State Test Review
10,000p¹²
(-10p³)⁴
-1000p¹²
(-10p⁴)³
-5/x
(-15x²)/(3x³)
-27w⁶
(-3w²)³
9w⁶
(-3w³)²
-35x¹¹
(-5x⁴)(7x⁷)
-25/x⁵
(-5x⁻³)(5x⁻²)
6x³ - 49x² + 2x + 48
(-6x² + x + 6)(-x + 8)
x⁸y⁴
(-x²y)⁴
-x¹⁰y¹⁵
(-x²y³)⁵
5 + 37x + 42x²
(1 + 6x)(5 + 7x)
-5y³/x⁷
(10xy⁵)/(-2x⁸y²)
10a⁹
(2a³)(5a⁶)
2a⁸
(2a³)³/(4a)
32a¹⁵
(2a³)⁵
4x² - 24x + 36
(2x - 6)²
32x⁵
(2x)⁵
1/(8x³)
(2x)⁻³
8x⁶
(2x²)³
16x¹⁶y¹²z⁴
(2x⁴y³z)⁴
1/(5x⁵)
(2x⁻³)/(10x²)
a/2
(3a²b)/(6ab)
18x³ + 9x² - 26x + 7
(3x - 1)(6x² + 5x - 7)
9x² - 64
(3x - 8)(3x + 8)
9x⁴
(3x²)(3x²)
21x⁸
(3x²)(7x⁶)
9x⁶
(3x³)²
6x⁹
(3x⁸)(2x)
243y¹⁵
(3y³)⁵
32p⁹x⁷
(4p⁶x⁶)(8p³x)
1/(2mn²)
(5mn)/(10m²n³)
35x² + 4x - 4
(5x + 2)(7x - 2)
35x² - 5x - 30
(5x - 5)(7x + 6)
5/x
(5x²)(x⁻³)
1/(125x⁶)
(5x²)⁻³
25x⁶
(5x³)²
5x
(5x⁻²)(x³)
x⁶/125
(5x⁻²)⁻³
25/x²
(5x⁻¹)²
x⁵/25
(5⁻²x²)/(x⁻³)
(3k¹⁶)/(5p²)
(6k²⁴p⁹)/(10k⁸p¹¹)
1/5
(6x⁻²)/(30x⁻²)
14x² + 25x - 25
(7x - 5)(2x + 5)
Box plot
(Also called a box-and-whisker plot) can be used to summarise a data set. It divides the data set into four groups that are approximately equal in size.
vertex
(h,k)
k⁸
(k²)⁴
m⁶
(m²)(m⁴)
p⁹
(p⁶)(p³)
x⁴y⁶
(x²y³)²
5x⁵
(x³)(5x²)
x¹²
(x³)⁴
What are the solutions of the system? {y=6x+6 {y=−x²+5x+6
(−1, 0) and (0, 6)
15d⁹
(−3d)(5d⁵)(−d³)
12m²
(−4m)(−3m)
-3c⁶
(−c⁴)(3c²)
-x⁵
(−x⁷)(x⁻²)
arithmetic common difference 7
, , 29, 36, 43, 50, ...
arithmetic common difference 6
, , 30, 36, 42, 48, ...
arithmetic common difference 4
, , 62, 66, 70, 74, ...
arithmetic common difference 5
, , 68, 73, 78, 83, ...
arithmetic common difference -4
, , 83, 79, 75, 71, ...
arithmetic common difference -7
, , 85, 78, 71, 64, ...
arithmetic common difference -2
, , 95, 93, 91, 89, ...
(4,-6)
-10x + 5y = -22 10x + 3y = 22
225; two real solution
-10x² + 5x +5 = 0
-79; no real solution
-10x² - x -2 = 0
-11; no real solution
-3x² + x -1 =0
13√2
-4√8+ 7√18
-111; no real solution
-6x² +9x - 8 =0
1; two real solution
-6x² - 7x - 2 = 0
144; two real solution
-9x² -6x+3=0
81; two real solution
-x² - 9x = 0
√0=
0
√1=
1
geometric common ratio 3
1, 3, 9, 27, , , ...
10x1
10
2x5
10
5x2
10
√100=
10
√289=
17
5x7
35
7x5
35
3x6
18
6x3
18
9x2
18
√324=
18
geometric common ratio 1/3
189, 63, 21, 7, , , ...
√361=
19
1x2
2
How many solutions does the system have? {y=−2x+2 {y=x²−3x Enter your answer in the box.
2
√4=
2
10x2
20
4x5
20
5x4
20
√400=
20
(2x+y)(x-3)
2x²-6x+yx-3y
-6x⁸
2x³ × -3x⁵
¼
2⁻²
0
2√5 - √20
9√5
2√5+ 7√5
-3√5
2√5- √125
10√2
2√50
√9=
3
12x4
48
4x12
48
6x8
48
8x6
48
11x6
66
6x11
66
1
Any non zero number to the 0 power is
Itself
Any number to the 1st power is
(a + b) + c = a + (b + c)
Associative Property of Addition
244.902
Cheyanne accidentally eats a virus from the planet Mars that gives her super powers. To show off her new super powers she serves a volleyball straight up into the air at an initial velocity of 1,200 meters per second. Cheyanne hits it from 2 meters off the ground. How many seconds will it take for the ball to hit the ground?
a + b = b + a
Commutative Property of Addition
Bivariate
Data with two variables, or pairs of numerical observations
Positive Relationship
Describe the association: The longer Tim studies, the higher his grades will be
a(b + c) = ab + ac
Distributive Property
a/c = b/c
Division Property of Equality
x-values
Domain, Independent Variable, Input
term
Each number in a sequence
4.082
Evette is laying on the ground and launches a ball straight up into the air at an initial speed of 20 m/s. How many seconds will it take the ball to hit the ground?
