Algebra 2 Review
Is this a quadratic function? (6.1)
yes
Determine if it is a polynomial and state the degree: (5.2) 1/6x³y⁵ - 9x⁴
yes, 8th degree
Solve 3ˣ = 11. (Only write the first four decimal places) (10.4)
2.1828
stem plot (Unit S)
A data display that shows each data value in two parts according to its place value. The stem represents the first digit or digits, and the leaf represents the last digit of the number.
box plot (Unit S)
A graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median.
Simplify: -2i x 7i (5.9)
14
2x (7x² - 3x + 5) (5.2)
14x(cubed) - 6x(squared) + 10x
Do this equation following the Order of Operations: [2 (10-4)² + 3] ÷ 5 (1.1)
15
standard form (2.2)
Ax + By = C (A, B, and C are integers whose greatest common factor is 1; A>=0; A + B are not 0)
What is this photo illustrating? (12.7)
Skewed left vs skewed right.
______ is also referred to as rate of change. (2.3)
Slope
Why do you always check absolute value equations? (1.4)
Sometimes the answers may not be actual solutions of the original equation.
linear function (2.2)
a function whose order parts satisfy a linear equation and can be written f(x) = mx + b (m and b are real numbers)
dot plot (Unit S)
a graphical device that summarizes data by the number of dots above each data value on the horizontal axis
family of graphs (2.3)
a group of graphs with one or more similar characteristics
line of fit (2.5)
a line that closely approximates a set of data
common logarithm (10.4)
a logarithm with base 10 (LOG key on a calculator)
step function (2.6)
a nonlinear graph that consists of line segments or rays
real number (1.2)
a number that represents exactly one point on a number line
Greatest Common Factor (GCF) General Case (5.4)
a³b² + 2a²b - 4ab² = ab (a²b + 2a - 4b)
multiplication and division properties (1.3)
for all numbers a, b, and c if a=b then a*c=b*c and if c does not equal 0 then a/c=b/c
Trichotomy Property (property of order) (1.5)
for any two real numbers, a and b, exactly one of the following statements is true: a < b , a = b, and a > b
When dividing two functions, (f/g)(x) is equal to __________ as long as g(x) does not equal 0. (7.7)
f(x)/g(x)
Dividing Rational Expressions (9.1)
factor expressions, identify restricted values, change to multiplication (multiply the reciprocal by the divisor), reduce common factors
Multiplying Rational Expressions (9.1)
factor, identify restricted values, reduce common factors
Commutative and associative properties of multiplication hold true for _____ imaginary numbers. (5.9)
pure
A composition of two functions only works if the ______ of the leading function is equal to the ________ of the other function. (7.7)
range, domain
imaginary number (5.9)
root of a negative number
The entry in the first row and the first column of AB is found by multiplying corresponding elements in the first _____ of A and the first _____ of B and then adding. (4.3)
row, column
parent graph (2.3)
simplest graph of the family
prediction equation (2.5)
the equation of a line of fit that can be used to predict one variable given the other
set-builder notation (1.5)
the expression of the solution set of an inequality (x|x)
intersection (1.6)
the graph of a compound inequality containing "and" (the inequalities connecting/overlapping)
Union (1.6)
the graph of a compound inequality containing "or" (to put together)
boundary (2.7)
the linear equation that separates the graph into for a linear inequality
quotient property of radicals (5.6)
the nth of a/b is equal to the nth of a divided by the nth of b (a and b are real numbers, a and b are not 0, n is greater than 1, all roots are defined)
In complex numbers, i is equal to _______. (5.9) (Write out your answer in words.)
the square root of -1
Associative Property (1.2)
(a+b)+c=a+(b+c), (a·b)·c=a·(b·c)
In completing the square, what equation do you use to find c? (6.4) (Write out your answer in words.)
