Patterns, Functions and Algebra
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Transcript of Patterns, Functions and Algebra
Patterns, Functions and Algebra
Released SOLs
Notes
• Questions from all released SOLs• 2004 and 2007 questions are labeled as such in
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questions
Which is true for all pairs of values in the table? (SOL 8.14a)
25% 25%25%25%
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1. y = 2x – 22. y = 2x + 23. y = 4x4. y =x +3
What value of y makes y +(4 - 2y) = 2 true? (SOL 8.15)
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1. 02. 23. 34. 4
When 10 is added to the product of 5 and a number, the result is 50. What is the number? (SOL 8.15)
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1. 52. 83. 104. 12
Which graph shows a line thatcontains the points in the table of ordered pairs? (SOL 8.16)
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A.B.
C. D.
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1. A2. B3. C4. D
x y3 10 -2-3 -5
The Vasquez family drove 165 miles in 3 hours. At this same rate, how many miles could they
travel in 8 hours? (SOL 8.17)
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1. 61.8752. 423.33. 4404. 520
A rock that weighed 1.2 pounds on the moon weighed 7.06 pounds on Earth. About how much would an astronaut who
weighs 174 pounds on Earth weigh on the moon? (SOL 8.17)
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1. 14.5 lbs2. 24.65 lbs3. 29.58 lbs4. 1, 023.53 lbs
A car-rental agency charges $38 per day plus $0.21 for each mile driven. Sandra paid $88.40 for renting a car from them for one day. Which of the following
could be used to find the number of miles she drove that day? 8.17
1 2 3 4 5 0.21
x + 38
= 8..
.
0.21
x = 88
.4
38x =
0.21
(88....
38x +
0.21
= 8..
.
25% 25%25%25%A. 0.21x + 38 = 88.4B. 0.21x = 88.4C. 38x = 0.21(88.4)D. 38x + 0.21 = 88.4
2004
What value for t makes this equation true? 8.15
1 2 3 4 5
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2004
A. 17B. 31C. 89D. 103
Which number replaces the ‘‘?’’ in the table? 8.14b
1 2 3 4 5
25% 25%25%25%A. 1/81B. 1/9C. -1D. -9
2004
Ron wanted to find a rule for finding the terms in this sequence of numbers.
1 2 6 24 ...He rewrote the first four terms this way.
1 1·2 1·2·3 1·2·3·4If Ron continues to write terms this way, what will
be the sixth term in the sequence? 8.17
1 2 3 4 5 216
480
600
720
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2004
A. 216B. 480C. 600D. 720
Jeffrey’s dogs ate 42 pounds of food during July. At that rate, which is closest
to the number of days a 100-pound bag of dog food would last? 8.17
1 2 3 4 5
3 74 135
140
25% 25%25%25%A. 3B. 74C. 135D. 140
2004
What is the solution to½x + 3 = 7? 8.15
1 2 3 4 52 4 5 8
25% 25%25%25%
2004
A. 2B. 4C. 5D. 8
Don is solving the sentence below for x.5x – 8 = 0
Which of the following is equivalentto this sentence? 8.15
1 2 3 4 5 x –
8 = 1/
5
x –
8 = -5
5x =
8
5x =
-8
25% 25%25%25%A. x – 8 = 1/5B. x – 8 = -5C. 5x = 8D. 5x = -8
2004
Laureen is studying her genealogy and has started a family tree of ancestors from which she is directly
descended. Laureen has been able to identify direct ancestors for six previous generations. How many
direct ancestors does she have in the 6th generation before hers? 8.17
1 2 3 4 5 12 16 32 64
25% 25%25%25%
2004
A. 12B. 16C. 32D. 64
Laurie used 5 yards of fabric to make 2 costumes for the school play. How many yards of fabric would she need to make 20 more of
these costumes? 8.17
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A. 8B. 27C. 40D. 50
2004
Part of the statement below is circled. Which best describes the circled part of
the statement? 8.18
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2004
A. CoefficientB. VariableC. TermD. Expression
Which graph corresponds toy = 2x - 2? 8.16
1 2 3 4 5
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A. B.
C. D.
A. AB. BC. CD. D
2004
Which means “the sum of 8 and 4 times a number is 36”? 8.15
1 2 3 4 5 8x
+ 4 =
36
4x +
8 = 36
4(x +
8) = 36
4x =
36 +
8
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2004
A. 8x + 4 = 36B. 4x + 8 = 36C. 4(x + 8) = 36D. 4x = 36 + 8
A parking garage charges $2.00 for the first hour and $0.80 for each additional hour.
Which of the following could be used to find C, the cost in dollars of parking h hours? 8.15
1 2 3 4 5 C = 0.
80(h
- 1...
C = 2(h - 1
) +...
C = 2.80
(h - 1
...
C = 3.60
(h - 1
...
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2004
A. C = 0.80(h - 1) + 2B. C = 2(h - 1) + 0.80C. C = 2.80(h - 1)D. C = 3.60(h - 1)
Which is the function described by thetable of ordered pairs? 8.14a
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2004
A. y = x + 1B. y = 3xC. y = 2x + 3D. y = x + 13
A taxi charges $2.00 for up to and including the first mile, and $1.60 for each mile
thereafter. What would the taxi charge for a trip of 4 miles? 8.17
1 2 3 4 5$6.40 $6.80 $8.00 $8.40
25% 25%25%25%A. $6.40B. $6.80C. $8.00D. $8.40
2004
A bottle of liquid dog vitamins indicates that a dog gets 2 drops of vitamins each day for
every 5 pounds of body weight. How many drops of vitamins should a 20-pound dog get
each day? 8.17
1 2 3 4 5 2 4 8 22
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A. 2B. 4C. 8D. 22
2004
A function of x containing four ordered pairs of the form (x, y) is shown below.