depreciates/decreases
Exponential Decay
a Half of the amount
Exponential Decay 1/2 or 0.50
a Third of the amount
Exponential Decay 1/3 or 0.33
a Quarter of the amount
Exponential Decay 1/4 or 0.25
increases
Exponential Growth
The population doubles
Exponential Growth Growth Factor of 2
the amount triples
Exponential Growth Growth Factor of 3
Four Times as many of the amount
Exponential Growth Growth factor of 4
1/(16n²)
Express with positive exponents: (4n)⁻²
1/(5x)
Express with positive exponents: (5x)⁻¹
4/n²
Express with positive exponents: 4n⁻²
5/x
Express with positive exponents: 5x⁻¹
(2a - 5)(2a + 5)
Factor Completely
(3a + 7)(2a + 3)
Factor Completely
(3v + 2)(v - 1)
Factor Completely
(3x - 1)(x + 3)
Factor Completely
(4k + 1)(4k - 1)
Factor Completely
(4m + 1)²
Factor Completely
(4n - 1)²
Factor Completely
(n - 7)(10n + 1)
Factor Completely
(r + 6)(r - 9)
Factor Completely
(x - 9)(x - 4)
Factor Completely
2(1 - r)²
Factor Completely
2(2n + 3)(5n + 2)
Factor Completely
2(2x + 3)(2x - 3)
Factor Completely
2(p - 9)(p + 8)
Factor Completely
3(2x + 5)²
Factor Completely
3(7n + 8)(n + 5)
Factor Completely
5(5p + 4)(5p - 4)
Factor Completely
6(2r + 5)(r - 4)
Factor Completely
6(x - 1)(9x - 8)
Factor Completely
b = 10
Fin the y-intercept: y = x + 10
m = -1/4
Find Slope: (-12, -5) and (0, -8)
m is Undefined
Find Slope: (-18, -20) and (-18, -15)
m = -3/4
Find Slope: (-20, -4) and (-12, -10)
m = -1/14
Find Slope: (-3, 1) and (-17, 2)
m = 0
Find Slope: (-5, 7) and (5, 7)
m = -18/13
Find Slope: (-6, 9) and (7, -9)
m = -1
Find Slope: y = - x - 5
m = -2/3
Find Slope: y = -2/3 x + 4
m = 2
Find Slope: y = 2x
m = 4/5
Find Slope: y = 4/5 x + 3
24
Find f(-2) = -10x + 4
-3
Find f(-2).
3
Find f(-2).
4
Find f(-3).
6
Find f(0).
-2
Find f(1)
50
Find f(1)
126
Find f(12) = 10x+6
0
Find f(2).
1
Find f(2).
-4
Find f(3)
-1
Find f(5)
-8
Find f(x) = 5x - 6 when f(-46)
-20
Find f(x)= -7x +1 when f(3)
17
Find f(x)= -x+10 when f(-7)
m = -4/15
Find slope: (8, 10) and (-7, 14)
90
Find the 22nd term: 6, 10, 14, 18,...
142
Find the 24th term: 4, 10, 16, 22,...
-62
Find the 24th term: 7, 4, 1, -2,...
105
Find the 31st term: -15, -11, -7, -3,...
-138
Find the 31st term: 12, 7, 2, -3,...
9
Find the common ratio for the sequence 2, 18, 162, 1458
3
Find the common ratio for the sequence 5, 15, 45, 135
6
Find the common ratio for the sequence 5, 30, 180, 1080
1/5
Find the common ratio for the sequence 500, 100, 20, 4
16
Find the first term of the sequence ?, 32, 64, 128
-10
Find the first term of the sequence ?, 40, -160, 640
10
Find the first term of the sequence: ?, 40, 160, 640.
189
Find the fourth term of the sequence: -7, 21, -63
15
Find the missing term: 3, ___, 75, 375
24
Find the next term in the sequence 3, 6, 12, ...
-135
Find the next term in the sequence 5, -15, 45, ...
x = 1 and y = 5
Find the solution: 4x + 2y = 14 7x - 3y = -8
b = -2
Find the y-intercept: y = -3x - 2
b = 6
Find the y-intercept: y = 2x + 6
-9
Find x for f(x) = -6x + 7 when f(x) = 61
-5
Find x for f(x) = -6x -5 when f(x) = 25
m = -30
Fins Slope: (12, -18) and (11, 12)
growth
Growth or Decay . y = 5(1.2)^t
decay
Growth or Decay y = 2(0.43)^t
28
How many days it will take a penny to become a million dollars if it doubles every day.
y=100−2x
How much money is left on your $100 gas gift card if gas currently costs $2 per gallon...
h(t)= 150 + 290t - 16t²
Initial height is 150ft and initial velocity is 290ft/s upward.
h(t)= 1700 - 95t - 16t²
Initial height is 1700ft and initial velocity is downward 95ft/s
h(t)= 29 + 159t - 16t²
Initial height is 29ft and initial upward velocity is 159ft/s.
h(t)= 300 + 88t - 16t²
Initial height is 300ft and initial velocity is 88ft/s upward.
h(t)= 38 + 74t - 16t²
Initial height is 38ft and initial velocity is 74ft/s upward
h(t)= 3 + 80t - 16t²
Initial height is 3ft and velocity is upward 80ft/s
h(t)= 292 - 12t - 16t²
Initial velocity is 12ft/s downward and initial height is 292ft.
h(t)= 700 - 95t - 16t²
Initial velocity is 95ft/s downward and initial height is 700ft
Exponential Decay
Is this growth or decay?
Exponential Growth
Is this growth or decay?
It won't :(
Jasmine is stuck in a 500 meter ditch. She has a bow and arrow. She attaches a "help" note and shoots it out of the ditch at an initial velocity of 200 m/s. How long will it take Jasmine's note to reach the ground above?