(b/2)(squared)
Solve 5e⁻ˣ - 7 = 2. (10.5)
-0.5878
Find the slope of the line that passes through (-1, 4) and (1, -2). (2.3)
-3
Solve |a| < 4 (1.6)
-4 < 0 < 4;
Names for degrees in a polynomial. (5.2)
0 - Constant, 1 - Linear, 2 - Quadratic, 3 - Cubic, 4 - Quartic, 5 - Quintic, nth degree
exponential decay range for b (10.1)
0 < b < 1
a⁰ (5.1)
1
Solve 13 < 2x + 7 <= 17 (1.6)
3 < x < 5; [-1,2)
Simplify: 2√12 - 3√27 + 2√48 (5.6) (write out your answer with "times the square root of")
3 times the square root of 3
What is the dimension of the matrix pictured? (4.1)
3 x 3 (rows, then columns)
Solve log E = 24.55 for E. (10.4)
3.55 x 10 (to the 24th power)
Solve log⁴ n = 5/2 (10.2)
32
Find the LCM of 18r²s⁵, 24r³st², and 15s³t. (9.2)
360r³s⁵t²
(5√3 - 6)(5√3 + 6) (5.6)
39
Simplify: √-18 (5.9) (Write out your answer in words.)
3i times the square root of 2
Write in standard form and identify A, B, and C: -3/5x = 3y -2 (2.2)
3x + 15y = 10; A = 3, B = 15, C = 10
Simplify: √16p⁸q⁷ (5.6) (Write out your answer in words.)
4 p to the 4th power times q to the 3rd power times the square root of q
State degree and leading coefficient of the following equation: 7x⁴ + 5x² + x - 9 (7.1)
4, 7
Solve where x=8 and y=1.5: x²-y(x+y) (1.1)
49.75
State degree and leading coefficient of the following equation: 1/2x² + 2x³ - x⁵ (7.1)
5, -1
histogram (Unit S)
A bar graph where the data values are placed in ranges and the frequency that data falls a range is graphed.
frequency table (Unit S)
A table for organizing a set of data that shows the number of times each item or number appears.
Solve for the area of a trapezoid where the formula is A=½h(b¹+b²) and h=10in, b¹=16in, and b²=52in (1.1)
A=340
Find the dimensions: A(2×3) × B(3×4) (4.3)
AB(2×4)
Solution |a| > -4 (1.6)
All real numbers
linear equation (2.2)
An equation with all of the following true: 1. No operations other than addition, subtraction, and multiplication of a variable by a constant 2. Variables are not multiplied together or appear in a denominator 3. No exponents greater than 1 4. The graph of the equation is a line
natural base e (10.5)
An irrational number approximately equal to 2.71828... .
Name the Property: 3(4x)=(3·4)x (1.2)
Associative Property of Multiplication
_____ in an interval notation means that the endpoint is included in the set. (1.5)
Bracket
Name the Property: (5+7)+8=8+(5+7) (1.2)
Commutative Property of Addition
Categorical vs. Quantitative Data (Unit S)
Data are categorical if they fall into groups or categories and data are quantitative if they take on numerical values where it makes sense to find an average.
The _____ variable depends on the _____ variable. (2.1)
Dependent, Independent
What is the domain and range of y = 2x + 1? Is it a function? (2.1)
Domain and range: all real numbers Yes, it is a function.
What is the domain and range of x = y(y) - 2? Is it a function? (2.1)
Domain: {x|x >= -2} Range: all real numbers Not a function.
Solution |a| < -4 (1.6)
Empty Set
Even or odd degree? How many zeros? (7.1)
Even, 2
Even or odd degree? How many zeros? (7.1)
Even, 4
How to find the LCM (9.2)
Factor each number, them multiply each (differing) factor the greatest power that is is represented by together
addition and subtraction properties (1.3)
For all numbers a, b, and c, if a=b, then a+c=b+c and a-c=b-c
Square Root Property (6.4)
For any real number n, if x² = n, then x = +-√n.
zero product property (6.3)
For any real numbers a and b, if ab = 0, then either a = 0 or b = 0 or both.
