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Algebra Chapter 1 Summative Review ('18-'19)
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Terms in this set (70)
1. Translate into symbols:
double a number
double a number
2n
2. Translate into symbols:
the sum of a number and 6
the sum of a number and 6
n+6
3. Translate into symbols:
a number increased by 5
a number increased by 5
n + 5
4. Translate into symbols:
a number cubed
n³
5. Translate into symbols:
12 subtracted from a number
12 subtracted from a number
n - 12
6. Translate into symbols:
a number squared
a number squared
n²
7. Translate into symbols:
the difference between a number and 10
the difference between a number and 10
n - 10
8. Translate into symbols:
5 divided by a number
5 divided by a number
5/n
9. Translate into symbols:
6 less than a number
6 less than a number
n - 6
10. Translate into symbols:
the product of a number and 8
the product of a number and 8
8n
11. Translate into symbols:
the quotient of 12 and a number
the quotient of 12 and a number
12/n
12. Translate into symbols:
triple a number
triple a number
3n
13. Translate into symbols:
a number decreased by 9
a number decreased by 9
n - 9
14. Translate into symbols:
half of a number
half of a number
0.5n OR ½n OR n/2
15. Stephanie adds pennies, nickels, and quarters to a scale. Each penny has a mass of 2.5 grams, each nickel has mass 5 grams, and each quarter has mass 5.7 grams.
Write an algebraic expression to model total weight of the coins on the scale, where x is number of pennies, y is number of nickels, and z is number of quarters Stephanie has placed on the scale.
2.5x + 5y + 5.7z
16. Mr. Martinez orders 250 keychains printed with his athletic team's logo and 500 pencils printed with their web address. Each keychain costs k dollars, and each pencil costs p dollars.
Write an algebraic expression that represents the total cost for his order.
250k + 500p
17. Write the algebraic expression that represents the answer to the given question.
Mr. Bailey purchased groceries that cost d dollars. He paid with a $20 bill. How much change he will receive?
Change he will receive:
20 - d
18. Write the algebraic expression that represents the answer to the given question.
6 of your friends earn a total of d dollars by selling candy bars. They decide to split this money evenly. How much money will each person get?
Money each person will get:
d/6
19. Write the algebraic expression that represents the answer to the given question.
Your mother gives you $10 per week. If you save this money, how much money will you have after w weeks go by?
Total money after w weeks go by:
10w
20. Write the algebraic expression that represents the answer to the given question.
Your mother gives you x number of apples, and then you eat 3 of them. How many apples are left?
Number of apples left:
x - 3
21. You have $20 to spend on rides at the fair, and each ticket costs $1.25.
Suppose t is the number of tickets you purchased. Write an algebraic expression to represent the amount of money you will have LEFT after purchasing t tickets.
Amount of money LEFT after purchasing t tickets:
20 - 1.25t
22. Henry places x marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression 5x+12.
What part of the expression represents the weight of the empty bucket?
Weight of empty bucket:
12
23. Henry places x marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression 5x+12.
What part of the expression represents the weight of each marble?
Weight of each marble:
5
24. Henry places x marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression 5x+12.
What part of the expression represents the total weight of ALL the marbles in the bucket?
Weight of ALL the marbles in the bucket:
5x
25. Henry places x marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression 5x+12.
What part of the expression represents the number of marbles in the bucket?
Number of marbles in the bucket:
x
26. What property is demonstrated by the given equation?
x + 0 = x
Associative (I can regroup)
Commutative (I can rearrange)
Distributive (I can rainbow multiply)
Identity (I can add 0, or multiply by 1)
Zero Property of Mult. (0×ANYTHING = 0)
x + 0 = x
Identity (I can add 0...)
27. What property is demonstrated by the given equation?
1x = x
Associative (I can regroup)
Commutative (I can rearrange)
Distributive (I can rainbow multiply)
Identity (I can add 0, or multiply by 1)
Zero Property of Mult. (0×ANYTHING = 0)
1x = x
Identity (I can multiply by 1...)
28. What property is demonstrated by the given equation?
3(2x+5) = 6x + 15
Associative (I can regroup)
Commutative (I can rearrange)
Distributive (I can rainbow multiply)
Identity (I can add 0, or multiply by 1)
Zero Property of Mult. (0×ANYTHING = 0)
3(2x+5) = 6x + 15
Distributive (I can rainbow multiply...)
29. What property is demonstrated by the given equation?
3 + 2x + 5 = 3 + 5 + 2x
Associative (I can regroup)
Commutative (I can rearrange)
Distributive (I can rainbow multiply)
Identity (I can add 0, or multiply by 1)
Zero Property of Mult. (0×ANYTHING = 0)
3 + 2x + 5 = 3 + 5 + 2x
Commutative (I can rearrange...)