10.765
Kyndal is clumsy and likes to travel. She is walking along the world's highest bridge, The Beipanjiang Bridge, in China. The bridge is 1,854 feet tall. She trips and drops her phone off the bridge. Assuming it has not initial velocity. How many seconds will it take for her phone to hit the water below?
0.7
Leony punts a soccer ball straight into the air. When he strikes the ball it is 1 meter off the ground. He can't kick very hard. The ball travels at an initial velocity of 2 m/s. How many seconds does it take for the ball to hit the ground?
6.919
Modern art is weird. Kimberly is making a $50,000 painting by simply spilling paint off a building onto a giant canvas. The building is 766 feet above the canvas. How many seconds does it take for Kimberly's paint to hit the canvas?
a • c = b • c
Multiplication Property of Equality
a x 1 = 1 x a = a
Multiplicative Identity Property
9.267
Myah is playing the Ukulele at a rooftop restaurant in downtown Charlotte. The building is 1,800 feet tall. Then she sees her arch nemesis, the man who killed all the dinosaurs. He is 6 feet tall. She throws her string instrument at him straight down with an initial velocity of 45 feet per second. How many seconds will it take for her instrument to hit him?
uniform distribution
No clear peaks, data spread uniformly across the graph
about 4.5 weeks
Our next break from school starts in...
Skewed right
Peak of the data is to the left and a tail to the right
Skewed left
Peak of the data is to the right and a tail to the left
y-values
Range, Dependent Variable, Output
a = a
Reflexive Property
y=500-100X
Sammy received $500 for his birthday and decides to spend $100 each week hanging out with his friends...
1,113,402
Since January 1980, the population of a city has grown according to the model, where x represents the number of years since January 1980. If the population continues to grow at this rate, what will it be (to the nearest whole person) in the year 2000?
1996
Since January 1980, the population of a city has grown according to the model, where x represents the number of years since January 1980. Use the model to predict the year the population will reach 1 million.
The population is growing at a rate 2.2% each year.
Since January 1980, the population of a city has grown according to the model, where x represents the number of years since January 1980. What does 1.022 mean?
The population of the city in 1980
Since January 1980, the population of a city has grown according to the model, where x represents the number of years since January 1980. What does 720,500 represent?
a = 10, -10
Solv for a: | 7a | + 3 = 73
x=1 or x=-2.5
Solve 2x²+3x-5=0 using the Quadratic Formula.
x = -1.5 or x = -1
Solve 2x²+5x+3=0 using the Quadratic Formula.
x = .68 or x = -3.69
Solve 2x²+6x-5=0 using the Quadratic Formula.
no real solutions
Solve 2x²-3x+2=0 using the Quadratic Formula.
x = 3.64 or x = -0.14
Solve 2x²-7x-1=0 using the Quadratic Formula.
x = 3/2
Solve 4x²-12x+9 =0 using the Quadratic Formula.
x=1.11 or x = -1.11
Solve 4x²-5=0 using the Quadratic Formula.
x = -6 or x = 2.8
Solve 5x²+16x-84=0 using the Quadratic Formula.
x = -2/3
Solve 9x²+12x+4=0 using the Quadratic Formula.
a = 6, -22
Solve for a (absolute value | |): 4 | a + 8 | = 56
a = (2m + 3)/3
Solve for a: -3a + 2m = -3
a = 4
Solve for a: 10√(9a) = 60
a = 1/3m
Solve for a: 12am = 4
a = 22
Solve for a: 5 = √(a + 3)
a = 1/(m - 2)
Solve for a: m = (1 + 2a)/a
a = 33, -15
Solve for a: | -9 + a | / 8 = 3
a = 1, -1
Solve for a: | a | + 1 = 2
a = -2
Solve for a: √(3a + 12 = √(a + 8)
a = -8
Solve for a: √(a + 9) = 1
No solution
Solve the system of linear equations using the Elimination method: -3x + 3y = 4 -x + y = 3
(1, 7)
Solve the system using elimination: 2x + y = 9 -2x + y = 5
(-1, 1)
Solve the system using elimination: 3 = -2x + y -3 = 10x + 7y
(7, -1)
Solve the system using elimination: 4x + 8y = 20 -4x + 2y = -30
(2, 0)
Solve the system using elimination: -14 = -20y - 7x 4 = -10y + 2x
(-1, 3)
Solve the system using elimination: -2x - 9y = -25 -4x - 9y = -23
(-4, -4)
Solve the system using elimination: -3x + 7y = -16 -9x + 5y = 16
No Solutions
Solve the system using elimination: -3x - 9y = -9 x + 3y = 6
(8, -1)
Solve the system using elimination: -4x - 15y = -17 -x + 5y = -13
(6, -6)
Solve the system using elimination: -4x - 2y = -12 4x + 8y = -24
(-1, -5)
Solve the system using elimination: -4x - 2y = 14 -10x + 7y = -25
(-1, -1)
Solve the system using elimination: -6x + 5y = 1 6x + 4y = -10
(5, 6)
Solve the system using elimination: -6x + 6y = 6 -6x + 3y = -12
(2, -5)
Solve the system using elimination: -7x + y = -19 -2x + 3y = -19
(1, -2)
Solve the system using elimination: -7x - 8y = 9 -4x + 9y = -22
(0, -2)
Solve the system using elimination: -x - 7y =14 -4x - 14y =28
(0, -1)
Solve the system using elimination: 16x - 10y = 10 -8x - 6y = 6
(2, -1)
Solve the system using elimination: 2x + 5y = -1 x + 2y = 0
Infinite Solutions
Solve the system using elimination: 2x + 8y =6 -5x -20y = -15
(4, 8)
Solve the system using elimination: 3x + y = 20 x + y = 12
(-2, -4)
Solve the system using elimination: 3x - 2y = 2 5x - 5y = 10
(-6, 4)
Solve the system using elimination: 5x + 4y = -14 3x + 6y = 6
(-6, 0)
Solve the system using elimination: 5x + 4y = -30 3x - 9y = -18
(1, 4)
Solve the system using elimination: 5x + y = 9 10x - 7y = -18
(6, -9)
Solve the system using elimination: 7x + 2y = 24 8x + 2y = 30
(4, -2)
Solve the system using elimination: 8x + 14y = 4 -6x - 7y = -10
(-1, -8)
Solve the system using elimination: 8x + y = -16 -3x + y =-5
(10, -1)
Solve the system using elimination: x - y = 11 2x + y =19
x = 7 and y = -1
Solve using Elimination: 4x + 8y = 20 -4x + 2y = -30
x= -2 and y = -4
Solve using Elimination: 3x - 2y = 2 5x -5y = 10
x=4.19 or x = -1.19
Solve x²-3x-5=0 using the Quadratic Formula.
