Algebra Concepts
M11.D.1.1.1
Analyze a set of data for the existence of a pattern and represent the pattern
algebraically and/or graphically.
1. Look at the pattern below.
4, 8, 12, 16, ...
Which number sentence can be used to determine n, the 9th number in the
pattern?
A. n = 16 + 4
B. n = 4 + 9
C. n = 4 ÷ 9
D. n = 4 x 9
2. What is the missing number in this sequence?
-15 , -24 , -33 , ___ , -51
A. -39
B. -43
C. -44
D. -42
3. Which number correctly continues the following pattern?
0, 1, 3, 6, 10, 15, 21, __
A. 27
B. 25
C. 28
D. 26
4. What is the missing number in this sequence?
62 , 59 , 53 , ___ , 32
A. 41
B. 45
C. 44
D. 47
5. The following pattern of numbers shows the first eight numbers. What will
be the 20th number?
2, 4, 6, 8, 10, 12, 14, 16 . . .
A. 18
B. 40
C. 80
D. 20
6. What is the missing number in this sequence?
3 , 6 , 12 , ___ , 33
A. 21
B. 19
C. 24
D. 22
7. Look at the pattern below.
6, 10, 14, 18, ...
Which number sentence can be used to determine n, the 8th number in the
pattern?
A. n = (4 x 8) - 2
B. n = 4 + 8
C. n = (4 x 8) + 2
D. n = 4 x 8
8. What is the value of the 8th term in the sequence?
-4 , -7 , -10 , -13 , -16 , ...
A. -27
B. -26
C. -25
D. -23
9. What is the missing number in this recursive pattern?
1, 4, __, 64, 256
A. 16
B. 32
C. 80
D. 8
10. What is the pattern for this sequence?
26 , 32 , 44 , 62 , 86 , ...
A. Each number in the sequence is 6 more than the previous number.
B. The sequence increases by multiples of 1: first by 1, then 2, then 3, then 4.
C. The sequence increases by multiples of 6: first by 6, then 12, then 18, then
24.
D. Each number in the sequence is 7 more than the previous number.
11. Which expression below produces the nth term in the sequence?
17 , 19 , 21 , 23 , 25 , ...
A. 18 - 1n
B. 15 + 2n
C. 19 - 2n
D. 16 + 1n
12. Look at the pattern below.
66, 63, 60, 57, ...
Which number sentence can be used to determine n, the 7th number in the
pattern?
A. n = 69 - 3 - 7
B. n = 3 ÷ 7
C. n = 69 + (3 x 7)
D. n = 69 - (3 x 7)
13. The first five terms of a sequence are given below.
9, 14, 19, 24, 29, ...
Determine which of the following formulas gives the nth term of this
sequence.
A. 3n + 4 - 1
B. 4n + 4
C. 3(n-1) + 4
D. 5n + 4
14. What is the pattern for this sequence?
-12 , -20 , -28 , -36 , -44 , ...
A. Each number in the sequence is 8 less than the previous number.
B. Each number in the sequence is 4 less than the previous number.
C. The sequence decreases by multiples of 9: first by 9, then 18, then 27, then
36.
D. The sequence decreases by multiples of 8: first by 8, then 16, then 24, then
32.
15. What is the value of the 8th term in the sequence?
-4 , 1 , 6 , 11 , 16 , ...
A. 31
B. 23
C. 50
D. 26
Answers
1. D 9. A
2. D 10. C
3. C 11. B
4. C 12. D
5. B 13. D
6. A 14. A
7. C 15. A
8. C
M11.D.1.1.2
Determine if a relation is a function given a set of points or a graph.
M11.D.1.1.3
Identify the domain, range or inverse of a relation (may be presented as ordered
pairs or a table).
Relations & Functions
1.
W. X.
Y. Z.
Which graph above shows a relation with domain {-4, -2, -1, 1, 3, 5, 6} and
range {1, 3, -1, -2, -4, -5}?