30. What property is demonstrated by the given equation?
3 + (5 + 2x) = (3 + 5) + 2x
Associative (I can regroup)
Commutative (I can rearrange)
Distributive (I can rainbow multiply)
Identity (I can add 0, or multiply by 1)
Zero Property of Mult. (0×ANYTHING = 0)
3 + (5 + 2x) = (3 + 5) + 2x
Associative (I can regroup...)
31. What property is demonstrated by the given equation?
3(2x) = (3*2)x
Associative (I can regroup)
Commutative (I can rearrange)
Distributive (I can rainbow multiply)
Identity (I can add 0, or multiply by 1)
Zero Property of Mult. (0×ANYTHING = 0)
3(2x) = (3*2)x
Associative (I can regroup...)
32. What property is demonstrated by the given equation?
(2x + 1)3 = 3(2x + 1)
Associative (I can regroup)
Commutative (I can rearrange)
Distributive (I can rainbow multiply)
Identity (I can add 0, or multiply by 1)
Zero Property of Mult. (0×ANYTHING = 0)
(2x + 1)3 = 3(2x + 1)
Commutative (I can rearrange...)
33. Simplify.
7(-2x)
Given: 7(-2x)
Answer: -14x
34. Simplify.
7 + (x - 2)
Given: 7 + (x - 2)
Answer: x + 5
35. Simplify.
7(x - 2)
Given: 7(x - 2)
Answer: 7x - 14
36. Simplify.
-7(x - 2)
Given: -7(x - 2)
Answer: -7x + 14
37. Simplify.
(2 - x)(-7)
Given: (2 - x)(-7)
Answer: -14 + 7x
OR 7x - 14
38. Factor. Write your answer as a product, using a whole number greater than 1.
15x + 40
Given: 15x + 40
Factored: 5(3x + 8)
39. Simplify.
7 + 8r + 5r² + 9r + 6 + 4r²
Given: 7 + 8r + 5r² + 9r + 6 + 4r²
Answer: 9r² + 17r + 13
40. Simplify.
-6 + 9(2r - 3)
Given: -6 + 9(2r - 3)
Step 1: -6 + 18r - 27
Answer: -33 + 18r
OR 18r - 33
41. Simplify.
-12g + 8 + 2(3g + 5)
Given: -12g + 8 + 2(3g + 5)
Step 1: -12g + 8 + 6g + 10
Answer: -6g + 18
OR 18 - 6g
42. Simplify.
3(4y² + 5) - 8y² + 7y
Given: 3(4y² + 5) - 8y² + 7y
Step 1: 12y² + 15 - 8y² + 7y
Answer: 4y² + 7y + 15 (terms in any order)
43. A shipping company charges a cost per pound plus a fixed fee to ship a package. The total cost, y, in dollars, of shipping x pounds is modeled by the equation y=1.99x+2.99
What is the fixed fee charged by the shipping company?
Given: y=1.99x+2.99
Fixed fee is $2.99
44. A shipping company charges a cost per pound plus a fixed fee to ship a package. The total cost, y, in dollars, of shipping x pounds is modeled by the equation y=1.99x+2.99
What does the shipping company charge per pound?
Given: y=1.99x+2.99
$1.99 charged per pound
45. A shipping company charges a cost per pound plus a fixed fee to ship a package. The total cost, y, in dollars, of shipping x pounds is modeled by the equation y=1.99x+2.99
If a package weighs 4 pounds, what is the total shipping cost?
Find shipping cost for a package that weighs 4 pounds.
Calculations: $1.99(4) + $2.99
Answer: $10.95
46. The X-values "used" by the given relation or function.
Domain or Range?
Domain (x-values)
47. The Y-values "used" by the given relation or function.
Domain or Range?
Range (y-values)
48. The set of all first elements in a list of ordered pairs.
Domain or Range?
Domain (x-values in an (x, y) ordered pair)
49. The set of all values associated with the vertical axis in the coordinate plane.
Domain or Range?
Range (y-axis values)
50. The set of all values associated with the horizontal axis in the coordinate plane.
Domain or Range?
Domain (x-axis values)
51. The set of all second elements in a list of ordered pairs.
Domain or Range?