(-4,-4)
Solve: -3x + 7y = -16 -9x + 5y = 16
(5,-17)
Solve: 2x - 3y = 61 2x + y = -7
(2,7)
Solve: 5x - 6y = -32 3x + 6y = 48
(2,3)
Solve: 6x - 3y = 3 -6x + 5y = 3
x < 3
Solve: -3 - 6(4x + 6) > - 111
x ≥ -4
Solve: -5x - 6x ≤ 8 - 8x - x
x < -3
Solve: 167 < 6 + 7(2 - 7x)
x < -1
Solve: 3 < -5x + 2x
a - c = b - c
Subtraction Property of Equality
y=3x+15
Susan pays a gym membership fee of $15 plus $3 per hour in the gym...
a = b then b = a
Symmetric Property
35
The amount of Advil left in your system is modeled by the given equation. 280mg is the initial amount, t is the number of hours that have passed. How many milligrams (to the nearest milligram) of the medicine will remain in the body at 6:00 pm if the medicine was taken at 12:00pm?
a(n)=a(1)+(n-1)d
The arithmetic formula is
Negative Correlation
The association between the amount of rain and the attendance at a soccer game the same day.
Mean
The average of a set of numbers.
1,873
The bear population increases at a rate of 2% per year. There are 1,537 bear this year. How many bears will there be in 10 years?
Lower Quartile
The beginning of the box
Upper quartile
The end of the box
Maximum
The highest point on a graph, upper extreme
3.125
The initial amount of medicine in the body is 200 mg. How many milligrams (to the nearest milligram) of the medicine will remain in the body 12 hours later?
Minimum
The lowest point on a graph, lower extreme
81,920
The number of bacteria for influenza A if left untreated doubles every day. If you are exposed to 5 bacteria, how many bacteria would you have in two weeks?
No Correlation
The number of siblings a student has and the grade they have in an Algebra 1 class?
f(x) = (x)² - 1
The parabola translates down 1, does not shift horizontally.
f(x) is the parent function. What transformation happens in f(x) = (x + 2)² ?
The parabola translates left 2 units only.
f(x) is the parent function. What transformation happens in f(x) + 2 ?
The parabola translates up 2 units only.
662
The population of Grove City is 624 and is growing at a rate of 1.2%. Find the population after 5 years.
5552
The population of Litchfield is 6,688 and is declining at a rate of 2.3% every year. What will the population be in 8 years?
88
The population of a certain animal species increases at a rate of 3.5% per year. There are currently 80 animals. How many animals will there be in 36 months?
$ 91,108
The price of a new truck is expected to increase at a rate of 8.2% every year. If a new truck is $48,500 in 2017, what would the cost of a new truck be in 2025?
Interquartile Range
The range of the box
Arithmetic
The sequence 11, 6, 1, -4,... is
Not arithmetic
The sequence 7, 21, 30, 45
Given the equation: y = 6 - 6x What is the slope?
The slope is -6.
How do you identify the y-intercept of a line by looking at the graph?
The y-intercept is where the line crosses the y-axis.
y=15x+3
To play mini golf it cost $15 per hour plus a $3 rental fee for the golf club...
y=100x+5
To rent a van a company charges $100 a day plus a $5 cleaning fee...
y=100x+500
To save for college Jim starts a savings account with $500 and continues to add $100 every month throughout high school...
a = b and b = c, then a = c
Transitive Property of Equality
x² - d
Translate down d units
(x + 1)²
Translate left 1
y = -(x+1)² -4
Translate left 1 and down 4 and Reflect
(x + 3)²
Translate left 3
(x + 6)² - 2
Translate left 6 and down 2
(x + 9)² + 5
Translate left 9 and up 5
(x + c)²
Translate left c units
(x - 1)²
Translate right 1
(x - 3)²
Translate right 3
(x - 7)² + 1
Translate right 7 and up 1
(x - 9)² - 5
Translate right 9 and down 5
(x - c)²
Translate right c units
x² + 1
Translate up 1
x² + 3
Translate up 3
y = (x-2)²+ 5
Translate up 5 and right 2
x² + d
Translate up d units
bimodal distribution
Two clear peaks
What is the slope of a vertical line?
Undefined
Vertical Line Test
Use on a graph to determine if the graph represents a function. If the line intercepts the graph only once, it is a function.
y = 5(x + 1)²
Vertex (-1, 0)
y = 5x² - 1
Vertex (0, -1)
y = 3(x - 2)² - 1
Vertex (2, -1)
79
What is the maximum
90
What is the maximum
50
What is the median
10
What is the minimum
20
What is the minimum
70/100 70%
What is the percent of students favors rule?
12/40 30%
What is the percent of students who play both soccer and cricket given that they play soccer?