marginal relative frequency (L.T. P.4)
Found by dividing a row total or a column total by the grand total
addition of matrices (4.2)
If A + B are two m x n matrices, then A + B is an m x n matrix in which each element is the sum of the corresponding elements of a and b
subtraction of matrices (4.2)
If A + B are two m x n matrices, then A - B is an m x n matrix in which each element is the difference of the corresponding elements of a and b
Complex Conjugates Theorem (7.5)
If a + bi is a zero, then a - bi is also a zero.
addition property of inequality (1.5)
If a < b, then a + c < b + c
Rational Zero Theorem (7.6)
If p/q is a rational number in simplest form and is a zero of y = f(x), then p is a factor of the leading coefficient and q is a factor of the y-intercept.
point discontinuity (9.3)
If the original function is undefined for x = a but the simplest form is defined for x = a, then there is a hole in the graph at x = a.
What do you call a consistent and independent system of equations? (3.1)
Intersecting lines
TRACK AND FIELD In a 4-team track meet, 5 points were awarded for each first-place finish, 3 points for each second, and 1 point for each third. Find the total number of points for each school. Which school won the event? (4.3) Jefferson - 1st = 8, 2nd = 4, 3rd = 5 London - 1st = 6, 2nd = 3, 3rd = 7 Springfield - 1st = 5, 2nd = 7, 3rd = 3 Madison - 1st = 7, 2nd = 5, 3rd = 4
Jefferson
Examples of linear equations or not? 7a + 4b(4b) = -8 y = ***square root of***(x + 5) x + xy = 1 y = 1/x (2.2)
Not
Even or odd degree? How many zeros? (7.1)
Odd, 1
Even or odd degree? How many zeros? (7.1)
Odd, 5
68-95-99.7 rule (empirical rule) (Unit S)
Probability of: 1 standard deviation from the mean- 68% of the data 2 standard deviations from the mean- 95% of the data 3 standard deviations from the mean- 99.7% of the data
Inerquartile Range (IQR) formula (Unit S)
Q(3) - Q(1)
What do you call a consistent and dependent system of equations? (3.1)
Same lines
direct variation (9.4)
Special case of slope-intercept where m = k and b = 0; y varies directly as x
How do you determine which side of the boundary to fill in? (2.7)
You choose a point to test it on that is not on the boundary line (usually the origin) and whether that point make the inequality true or not dictates which side of the boundary you fill in.
If A = [7 3] and B = [9 6], find 5A - 2B. [-4 -1] [3 10] (4.2)
[ 17 3 ] [-26 -25]
Find RS if R = [2 -1] and S = [3 -9] [3 4] [5 7] (4.3)
[1 -25] [29 1]
Find A + B if A = [4 -6] and B = [-3 7] [2 3] [5 -9] (4.2)
[1 1] [7 -6]
Make a matrix based on the chart (picture) (4.1)
[24 26 31 35 35 32] [13 16 28 26 26 26]
Find PQ if P = [8 -7] and Q = [9 -3 2] [-2 4] [6 -1 -5] [0 3] (4.3)
[30 -17 51] [6 2 -24] [18 -3 -15]
Find A - B if A = [9 2] and B = [3 6] [-4 7] [8 -2] (4.2)
[6 -4] [-12 9]
If A = [2 8 -3], find 3A. (4.2) [5 -9 2]
[6 24 -9] [15 -27 6]
absolute value (1.4)
a number's distance from zero on the number line
matrix (4.1)
a rectangular array of variables or constants in horizontal rows and vertical columns, usually enclosed in brackets
Scatter Plot (2.5)
a set of data graphed as ordered pairs in a coordinate plane
relation (2.1)
a set of ordered pairs
aᵐ x aⁿ (5.1)
a to the m + n th power
aᵐ/aⁿ (5.1)
a to the m - n th power
(aᵐ)ⁿ (5.1)
a to the m times n th power
(a/b)ⁿ (5.1)
a to the power of n / b to the power of n
function (2.1)
a type of relation in which each element of the domain is paired with exactly one element of the range