A. W
B. X
C. Y
D. Z
2. Which of the following represents a function?
A. X -11 -9 -2 -9
Y 16 14 16 15
B. X -11 -9 -2 2
Y 16 14 22 16
C. X -11 -9 -11 2
Y 16 16 22 15
D. X -11 -9 -2 -2
Y 16 14 16 15
3. What is the range of the equation y = |x - 5| - 4?
A. y -4
B. y -9
C. y --1
D. y -4
4. What is the range of the equation y = |x - 1| - 10?
A. y -10
B. y -10
C. y -9
D. y -11
5. (-4,12)
(3,5)
(5,21)
(8,60)
What is the domain of the set of ordered pairs above?
A. {-4, 12}
B. {12, 5, 21, 60}
C. {8, 60}
D. {-4, 3, 5, 8}
6. (-4,7)
(0,-1)
(6,-13)
(9,-19)
Do the ordered pairs above represent a relation, a function, both a relation
and a function, or neither a relation nor a function?
A. neither a relation nor a function
B. both a relation and a function
C. relation only
D. function only
7. (-2,-6)
(3,-16)
(-2,-24)
(6,-22)
Do the ordered pairs above represent a relation, a function, both a relation
and a function, or neither a relation nor a function?
A. both a relation and a function
B. relation only
C. neither a relation nor a function
D. function only
8. (-4,15)
(3,8)
(7,48)
(8,63)
What is the domain of the set of ordered pairs above?
A. {8, 63}
B. {-4, 15}
C. {15, 8, 48, 63}
D. {-4, 3, 7, 8}
9. Which of the following relations is NOT a function?
A. (3,4), (-3, 2), (3, 1), (-6, 2)
B. (-6,4), (3, 3), (-3, 1), (8, 2)
C. (8,4), (-3, 2), (3, 1), (-6, 2)
D. (-3,4), (3, 2), (8, 1), (-6, 5)
10. If the relation 8x2 - 4y = 12 has the domain {-1, 2, 6}, then what is the
corresponding range?
A. {-1, 5, 69}
B. {5, 11, 75}
C. {-2, 1, 33}
D. {2, 8, 72}
11. (-6,4)
(-2,-4)
(1,-10)
(5,-18)
What is the range of the set of ordered pairs above?
A. {4, -4, -10, -18}
B. {-6, -2, 1, 5}
C. {-6, 4, 5, -18}
D. {4, -18}
12. (-7,7)
(-3,-1)
(1,-9)
(7,-21)
What is the range of the set of ordered pairs above?
A. {7, -1, -9, -21}
B. {7, -21}
C. {-7, -3, 1, 7}
D. {-7, 7, 7, -21}
13.
Does the graph above show a relation, a function, both a relation and a
function, or neither a relation nor a function?
A. both a relation and a function
B. neither a relation nor a function
C. relation only
D. function only
14.
y = |x| + 6
Does the equation above represent a relation, a function, both a relation
and a function, or neither a relation nor a function?
A. relation only
B. neither a relation nor a function
C. function only
D. both a relation and a function
15. What is the range of the equation y = (x - 1)4 + 7?
A. y 7
B. y -7
C. y -7
D. y 7
Answers
1. B
2. B
3. A
4. B
5. D
6. B
7. B
8. D
9. A
10. A
11. A
12. A
13. C
14. D
15. A
M11.D.2.1.1
Solve compound inequalities and/or graph their solution sets on a number line
(may include absolute value inequalities).
M11.D.2.1.2
Identify or graph functions, linear equations or linear inequalities on a coordinate
plane.
1. y = 3/2 x + 3
Which of the following graphs represents the equation above?
W. X.
Y. Z.
A. W
B. X
C. Y
D. Z
2. y = 3/2 x - 3
Which of the following graphs represents the equation above?
W. X.
Y. Z.
A. W
B. X
C. Y
D. Z
3.
Which inequality is graphed on the coordinate plane?
A. x 3y + 8
D. x > 3y + 8
4.
Which inequality is graphed on the coordinate plane?
A. x 4y + 1
D. x > 4y + 1
5.
Which of the following equations is graphed above?
A. y = x
2
B. y = x
C. y = x3
D. y = |x|
6. y = 3/2 x + 3
Which of the following graphs represents the equation above?
W. X.
Y. Z.
A. W
B. X
C. Y
D. Z
7.
Which of the following equations fits this graph?