(-1,-8)
What is the point of intersection of the following system of equations? 8x + y = -16 -3x + y = -5
(0,-1)
What is the point of intersection of the following system of linear equations? 16x - 10y = 10 -8x - 6y = 6
(4,-2)
What is the solution set for the following system of linear equations? 8x + 14y = 4 -6x - 7y = -10
30
What is the value of Quartile 1
45
What is the value of Quartile 1
55
What is the value of Quartile 3
70
What is the value of quartile 3
x = 5
What is the value of the x-coordinate in the following system of linear equations? -6x + 6y = 6 -6x + 3y = -12
x = 10
What is the value of the x-coordinate in the following system of linear equations? x - y = 11 2x + y = 19
y = -2
What is the value of the y-coordinate in the following system of linear equations? -x - 7y = 14 -4x - 14y = 28
y = -1
What is the value of the y-coordinate in the following system of linear equations? 16x - 10y = 10 -8x - 6y = 6
4/11 36.4%
What percent of boys that can not bike to school given that the student is a boy?
8/35 22.9%
What percent of coffee-lovers are chemistry students given that they are coffee-lovers?
58/400 14.5%
What percent of customers bought water and pizza?
228/800 28.5%
What percent of people exhibiting symptoms of arthritis?
36/67 53.7%
What percent of people surveyed prefer Hondas?
2/20 10%
What percent of students surveyed play on a sport team but do not play an instrument?
20/40 50%
What percent of those surveyed are left-handed?
39/240 16.25%
What percent of those surveyed are men who like sports cars?
80/160 50%
What percent of those surveyed are students who like skateboards and like snowmobiles?
8/30 26.7%
What percent of women preferring movies given that the adult is a woman?
75
What percentage of scores are above a 30
25
What percentage of scores is above 55
Non-linear association
When data points do not lie close to a line
No association or No correlation
When there is no pattern in the observed data
then there is no solution.
When under the square root is negative...
then there is one solution.
When under the square root is zero...
11x7
77
7x11
77
(x²+5)(7x-3)
7x³-3x²+35x-15
4x2
8
8x1
8
√64=
8
10x8
80
8x10
80
9x9
81
h(t)= 6 + 20t - 16t²
A basketball is chest-passed from a 6ft tall player at a rate of 20ft/s.
y = 6543(0.975)^t
A bear population depreciates by 2.5% every year. If there are currently 6,543 bears, what would the exponential function look like?
about 12 miles per hour
A bicyclist is traveling 12,650 inches per minute. What is his speed in miles per hour?
h(t)= 20 + 90t - 16t²
A cannon launches a ball from a height of 20ft with an upward velocity of 90ft/s.
about 13 miles per hour
A car is traveling at 2,300 feet in 2 minutes. What is the speed in miles per hour?
y=5x+100
A cement company charges $5 dollars per square ft of concrete plus $100 dollars for equipment rental....
y = 3(1.045)^35
A certain kind of bacteria increases at a rate of 4.5% per day. The sample began with 3 bacteria. What will the equation be to find the amount of bacteria after 35 days?
y = 6500(0.857)^t
A computer valued at $6500 depreciates at a rate of 14.3% per year. Write a function that would model the value of the computer.
y=30x
A dragonfly can beat its wings 30 times per second...
h(t) = 58t - 16t²
A football is kicked to start a game at a rate of 58ft/s.
8
A fossil decays at a rate of 7% per week. If there are 24 square centimeters of fossil how much will be left in 15 weeks?
h(t)= 165t - 16t²
A golf ball is hit with a velocity of 165ft/s.
Discrete Graph
A graph consisting of distinct, unconnected points.
Continuous Graph
A graph that can be graphed with a line or a smooth curve.
Scatterplot
A graph that shows the relationship between a data set with two variables, graphed as ordered pairs on a coordinate plane
y=50-5x
A hiker on top of a mountain starts at an elevation 50 meters then walks down to the base at rate of 5 meters per minute...
y=50x+2000
A hot air balloon is 2000ft in the air and starts to ascend at 50ft per second...
y=2000-50X
A hot air balloon is 2000ft in the air, and starts to descend at a rate of 50ft per min...
Line of best fit
A line that is very close to most of the data points in a scatter plot
y=50x+25
A machine shop charges $50 per hour of labor plus a $25 delivery fee...
y=8x+1.25
A movie theater charges $8 per bag of popcorn and an additional fee of $1.25 for butter...
Coefficient
A number multiplied by a variable in an algebraic expression.
about 16 miles per hour
A police officer saw a car travel 23 feet per second. What is the speed limit in miles per hour?
y=2000-10x
A pool containing 2000 gallons of water has a pump draining the water at 10 gallons per min...
y=10x+2000
A pool with 2000 gallons of water is being filled at a rate of 10 gallons per minute...
1021
A population of 800 beetles is growing at a rate of of 5% each month. How many beetles will there be in 5 months?
1437
A population of 800 beetles is growing at a rate of of 5% each month. How many beetles will there be in a year?
y = 800(1.05)^x
A population of 800 beetles is growing at a rate of of 5% each month. Write an equation to model the population of beetles in x months.
h(t)= 240 - 16t²
A pumpkin is dropped from a height of 240ft.
Exact Value (example)
A recipe that calls for 2 eggs is being doubled.
y=25x+50
A repair shop charges $25 per hour and a $50 diagnostic fee...
Approximation (example)
A square with a side 12 feet long has a diagonal of 16.97 feet.
experimental study
A study in which the researcher manipulates/controls one of the variables and tries to determine how the manipulation influences other variables.
Constant
A value that does not change
y=1.25x+8
A video store charges $1.25 per movie rented and a one time fee of $8 for membership...
y=3x
A video store charges $3 per movie rented...
Estimation (example)
A wedding planner needs to determine how many appetizers to order for between 200 and 220 guests.
h(t)= 485 - 16t²
A window cleaner drops his bucket from the scaffolding hanging 485ft above the ground.
percent
A word we use to express how many parts out one hundred
a + c = b + c
Addition Property of Equality
1.362
Amani throws a long pass up the basketball court. The function for the ball is modeled as the h(t) = -4.9x^2 + 3x + 5. How many seconds will it take for her pass to hit the ground and bounce to the player she is passing to?