Distributive Property (1.2)
a(b + c) = ab + ac and (b + c)a = ba + ca
intercept form (6.2)
a(x - p)(x - q); p and q are the x intercepts
Identity Property (1.2)
a+0=a=0+a, a·1=a=1·a
Commutative Property (1.2)
a+b=b+a, a·b=b·a
Simplify the following equations: a. ((x² + 2x - 8)/(x² + 4x + 3))((3x + 3)/(x - 2)) b. ((a + 2)/(a + 3))/((a² + a - 12)/(a² - 9)) (9.1)
a. (3x + 12)/(x + 3) b. (a + 2)/(a + 4)
Use a calculator to find (a.) log 3 and (b.) log 0.2 (answer with the first 4 places). (10.4)
a. 0.4771 b. -0.6990
Simplify the following equations: a. ⁸√x⁸ b. ⁴√81(a + 1)¹² (5.5)
a. IxI b. 3 I(a + 1)(cubed)I
Change from radical to rational form: a. a¹/⁴ b. ³√y (5.7)
a. a to the 4th root b. y to the 1/3 power
Exponential growth or decay? a. y = (1/5)ˣ b. y = 3(4)ˣ c. y = 7(1.2)ˣ (10.1)
a. decay b. growth c. growth
Write the following in logarithmic form: a. 10³ = 1000 b. 9¹/² = 3 (10.2)
a. log¹⁰ 1000 = 3 b. log⁹ 3 = 1/2
Solve: a. 3²ⁿ ⁺ ¹ = 81 b. 4²ˣ = 8ˣ ⁺ ¹ (10.1)
a. n = 3/2 b. x = -3
Reflexive Property (1.3)
a=a
General Trinomial General Case (5.4)
acx² + (ad + bc)x + bd = (ax + b)(cx + d)
You find the degree of a monomial by _________ the exponents of its variables. (5.1)
adding
Many properties of real numbers also hold true for matrices, including the commutative property of _________, ___________ property of addition, and the d___________ property. (4.2)
addition, associative, distributive
When solving a system of equations, a system with an answer that is always true means that the solution is ___ ____ _______. (3.2)
all real numbers
Rational functions can have breaks in continuity, including having a vertical ____________ and/or a point _____________. (9.3)
asymptote, discontinuity
Grouping General Case (5.4)
ax + bx + ay + by = x(a + b) + y(a + b) = (a + b)(x + y)
standard form (6.2)
ax squared + bx + c = 0
quadratic equation (6.2)
ax(x) + bx + c = 0
Perfect Square Trinomials General Case (5.4)
a² + 2ab + b² = (a + b)² or a² - 2ab + b² = (a - b)²
Difference of Two Squares General Case (5.4)
a² - b² = (a + b)(a - b)
Sum of Two Cubes General Case (5.4)
a³ + b³ = (a + b)(a² - ab + b²)
Difference of Two Cubes General Case (5.4)
a³ - b³ = (a - b)(a² + ab + b²)
complex number (5.9)
can be written in the form (a + bi) where a and b are real numbers and i is the imaginary unit
The numbers along the bottom row when using synthetic division are the ___________ of your answer. For the exponent of the variable, start with _ less exponent than the degree of the dividend. (5.3)
coefficients, 1
You can multiply two matrices if and only if the number of _____ in the first matrix is equal to the number of _____ in the second matrix. (4.3)
columns, rows
An absolute value inequality can be solved by rewriting it as a _____ inequality (1.6)
compound
Must have equivalent ___________ to add or subtract rational expressions. (9.2)
denominators
Matrices can be added if and only if they have the same __________. (4.2)
dimensions
Relations and functions can be represented by _____. (2.1)
equations
When the base of a monomial is a negative number, if the exponent is _____, the expression is not defined. (5.7)
even
Solve f(x) = x(x) + 2 for f(-3). (2.1)
f(-3) = 11
If the degree of a polynomial is ODD and the leading coefficient is NEGATIVE then the end behavior of the graph is... (7.1)
f(x) -> positive infinity as x -> negative infinity, f(x) -> negative infinity as x -> positive infinity