Range (y-values in an (x, y) ordered pair)
52. For a relation to be considered a function, each X-VALUE can be paired with only ONE _____________.
Y-value
(To be a function, each X-VALUE can be paired with only one Y-VALUE)
53. For a relation to be considered a function, each DOMAIN value can be paired with only ONE ________________.
Range
(To be a function, each DOMAIN VALUE can be paired with only one RANGE VALUE)
54. For a relation to be considered a function, each INPUT can be paired with only ONE ______________.
Output
(To be a function, each INPUT can have only one possible OUTPUT)
55. The expression 50 + 12x + 2y gives total monthly cost, in dollars, of a family cell phone plan if x is number of phone lines used and y is the number of gigabytes (GB) of data used. The cost also includes a monthly base fee that is the same no matter how many phones or GB of data are used.
What is the base fee?
What is the cost per GB of data used?
What is the cost per phone line used?
Base fee - $50
Cost per GB of data used - $2
Cost per phone line used - $12
56. Is k= -3 a solution?
YES / NO
72 = 2(k-2)²+22
Is k = -3 a solution?
72 = 2(-3-2)²+22
72 = 2(-5)²+22
72 = 2(25)+22
72 = 50+22
72 = 72
YES.
57. Is b=36 a solution?
YES / NO
|-5 |+√(b) = 1
Is b=36 a solution?
Review: absolute value = distance from zero! Always (+)!
|-5 |+√(36) = 1
5 + 6 = 1
11 = 1
NO.
58. What are the domain and range of this relation?
(8, 13)
(4, 6)
(-19, 8)
(11, 1)
(12, 0)
(10, 4)
Domain: {8, 4, -19, 11, 12, 10}
59. FLIP THE CARD TO SEE QUESTION.
Answer:
Domain: {-5, 0, 1, 2, 4, 5}
Range: {-5, -4, -2, 0, 1, 4}
Question: What are the domain and range of this relation?
60. FLIP THE CARD TO SEE QUESTION.
Answer: The FIRST one (purple).
Explanation: In this table, none of the X-values are repeated -- each x-value is paired with one y-value.
Question: Which of these relations is a function?
61. FLIP THE CARD TO SEE QUESTION.
Answer: YES.
Explanation: Each domain value is paired with only ONE range value.
Question: Look at this mapping diagram. Is this relation a function?
62. FLIP THE CARD TO SEE QUESTION.
Answer: NO.
Explanation: The domain value of 12 is paired with MORE THAN ONE range value.
Question: Look at this mapping diagram. Is this relation a function?
63. FLIP THE CARD TO SEE QUESTION.
Answer: NO.
Explanation: The relation FAILS the Vertical Line Test. It contains points which line up VERTICALLY with one another (share the same x-coordinate but have different y-coordinates.)
Question: Is this relation a function?
64. FLIP THE CARD TO SEE QUESTION.
Answer: YES.
Explanation: The relation PASSES the Vertical Line Test. It does NOT contain points which line up VERTICALLY with one another (each x-coordinate is paired with only one possible y-coordinate.)
Question: Is this relation a function?
65. Use the given function to find the requested function value.
f(x) = 2x²-5
f(-3) =
Answer: f(-3) = 13
Solution:
f(x) = 2x² - 5
f(-3) = 2(-3)² - 5
= 2(-3)(-3) - 5
= 2(9) - 5
= 18 - 5
= 13
66. Use the given function to find the requested function value.
f(x) = | -3 | + √(x)
f(16) =
Answer: f(16) = 7
Solution:
f(x) = | -3 | + √(x)
f(16) = | -3 | + √(16)
= 3 + 4
= 7
67. Use the given function to find the requested function value.
f(x) = 4x² - 6x
f(3) =
Answer: f(3) = 18
Solution:
f(x) = 4x² - 6x
f(3) = 4(3)² - 6(3)
= 4(3)(3) - 6(3)
= 4(9) - 6(3)
= 36 - 18
= 18
67. Use the given function to find the requested function value.
f(x) = 4x² - 6x
f(-3) =
Answer: f(-3) = 54
Solution:
f(x) = 4x² - 6x
f(3) = 4(-3)² - 6(-3)
= 4(-3)(-3) - 6(-3)
= 4(9) - 6(-3)
= 36 - -18
= 36 + 18
= 54
69. The amount of data used for streaming video content is given by the function f(x)=10x, where x is the number of minutes spent streaming video content, and f(x)is the total MB of cellular data consumed.
Therefore, f(8) = 80.
What does this mean in the context of the problem?
8 minutes spent streaming video content will consume 80 MB of data.
Explanation: We are told x → # of minutes spent streaming video content, so f(8) means x is 8 minutes, therefore 80 is the total MB of cellular data consumed.
70. FLIP THE CARD TO SEE QUESTION.
Answer:
x-column:
Use ANY # EXCEPT -5 or 8
f(x) column:
Use ANY #
Question: What value(s) could be used to complete this table such that f(x) IS a function?
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