0.911
Amaya Renee Tolbert is cheerleading at Penn State University. Her teammates are strong and launch her into the air 6 feet off the ground at an initial velocity of 8 f/s. Then Penn State scores a touchdown and the other cheerleaders celebrate and forget to catch her. How many seconds will it take for Maya to hit the ground?
$5,695.31
An $18,000 car depreciates 25% each year. How much will the car be worth in 4 years?
A pattern of numbers that use addition or subtraction to go up or down by the same amount each time
An arithmetic sequence is
h(t)= 1300 - 88t - 16t²
An arrow is shot downwards from a height of 1300ft with a velocity of 88ft/s.
Linear association
An association in which the data appear to lie close to a line
9.293
Wile E Coyote is at a rooftop restaurant in Charlotte listening to the finest Ukulele music he has ever heard. When all of a sudden he sees the Road Runner and he launches an anvil toward the ground at an initial velocity of 45 feet per second off of an 1800 foot building. He misses and the and the anvil hits the ground. How long does it take to hit the ground?
272 feet
With no air resistance, an object would fall 16 feet during the first second, 48 feet during the second second, 80 feet during the third second, 112 feet during the fourth second, and so on. How many feet will the object fall during the ninth second?
$ 2586.70
Yolonda invests $2000 at an interest rate of 1.4%. How much will she have in 18 years?
$ 3392.55
You invest $2500 at a 3.1% interest rate. Find the value of the investment after 10 years.
2
Your new computer was worth $1500 but it depreciates in value by 18% each year. After how many years will your computer be worth $1000?
$306.62
Your new computer was worth $1500 but it depreciates in value by 18% each year. How much will your computer be worth (to the nearest penny) after 96 months?
y = 1500(.82)^t
Your new computer was worth $1500 but it depreciates in value by 18% each year. Write an equation to model the value of the computer after t years.
data set
a collection of numbers that answer a statistical question
histogram
a diagram of data grouped into ranges; each bar represents a range of data
box plot
a diagram of range, median, and interquartile range;
line plot
a diagram that uses x's and a number line to show the values in a data set
histogram
a graph that uses intervals to describe the categories, it is a frequency graph
Clustering
a group of data points bunched up together
measure of center
a measurement that identifies a center of distribution in a data set; such as the mean and median
outlier
a number that is different from other numbers in the data set; it stands apart from the other data
Outlier
a point that lies outside of the data
Exponential decay is when...
a quantity decreases by the same factor over time.
Exponential growth is when...
a quantity increases by the same factor over time.
Function
a relation where every x-value has exactly one y-value
Relation
a set of ordered pairs
observational study
a study based on data in which no manipulation of factors has been employed
Estimate (definition)
a value made inexact on purpose in order to make calculations easier
Approximation (definition)
a value used to represent a true measurement when an exact answer is not possible
nth term definition
any term in the sequence
y = 2(x - 3)² + 1
axis of symmetry x = 3
y = 2(x + 2)² - 1
axis of symmetry x= -2
a¹²
a⁶⋅a⁶
1
a⁷/a⁷
1
a⁷⋅a⁻⁷
What is the y-intercept of the following line: y = 7 + 5/3x
b = 7
1/c³
c³/c⁶
c³
c⁶/c³
c⁵
c⁹⋅c⁻⁴
1/c⁵
c⁻⁹⋅c⁴
Normal distribution
describes a symmetrical, bell shaped curve that shows the distribution of
Range
difference between lowest and highest values
first term
f(1)
second term
f(2)
third term
f(3)
fourth term
f(4)
nth term symbol
f(n)
next term
f(n+1)
previous term
f(n-1)
Function Notation
f(x)
2
f(x)=1/2 x - 3 Find f(10).
-1
f(x)=1/2 x - 3 Find f(4).
26
f(x)=1/2 x - 3 Find x if f(x) = 10
28
f(x)=1/2 x - 3 Find x if f(x) = 11
36
f(x)=1/2 x - 3 Find x if f(x) = 15
56
f(x)=1/2 x - 3 Find x if f(x) = 25
22
f(x)=1/2 x - 3 Find x if f(x) = 8
Exponential Function
f(x)=a(b)^x
0
find f(-2) = 5x + 10
-31
find f(-8) = 3x - 7
12
find f(-9) - g(8) when f(x) = -2x -5 and g(x) = (1/2)x -3
Factoring Method
find two numbers that multiply to get ac and add/subtract to get b, and then factor by grouping
10
find x for f(x) = -4x - 8 when f(x) = -48
-1
find x for f(x) = 4x + 2 when f(x) = -2
-5
g(x)= -4x + 7 Find g(3).
-21
g(x)= -4x + 7 Find g(7).
5
g(x)= -4x + 7 Find x if g(x) = -13
-4
g(x)= -4x + 7 Find x if g(x) = 23
1
g(x)= -4x + 7 Find x if g(x) = 3
0
g(x)= -4x + 7 Find x if g(x) = 7
Domain & Range of a Discrete Graph
given as a list {3, 4, 5}
Domain & Range of a Continuous Graph
given as an inequality 4<x<9
Graphing Method
graph the equation and the solution is the x-intercept, where the parabola meets or crosses the x-axis
-18
h(x)=6x Find h(-3).
30
h(x)=6x Find h(5).