A. y = x2 + 6x + 9
B. y = -3x2 + 6x + 9
C. y = -x2 + 9
D. y = x2 - 9
8. y = 3/2 x - 3
Which of the following graphs represents the equation above?
W. X.
Y. Z.
A. W
B. X
C. Y
D. Z
9.
Which of the following equations is graphed above?
A. y = x
B. y = -|x|
C. y = x3
D. y = -x2
10.
-3 -2 -1 0 1 2 3 4 5 6 7 8 9
Which inequality is graphed on the number line?
A. x 2
D. x > 2
Answers
1. D
2. D
3. C
4. A
5. A
6. C
7. C
8. C
9. B
10. B
M11.D.2.1.3
Write, solve and/or apply a linear equation (including problem situations).
1. The cost of a long-distance telephone call is given by the function
C(m) = 0.15m + 1.25
where m is the length of the call in minutes. Determine how long a phone
call can be made for $7.25.
A. 45 minutes
B. 40 minutes
C. 48 minutes
D. 35 minutes
2. Samson Trucking uses the function
S(t) = -5,600t + 44,800
to determine the salvage value S(t), in dollars, of a truck t years after its
purchase. How long will it take the truck to depreciate completely?
A. 10 years
B. 7 years
C. 9 years
D. 8 years
3. Mavity's Furniture discounts all furniture 7% to customers paying in cash.
Rhonda paid $1,176.83 in cash for a sofa, loveseat and chair. What was the
original price of the furniture?
A. $823.78
B. $1,259.21
C. $1,265.41
D. $1,094.45
4. PawTraxx manufactures hiking boots. The production facility has fixed costs
of $400 a day and total costs of $6,400 per day at an output of 100 pair of
boots per day. Which of the following equations represents the daily
production cost based on the number of pairs of boots manufactured?
(Let C(x) represent the daily production cost and x represent the number of
pairs of boots manufactured)
A. C(x) = 60x + 400
B. C(x) = 60x - 400
C. C(x) = 64x
D. C(x) = 70x + 400
5. Stacy is going to the state chili cook-off with her friends but can only stay
for 4 hours. The event offers two different pricing structures. Stacy can
purchase an all day pass with unlimited food samples for $30.00 or she can
pay an admission fee of $6.00 and pay $2.00 for each bowl of chili. If she is
planning on having 11 bowls of chili, which deal should she take?
A. the all day pass with unlimited food samples for $30.00
B. both pricing structures ending up costing the same amount
C. Stacy does not have enough money to go to the fair
D. the admission fee of $6.00 plus $2.00 for each bowl of chili
6. Catherine paid $219.24 for an MP3 Player. If the price paid includes a 8%
sales tax, which of the following equations can be used to determine the
price of the MP3 Player before tax?
(Let x represent the cost of the MP3 Player and y represent the total cost
after tax)
A. y = x + 8x
B. y = 0.92x
C. y = 1.08x
D. y = 1.8x
7. The Bridgeport water department has a monthly service charge of $11.80
and a volume charge of $1.16 for every 100 cubic feet of water. Which of
the following equations can be used to determine the Morgan family's
monthly water bill?
(Let x represent 100 cubic feet of water and y represent the monthly cost)
A. y = 12.96x
B. y = 0.0116x + 11.80
C. y = 1.16x + 11.80
D. y = 1.16x - 11.80
8. At the afternoon matinee movie 2 adult tickets and 5 child tickets cost $38,
and 6 adult tickets and 1 child tickets cost $58. Which system of linear
equations below can be used to determine the price of each ticket?
(Let x represent the cost of an adult ticket and y represent the cost of a
child ticket)
A. 8x + 6y = 96
B. 2x + 6x = 72
5y + 1y = 24
C. 2x + 5y = 38
6x + 1y = 58
D. 2x + 6y = 38
5x + 4y = 58
9. Shannon is moving from San Antonio to Mineral Wells and rented a truck
from U-Move-It truck rentals. The cost of a one-day truck rental is given by
C(m) = 0.8m + 45
where m is the number of miles driven. If Shannon drives 250 miles, what is
the cost of the truck rental?
A. $250.00
B. $245.00
C. $200.00
D. $270.00
10. A company manufactures and sells mini-recorders. A survey of office
supply stores indicated that at a price of $93 each, the demand would be 2
hundred recorders, and at a price of $43 each, the demand would be 12
hundred recorders. If a linear relationship between price and demand
exists, which of the following equations models the price-demand
relationship?