{(1,3),(2,4),(5,7),(6,8)}What is the domain of the function? 8.14a
{1,2,5,6}
{3,4,7,8}
{1,2,3,4}
{5,6,7,8}
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A. {1,2,5,6}B. {3,4,7,8}C. {1,2,3,4}D. {5,6,7,8}
2007
Given the function of x defined byy = 3x + 5,
if the domain is {−4,−1,2,5}, what is the range?8.14a
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A. {−20,−11,−2,7}B. {−7,−3,−2,−1}C. {−3,−2,−1,0}D. {−7,2,11,20}
2007
Which statement generalizes the pattern shown in the table below? 8.17
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A. Choice OneB. Choice TwoC. Choice ThreeD. Choice Four
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2007
What is the solution to
4 6 96144
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A. 4B. 6C. 96D. 144
2007
8.15
The formula shows that c, the total cost of buying pizzas at Al’s Restaurant, depends on p, the number
of pizzas ordered.c = 9p
What is the independent variable in the formula? 8.18
p c 9 =
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A. pB. cC. 9D. =
2007
A. 275B. 27.5C. 9.09D. 9
What is the solution to the proportion below? 8.17
27527.5
9.09 9
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2007
Which table could be used to graph the following? 8.14b
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A. AB. BC. CD. D
A. B. C. D.
2007
Which is the closest to the circumference of a circle with a diameter of 17 inches? 8.17
27 in.
53 in.
227 in.
907 in.
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A. 27 in.B. 53 in.C. 227 in.D. 907 in.
2007
A cylindrical chemical tank is 12 feet high and has a diameter of 45 feet.Which is closest to the number of cubic feet of liquid the tank will hold? 8.17
3815119076
15890141
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A. 38,151B. 19,076C. 15,890D. 141
2007
Which is true for all pairs of values in the table below? 8.14b
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A. AB. BC. CD. D
A. B.
C. D.
2007
What value of x makes the following statement true? 8.15
19 = 5x + 4
23 15 4 3
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A. 23B. 15C. 4D. 3
2007
Which is one of the solutions to the following? 8.15
2x + 4 < 12
6 5 4 3
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A. 6B. 5C. 4D. 3
2007
Which is a table of ordered pairs defined by y = 2x − 12? 8.14b
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A. AB. BC. CD. D
A. B.
C. D.
2007
Which table of ordered pairs could be used to graph y = 4x – 5? 8.14b
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A. AB. BC. CD. D
A. B.
C. D.
2007
A towing company charges a flat fee of $50 in addition to $2 a mile to tow vehicles. Which equation shows the relation between y, the
total cost, and x, the number of miles a vehicle is towed?
A B C D
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A. A
B. B
C. C
D. D
Which graph best represents the following? y = x − 3
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A. AB. BC. CD. D
A. B.
C. D.
Which is one value of the set of x that makes the following true? 7x + 3 > 17
0 1 2 3
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A. 0B. 1C. 2D. 3
Which ordered pair (x, y) is a solution to the following? Y = 3x + 10
(2,13)
(1,11)
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A. (2,13)B. (−2,16)C. (−3,1)D. (1,11)
Steven read that the actual distance between Memphis and Chicago is about 525 miles. On a
map, the distance between the two cities is about 10½ inches. Which is most likely the
scale used to make the map?
1 inch
represe...
1 inch
repre
se...
1 inch
represe...
1 inch
represe...
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A. 1 inch represents 50 milesB. 1 inch represents 25 milesC. 1 inch represents 30 milesD. 1 inch represents 40 miles
The following is a graph of a function of x. Which set best represents the domain of the function?
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A. {−7,−5,−2,0,3,5,8}B. {0, 2, 3, 5, 6, 8, 9}C. {−7,−5,−2,0,2,3,5,6,8,9}D. {0, 3, 5, 8}
Which ordered pair makes the equation false ?
(0,2)
(2,3)
(1,4)
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A. (−1,0)B. (0,2)C. (2,3)D. (1,4)
Which graph most likely contains all the ordered pairs in the table?
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A. AB. BC. CD. D
A. B. C. D.
What value for n makes the following sentence true?5n=8+3n
n = 4
n = 2
n = 8/3
n = 8/5
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A. n = 4B. n = 2C. n = 8/3D. n = 8/5
Which of the following graphs contains all the ordered pairs in the table?
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A. AB. BC. CD. D
A. B. C. D.
In which table do all of the ordered pairs make the equation true?y = 2x + 4
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A. AB. BC. CD. D
A. B. C. D.
Mrs. Garcia used 5 cups of flour to make 3 loaves of bread. How many loaves of bread can she make with 30 cups of flour?
10 18 28 50
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A. 10B. 18C. 28D. 50
Which ordered pair makes the equation true?2x=18−y
(0,9)
(1,4)
(4,1)
(9,0)
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A. (0,9)B. (1,4)C. (4,1)D. (9,0)
What value for w makes the equation true?4w−8=16
-6 -2 2 6
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A. -6B. -2C. 2D. 6
Fran drove m miles in a car she rented. To find R, the total cost of renting the car, she used the following
formula.R=0.50m+35
What is the dependent variable in the formula?
R .5 m 35
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A. RB. 0.50C. mD. 35