-2
h(x)=6x Find x if h(x) = -12
4
h(x)=6x Find x if h(x) = 24
8
h(x)=6x Find x if h(x) = 48
10
h(x)=6x Find x if h(x) = 60
11
h(x)=6x Find x if h(x) = 66
Accuracy (definition)
how close a measurement or calculation is to its actual value
first quartile
it is the middle number between the lower extreme (smallest number) and the median of a data set
maximum or minimum value
k
What is the slope of a horizontal line?
m = 0
Median
middle number in a set of data
Irrational
non-terminating decimals, non-repeating decimals, π
-a
parabola open downward
+a
parabola opens upward
Quadratic Formula Method
plug in a, b, and c into the quadratic formula and solve
y-intercept
point where a line crosses the y-axis
1/p⁴
p³/p⁷
p⁴
p⁷/p³
r
rate (in decimal form)
slope
rise over run
m
slope
y=mx+b
slope intercept form
Rational
terminating decimals, repeating decimals, ratios/fractions, integers, perfect squares, whole numbers
mean absolute deviation
the average distance from the mean to the numbers in the data set
mean
the average of all of the values in the data set; is a measure of center
interquartile range
the difference between the first quartile and the third quartile of a data set; it is a measure of range
range
the difference between the lowest value and the highest value in a data set
b
the growth or decay factor in an exponential function.
Independent variable
the input of an equation
skewed data distribution
the mean is too far to the right or left of the peak
third quartile
the middle number between the median and the upper extreme (largest number) of a data set
median
the middle value in a data set that is arranged in ascending order; is a measure of center
frequency
the number of times an event occurs
mode
the number that appears most often in a data set
Mode
the number that appears the most often in a list of numbers
Dependent variable
the output of an equation
distribution
the overall shape of data related to a statistical question; it can include normal, bimodal, or the data can be left or right skewed
Discriminant
the part of the quadratic equation which is located inside of the square root= b squared - 4ac
joint relative frequency
the relative frequency in a two-way table that joins two separate subcategories
Domain
the set of all x-values
Range
the set of all y-values
initial value
the starting amount or y-intercept of the graph
marginal relative frequency
the sum of the joint relative frequencies in a row or column in a two-way table
quartile
the values that divide a data set into quarters
a
the variable the represents the initial amount in an exponential function
x = 2
x = 2
x = 4
x = 4
Axis of Symmetry
x = h
(y+3)(x+5)
xy+5y+3x+15
0; one real solution
x² +4x+4=0
(x+5y)(x+3)
x²+3x+5yx+15y
(x - 2a)(x-144)
x²-144x-2ax+288a
(x²+3)(1-5y)
x²-5yx²+3-15y
x⁴y⁵
x²y² × x²y³
x⁹
x³ × x⁶
(x+a)(x²+b)
x³+bx+ax²+ab
(x²+3)(x-6)
x³-6x²+3x-18
1
x⁰
(x³+5)(x+1)
x⁴+x³+5x+5
x⁶
x⁵⋅x
x³
x⁸ / x⁵
x³
x⁹ / x⁶
x³ / y⁶
x⁹y³ / y⁹x⁶
x⁶
x⁻² × x³ × x⁵
b
y-intercept
Bananas sell at 60 cents per pond
y=.6x
A video store charges $1.25 per movie rented and a one time fee of $8 for membership
y=1.25x+8
To rent a van a company charges for $100 a day plus a $5 cleaning fee
y=100x+5
to save for college Jim puts $500 into a saving account and continues to add $100 every month throughout high school.
y=100x+500
You use a $100 gas card to pay for gas at $2 per gallon
y=100−2x
A pool with 2000 gallons of water is being filled at a rate of 10 gallons per minute
y=10x+2000
to play mini golf it cost $15 per hour plus a $3 rental fee for the golf club.
y=15x+3
A pool containing 2000 gallons of water has a pump draining the water at 10 gallons per min
y=2000-10x
a hot air balloon at 2000 ft starts to descend at a rate of 50ft per min
y=2000-50X
A repair shop charges $25 per hour and a $50 diagnostic fee
y=25x+50
a dragon fly can beat its wings 30 times per second
y=30x
A video store charges $3 per movie rented
y=3x
Susan pays a membership fee of $15 plus $3 per hour
y=3x+15
a hiker on top of a mountain starts at an elevation 50 meters then walks down to the base at rate of 5 meters per minute
y=50-5x
Sammy received $500 for his birthday and decides to spend $100 each week hanging out with his friends
y=500-100X
A hot Air balloon at 2000 ft starts to ascend at 50 ft per second
y=50x+2000
A machine shop charges $50 per hour of labor plus a $25 delivery fee
y=50x+25
a cement company charges $5 dollars per square ft of concrete plus $100 dollars for equipment rental.
y=5x+100
A balloon released from the top of a building 50 meters tall rises at a rate of 5 meters per second
y=5x+50
A movie theater charges $8 per bag of popcorn and an additional fee of 1.25 for butter
y=8x+1.25
Function for exponential growth
y=a(1+r)^x so that b>1
Function for exponential decay
y=a(1-r)^x so that b< 1
This set of ordered pairs is a function
{(0, 1), (1, 2), (3, 4), (5, 4)}
This set of ordered pairs is NOT function
{(1, 5), (2, 4), (3, 6), (2, 9)}
The graph shows the system {y=−x+2 {y=−x²+x+1 . Which ordered pair is the solution of the system?
(1, 1)
2z⁴√(3xy)
√(12xyz⁸)
2x³y⁶z⁴√(3z)
√(12x⁶y¹²z⁹)
2x⁵y⁵√(2xy)
√(18x⁸y⁶z¹²)
3x⁴y³z⁶√(2x)
√(18x⁹y⁶z¹²)
3x⁵y⁴z³√(3xy)
√(27x¹¹y⁹z⁶)
4x³y√(3y)
√(48x⁶y³)
7/4
√(49/16)
5xy√(2y)
√(50x²y³)
2√6
√(6)*√(4)
5x²y√(3xy)
√(75x⁵y³)
2x√(2x)
√(8x³)
2√3
√12
7√3
√12+ 5√3
5√5
√125
3√2
√18
8√2
√18+ 5√2
2√5
√20
10√2
√200
2√6
√24
3√3
√27
10√3
√300
4√2
√32
3√5
√45
4√3
√48
-√5
√5 - 2√5
5√2
√50
10√5
√500
3√6
√54
5√3
√75
2√2
√8
7x4
28
√784=
28
11x3
33
3x11
33
7√2
3√2 + 4√2
8√3
3√3 + 5√3
6√2
3√8
2x2
4
4x1
4
√16=
4
geometric common ratio 5
4, 20, 100, 500, , , ...
