than a number x - 12
22. seven times the sum of a number and three 7(x + 3)
23. 5 times a quantity divided by 10 5x/10
24. What is the solution to the equation 25 = 2x – 7?
Add 7 to both sides which equals 25 = 2x. x equals 5 since 25 equals 32.
Write an equation for each of the quantities being compared. Remember: is/was means equal.
25.
The length of a rectangle is 20 inches more than double the width.
Variable for length L Variable for width w
L = 2w + 20
26. The value of the exports of Canada is triple the value of the exports of Mexico.
Variable for Canada c Variable for Mexico m
c = 3m
27. The cost of Hannah’s biology book was $15 more than the cost of her history book. The cost of her English book was $5 less than the cost of her history book. (write 2 equations)
Variable for biology book b Variable for history book h Variable for English book e
b = h + 15 e = h = 5
28.
What is the solution to the equation 4x = ?
x = -3
Write the domain and range of the graph below using brackets and inequality notation.
29. Domain [1, 6]
30. Range [43, 67]
31. Domain 1 x 6
32. Range 43 x 67
33. 3x – 2 = 27
Write the equation as x – 2 = 3 since the exponent must equal 3 since 33 = 27. To solve the equation, add 2 to both sides. The solution is x = 5.
34. 108x - 5 = 1,000
Write the equation as 8x – 5 = 3 since the exponent must equal 3 since 103 = 1000. To solve the equation, add 5 to both sides which equals 8x = 8. Divide both sides by 8. The solution is x = 1.
Solve for the bolded letter.
35. w = x + ym
Subtract x from both sides which equals w – x = ym. Divide both sides by y which equals
w/y – x/y = m.
36. p = m- n
Add n to both sides which equals p + n = m. Subtract p from both sides which equals n = m-p.
37. e = fg
Divide both sides by f which equals e/f = g.
38. y = mx+b
Subtract b from both sides which equals y – b = mx. Divide both sides by x which equals
y/x – b/x = m.
39. Luc received $50 from his grandparents for his birthday. He makes $75 each week as a cashier at the supermarket. Since his birthday, he has saved more than enough money to buy a game system that costs $450. How many weeks ago was Luc’s birthday?
The inequality is 50 + 75x 450. Subtract 50 from both sides which equals 75x 400. Divide both sides by 75 which equals x 5.3. Round 5.3 to 6; the solution is 6 weeks.
40. After purchasing the game system, will Luc have any money left over? How do you know?
Luc will have $50 left over. After 6 weeks of working at $75 for 6 weeks, he will have
$450. When adding the $50 he received from his grandparents, he has a total of $500.
41. The starting balance of Adam’s saving account is $575. Each month (m), Adam deposits $60.
Use function notation to write an equation to represent this situation. f(x) = 60m + 575
Name ______Date ______Period 1 3 4 5 6 7
42. What is the form of a linear equation? y = mx + b
43. What does m represent in y=mx+b? slope
44. What does b represent in y=mx+b? y-intercept
45. Which 2 variables don’t change in a linear equation? x and y
46. In the equation y = 2x – 9, what is the m? 2
47. In y = 2x – 9, what is the b? -9
48. In the equation y = -4x +3, what is the m? -4
49. In the equation y = -4x +3, what is the b? 3
50. How do you graph a linear equation? plot the y-intercept. Use the slope to plot the next point.
51. Explain how you would graph the equation y = -3x + 6. Plot 6 on the y-axis. Move down 3 and right 1 to plot the next point. Connect the points.
52. How do you find slope on a graph? Find 2 points on the graph. Moving left to right, move vertically and then horizontally.
53. How do you find the y-intercept on a graph? Find where the graph crosses the y-axis.
54. How do you find slope in a table? Find the change in y and divide by the change in x.
55. How do you find they-intercept in a table? Find zero in the domain; the y-value will equal the y-intercept.
56. How do you find slope in an equation? The coefficient of x
57. How do you find y-intercept in an equation? the b in y = mx + b
Find the m and the b for each table shown below.
x / y0 / 2
1 / 1
2 / 0
x / y
0 / -1
4 / 0
-4 / -2
x / y
0 / -3
2 / -3
4 / -3
x / y
5 / 0
5 / 1
5 / 2
Match the graphs below to one of the equations in the box.
Match each graph to one of the equations in the box.
Match each table to one of the equations in the box.
x / y5 / -1
5 / 0
x / y
0 / 3
4 / 3
x / y
0 / 2
2 / 0