(Let y represent the price per mini-recorder and x represent the demand in
hundreds)
A. y = -5(x) + 103
B. y = 5(x)
C. y = -12(x) + 149
D. y = 2 1/2(x) + 73
Answers
1. B
2. D
3. C
4. A
5. D
6. C
7. C
8. C
9. B
10. A
M11.D.2.1.4
Write and/or solve systems of equations using graphing, substitution and/or
elimination (limit systems to 2 equations).
1. The system of equations
5x - 4y = -6
3x + 4y = 22
is graphed below. Find the solution to the system.
A. x = -2, y = 4
B. x = 2, y = 4
C. x = -2, y = -4
D. x = 2, y = -4
2. The system of equations
-2x - 2y = 2
-4x + 2y = 22
is graphed below. Find the solution to the system.
A. x = -3, y = 3
B. x = 3, y = -4
C. x = -4, y = 4
D. x = -4, y = 3
3. 10x + 2y = 52
3x + y = 8
Using the two equations above, solve for x?
A. x = 9
B. x = 11
C. x = 6
D. x = 2
4. Find the solution to the system of equations below.
-x + 2y = 2
4x + 4y = 4
A. x = -4, y = 2
B. x = -1, y = 1
C. x = 0, y = 1
D. x = 1, y = 1
5. 3x - 2y = 28
2x + y = 14
Using the two equations above, solve for y?
A. y = 11
B. y = 4
C. y = -2
D. y = 0
6. Find the solution to the system of equations below.
4x + y = 4
3x - 3y = 18
A. x = 2, y = -2
B. x = 2, y = -6
C. x = 1, y = -1
D. x = 2, y = -4
7. Describe the solution to the system of equations below.
4x - 1y = 6
20x - 5y = 24
A. The system has the unique solution (-6, -30).
B. The system has the unique solution (3, 6).
C. The system has no solution.
D. The system has infinitely many solutions of the form y = 4x - 6 where x is
any real number.
8. Describe the solution to the system of equations below.
4x - y = 6
16x - 4y = 24
A. The system has no solution.
B. The system has the unique solution (2, 2).
C. The system has the unique solution (-5, -26).
D. The system has infinitely many solutions of the form y = 4x - 6 where x is
any real number.
9. Describe the solution to the system of equations below.
5x - 1y = 8
15x - 3y = 16
A. The system has the unique solution (4, 12).
B. The system has infinitely many solutions of the form y = 5x - 8 where x is
any real number.
C. The system has the unique solution (-2, -18).
D. The system has no solution.
10. 6x - 2y = 40
2x + y = 20
Using the two equations above, solve for y?
A. y = 4
B. y = -4
C. y = 0
D. y = 8
Answers
1. B
2. D
3. A
4. C
5. C
6. D
7. C
8. D
9. D
10. A
M11.D.2.1.5
Solve quadratic equations using factoring (integers only – not including
completing the square or the Quadratic Formula).
1. Find solution(s) for x:
x(x - 8) = 9
A. x = 1; x = -9
B. x = -1; x = 9
C. x = -1; x = -9
D. x = 1; x = 9
2. Find the solution(s) for x:
x2 - 9x + 14 = 0
A. x = 5; x = 7
B. x = 2; x = 7
C. x = -2; x = -7
D. x = 2; x = 6
3. Find the solution(s) for x:
(x + 5) (x - 14) = 0
A. x = 5; x = -14
B. x = 14
C. x = -5; x = -14
D. x = -5; x = 14
4. Find the solution(s) for x:
x2 + 7x + 6 = 0
A. x = 1; x = 6
B. x = -1; x = -6
C. x = 1; x = -6
D. x = -1; x = -7
5. Find the solution(s) for x:
x2 + 7x = 8
A. x = 4; x = -8 C. x = -1; x = 8
B. x = -1; x = 9 D. x = 1; x = -8
6. Multiply the binomials:
(2x + 5) (4x - 3)
A. 8x2 + 14x - 15
B. 8x2 - 14x - 15
C. 8x2 + 20x - 15
D. 8x2 + 14x + 15
7. Find the solution(s) for x:
x2 - 25 = 0
A. x = 3; x = -3
B. x = 5; x = -5
C. x = 7; x = -7
D. x = 4; x = -4
8. Multiply the binomials:
(1x + 6) (5x - 4)
A. 5x2 + 26x - 24
B. 5x2 + 30x - 24
C. 5x2 + 26x + 24
D. 5x2 - 26x - 24
9. Find solution(s) for x:
x(x - 6) = 40
A. x = 4
B. x = -4; x = -10
C. x = 4; x = 10
D. x = -4; x = 10
10. Find the solution(s) for x:
x2 + 3x = 28
A. x = 4; x = -7
B. x = 3; x = -5
C. x = -4; x = 7
D. x = -4; x = 8
Answers
1. B
2. B
3. D
4. B
5. D
6. A
7. B
8. A
9. D
10. A
M11.D.2.2.1
Add, subtract and/or multiply polynomial expressions (express answers in
simplest form – nothing larger than a binomial multiplied by a trinomial).