10x4
40
4x10
40
5x8
40
8x5
40
12x9
108
9x12
108
√169=
13
8x2
16
√256=
16
geometric common ratio 2
6, 12, 24, 48, , , ...
geometric common ratio 4
6, 24, 96, 384, , , ...
geometric common ratio 6
6, 36, 216, 1296, , , ...
5x12
60
6x10
60
8x8
64
arithmetic common difference -8
64, 56, , , 32, 24, ...
6x12
72
8x9
72
9x8
72
10x9
90
9x10
90
y = 50(1.03)^t
A baseball card bought for $50 increases 3% in value every year. What is the exponential equation that matches the given information?
y=5x+50
A balloon released from the top of a building 50 meters tall rises at a rate of 5 meters per second...
10x10
100
geometric common ratio 1/3
108, 36, 12, 4, 1, , , ....
geometric common ratio 1/6
1080, 180, 30, 5, , , ....
(5x+3)(2x-1)
10x²-5x+6x-3
5x⁷
10x⁹ / 2x²
11x1
11
This system has one solution. {y=5x−9 {y=x²−3x+7 What is the y-coordinate of the solution? Enter your answer in the box.
11
√121=
11
10x11
110
11x10
110
y = -11/3x -4
11x + 3y = -12
12x1
12
2x6
12
3x4
12
4x3
12
6x2
12
√144=
12
10x12
120
12x10
120
11x11
121
geometric common ratio 1/4
128, 32, 8, 2, , , ...
(3+x²)(4x-5)
12x-15+4x³-5x²
11x12
132
12x11
132
y = 13/2 x - 6
13x - 2y = 12
12√6
13√6 - √6
7x2
14
√196=
14
12x12
144
3x5
15
5x3
15
√225=
15
4x4
16
(4y-3)(5x+1)
20yx+4y-15x-3
3x7
21
7x3
21
√441=
21
11x2
22
√484=
22
√529=
23
12x2
24
3x8
24
4x6
24
6x4
24
8x3
24
√576=
24
5x5
25
√625=
25
Each piece of the box plot is worth what percent?
25%
√676=
26
3x9
27
9x3
27
√729=
27
4x7
28
√841=
29
10x3
30
3x10
30
5x6
30
6x5
30
√900=
30
4x8
32
8x4
32
12x3
36
3x12
36
4x9
36
6x6
36
9x4
36
24u⁸
3u²⋅8u⁶
y = -3/4x - 8
3x + 4y = -32
y = 3/4x - 2
3x - 4y = 8
36; two real solutions
3x² + 3 = 6
100; two real solution
3x² + 8x - 3 =0
(3x-1)(x+2)
3x²+6x-x-2
(3x+y)(x-6)
3x²-18x+xy-6y
(3x+1)(x-2)
3x²-6x+x-2
(3x²+1)(x-4)
3x³-12x²+x-4
3/x⁶
3x⁻⁶
9√2
3√18
6x7
42
7x6
42
11x4
44
4x11
44
5x9
45
9x5
45
7x7
49
64; two real solution
4m² - 4 = 0
y = -4/7x + 5
4x + 7y = 35
32x² + 4x
4x(8x + 1)
-76; no real solution
4x² +2x +5 =0
7√2
4√18- √50
5x1
5
√25=
5
10x5
50
5x10
50
6x9
54
9x6
54
11x5
55
5x11
55
7x8
56
8x7
56
10x6
60
12x5
60
y = -5x - 2
5x + y = -2
y = 5/2 x + 8
5x - 2y = -16
y = 5/7 x + 3
5x - 7y = -21
(5-3x)(x-2)
5x-10-3x²+6x
(5x+3)(x²-5)
5x³-25x+3x²-15
(5y+1)(x-3)
5yx-15y+x-3
2x3
6
3x2
6
6x1
6
√36=
6
arithmetic common difference -9
62, 53, , , 26, 17, ...
7x9
63
9x7
63
7x1
7
12x6
72
-204; no real solution
6x² - 6x +2 = -8
(2x-5)(3x+1)
6x²+2x-15x-5
30x⁷ - 42x⁶ + 6x⁵
6x⁵(5x² - 7x + 1)
15√2
6√2+ 3√18
Mike repairs televisions. His revenue, in dollars, can be modeled by the equation y = 25 + 30x, where x is the number of hours spent repairing televisions. His overhead cost, in dollars, can be modeled by the equation y=5x²−10 , where x is the number of hours spent repairing televisions. After how many hours does he break even? Note: The phrase break even refers to the value where the two functions are equivalent. Enter your answer in the box.
7
√49=
7
10x7
70
7x10
70
12x7
84
7x12
84
11x8
88
8x11
88
3x3
9
9x1
9
√81=
9
arithmetic common difference -5
92, 87, 82, 77, , , ...
arithmetic common difference -2
92, 90, 88, 86, , , ...
12x8
96
8x12
96
arithmetic common difference 3
97, 100, 103, 106, , , ...
11x9
99
9x11
99
y - 9/2x - 5
9x - 2y = 10
4; two real solution
9x² - 2x =0
$7800.40
A $12,500 car depreciates 9% each year. How much will the car be worth in 5 year?
8
A Geometric sequence has a first term of 16 and a common ratio of 1/2. Find the 2nd term.
32
A Geometric sequence has a first term of 4 and a common ratio of 2. Find the 4th term.
h(t)= 8 + 74t - 16t²
A ball is thrown from a height of 8ft with an upward velocity of 74ft/s.