M11.D.2.2.2
Factor algebraic expressions, including difference of squares and trinomials
(trinomials limited to the form ax2+bx+c where a is not equal to 0).
M11.D.2.2.3
Simplify algebraic fractions.
1. Which binomial is a factor of the polynomial below?
5x2 + 22x + 8
A. x + 2
B. 5x + 4
C. 5x + 2
D. x + 8
2. Simplify (3x + 8)2
A. 6x2 + 24x + 16
B. 9x2 + 48x + 64
C. 9x2 + 24x + 64
D. 9x2 + 64
3. Simplify:
4x2 + 24x + 20
3x2 + 23x + 40
A. 4x + 4
3x + 5
B. 4x + 5
3x + 8
C. 3x + 4
4x + 7
D. 4x + 4
3x + 8
4. Simplify: (9x3 - 3x2 + 6) + (4x3 + 6x + 3)
A. 5x3 - 3x2 + 6x + 3
B. 13x3 + 6x - 9
C. 13x3 - 3x2 + 6x - 9
D. 13x3 - 3x2 + 6x + 9
5. Simplify the following expression.
(10m - 4n) × (2m + 11n)
A. 12m + 15n
B. 20m2 + 102mn - 44n2
C. 20m2 - 44n2
D. 20m2 + 118mn - 44n2
6. Simplify
x2 + 4x - 45
(x + 9)(x + 5)
A. x - 5
x+9
B. 1
C. x-5
x+5
D. x + 9
x+5
7. Simplify the following expression.
(2x + 33y) + (13x + 40y)
A. 42x + 46y
B. 15x + 73y
C. 73x + 15y
D. 35x + 53y
8. Simplify: (3x + 4)(x - 5)
A. 3x2 - 19x - 20
B. 3x2 - 11x - 9
C. 3x2 + 11x - 20
D. 3x2 - 11x - 20
9. Simplify: (3x - 4)(3x + 4)
A. 9x2 + 24x - 16
B. 9x2 - 16
C. 9x2 - 8
D. 9x2 - 24x - 16
10. Simplify the following expression.
(12x + 45y) + (15x - 24y)
A. 27x + 21y
B. 27x + 69y
C. 57x + 39y
D. 57x + 9y
Answers
1. C
2. B
3. D
4. D
5. B
6. C
7. B
8. D
9. B
10. A
M11.D.3.1.1
Identify, describe and/or use constant or varying rates of change.
M11.D.3.1.2
Find, convert and/or compare the probability and/or odds of a simple event.
1. Marilyn rowed across the lake with her friend Teresa at a rate of 4 mph.
Teresa then rowed back at a rate of 3 mph. If the lake is 6 miles across,
how long did it take them to complete their trip?
A. 2 7/10 hours
B. 3 1/2 hours
C. 4 1/2 hours
D. 4 1/6 hours
2. A fish population obeys the logistic model of growth
6000
P=
30 + 30e-0.t
What is the eventual size of the population?
A. 240
B. 300
C. 200
D. 100
3. Marlow recently finished a three year project to construct a reservoir. City
officials determined that they can pump 1,250 gallons of water into the
reservoir every hour. If it can hold 900,000 gallons, how long will it take
them to fill up the reservoir?
A. 24 days
B. 36 days
C. 30 days
D. 18 days
4. Kurt's truck uses 8 gallons of gas to travel 96 miles. He has 4 gallons in the
tank. How much more gas he will need to drive 228 miles?
A. 19 gallons
B. 12 gallons
C. 16 gallons
D. 15 gallons
5. Steven took out a loan to help pay for his house. He borrowed $50,000 for
15 years at a yearly simple interest rate of 5%. How much interest will he
end up paying the bank?
A. $87,500
B. $12,500
C. $30,000
D. $37,500
6. James opened a money-market account that paid 3% simple interest yearly.
He started the account with $7,000 and made no further deposits. When he
closed the account, he had earned $1,260 in interest. How long did he keep
his account open?
A. 5 years
B. 6 years
C. 8 years
D. 7 years
7. If a pine tree grows 4 inches per year, how long will it take for the tree to
reach a height of 10 feet?
A. 30 years
B. 36 years
C. 33 years
D. 24 years
8. Charles invested $2,000 in a certificate of deposit that pays a rate of 5% per
year. What will be the approximate value of the CD in 10 years?
A. $3,300
B. $3,500
C. $2,900
D. $4,950
9. Cathy lives in a state where speeders are fined $9 for each mile per hour
over the speed limit. Cathy was given a ticket for $99 for speeding on a road
where the speed limit is 50 miles per hour. How fast was Cathy driving?
A. 67 mph
B. 58 mph
C. 65 mph
D. 61 mph
10. Phil is boiling water on the stove. The pot he is using contains 4 gallons of
water. If the water is dissipating at a rate of 2 cups per minute, how long
will it be before all the water is gone? (Hint: 1 gallon = 16 cups)
A. 40 minutes
B. 28 minutes
C. 36 minutes
D. 32 minutes
Answers
1. B
2. C
3. C
4. D
5. D
6. B
7. A
8. A
9. D
10. D
M11.D.3.2.1
Determine the number of permutations and/or combinations or apply the
fundamental counting principle. (Formula provided on the reference sheet).
M11.D.3.2.2
Given the graph of the line, 2 points on the line or the slope and a point on a line,
write or identify the linear equation in point-slope, standard and/or slope-
intercept form.
M11.D.3.2.3
Compute the slope and/or y-intercept represented by a linear equation or graph.
M11.D.4.1.1
Match the graph of a given function to its table or equation.
1. What is the y-intercept of the line given by the equation below?
2y = 3x - 2
A. (0, -1)
B. (0, 2)
C. (0, -2)
D. (0, -4)
2. Determine the slope of the line that passes through the points
(3, 3) and (4, 1).
A. 2
B. -2
C. -1/2
D. 4/7
E. -2/7
3. x -4 0 4
y 2 3 4
Which of the following graphs matches the table above?
W. X.
Y. Z.
A. W
B. X
C. Y
D. Z
4. Which of the following points lies on the line given by the equation below?
y = (4/5)x - 4
A. (5, 0)
B. (7, 0)
C. (4, 0)
D. (5, -1)
5. A line passes through the points (-2, 1) and (x2, y2), and has a slope of 7/6.
If point (x2, y2) is located in quadrant I, find x2.
A. -6
B. 6
C. -8
D. 8
E. 4
6.
Which of the following tables matches the graph above?
A.
B.
C.
D.
7. What is the slope of the line given by the equation below?
2y = (-1/2)x - 9
A. 1/4
B. -1/4
C. -1/2
D. 1/2
8.
Which of the following tables matches the graph above?
A.
B.
C.
D.
-5
9. What is the equation for a line that has a slope of /3 and passes through
the point (3, -9)?
-5
A. y = /3x - 5
-5
B. y = /3x + 14
-5
C. y = /3x - 4
-5
D. y = /3x - 14
-2
10. What is the standard form of an equation for a line that has a slope of /5
and passes through the point (3, -11)?
A. 2x + 7y = -71
B. 4x + 5y = -43
C. -2x + 5y = -61
D. 2x + 5y = -49
Answers
1. A
2. B
3. C
4. A
5. E
6. C
7. B
8. B
9. C
10. D