If the degree of a polynomial is EVEN and the leading coefficient is POSITIVE then the end behavior of the graph is... (7.1)
f(x) -> positive infinity as x -> negative infinity, f(x) -> positive infinity as x -> positive infinity
greatest integer function (2.6)
f(x) = [[x]]; means the greatest integer less than or equal to x
quadratic function (6.1)
f(x) = ax(x) + bx + c
constant function (2.6)
f(x) = b; horizontal line
rational function (9.3)
f(x) = p(x)/q(x) as long as q(x) is not equal to 0
identity function (2.6)
f(x) = x; m = 1, b = 0
absolute value function (2.6)
f(x) = |x|; V-shape
When multiplying two functions, (f x g)(x) is equal to... (7.7)
f(x) x g(x)
(Composition of functions) [f ° g](x) = (7.7)
f[g(x)]
You can solve a system by g_______, e__________, or s___________. (3.1 ish)
graphing, eliminating, or substituting
absolute value bars act as a ______ symbol (1.4)
grouping
Use the ___________ _________ test to determine of the inverse of a function is a function. (on a graph) (7.8)
horizontal line
What does slope measure? (2.3)
how steep a line is
An inverse function is true if and only if both of their compositions are the ________ function. ((f ° g)(x) = x and (g ° f)(x) = x) (7.8)
identity
Symmetric Property (1.3)
if a=b, then b=a
Fundamental Counting Principle (12.1)
if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways.
It is improper to have ________ numbers in the denominator of a fraction.
imaginary
Find A + B if A = [3 -7 5] and B = [2 9] [12 5 0] [4 -6] (4.2)
impossible
In a function, the variable is the _____ variable. (2.1)
independent
What is the arrow pointing to? (5.5)
index
Graphs of square root functions can be transformed <like or not like> quadratic functions. (7.9)
like
perpendicular lines (2.3)
lines with opposite reciprocal slopes; two not horizontal or vertical lines with the product of their slopes as -1
rationalizing the denominator (5.6)
multiply both the numerator and the denominator by something to make the denominator a perfect square
equation for turning points by degree (n) (7.2)
n - 1
(n² + 6n - 2) (n + 4) (5.2)
n(cubed) + 10n(squared) + 22n - 8
A radicand CAN NOT be ____________. (7.9)
negative
Is this a quadratic function? (6.1)
no
x + √x + 5 (5.2)
no
Solve √(x - 15) = 3 - √x (5.8)
no solution
Solve. 8x + 2y = 17 -4x - y = 9 (3.2)
no solution
When solving a system of equations, a system with an answer that is never true means that the solution is __ ________. (3.2)
no solution
parallel lines (2.3)
nonvertical lines with the same slope; all vertical lines are parallel
substitution method (3.2)
one equation is solved for one variable in terms of the other, and then you substitute it for the variable in the other equation
Solve log⁵ (p² - 2) = log⁵ p. (10.2)
p = 2
Simplify (r²/(r² - 25s²))/(r/(5s - r)) (9.1)
r/(r + 5s)
standard deviration (12.6)
square root of variance
The ___ value of the vertex of a quadratic function is the maximum value or minimum value obtained by a function. (6.1)
x
Simplify x² + 2x - 3 (over) x² + 7x + 12 (5.4)
x - 1 (over) x + 4
Write in standard form and identify A, B, and C: 3x - 6y - 9 = 0 (2.2)
x - 2y = 3; A = 1, B = -2, C = 3
When using synthetic division, the divisor must be in the form ______ with _ representing the constant of the divisor and being placed in the upper left corner. (5.3)
x - r, r
Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of f(x) = (x² - 9)/(x - 3). (9.3)
x = -3 represents a hole in the graph
Quadratic Formula (6.5)
x = -b ± √(b² - 4ac)/2a
In a quadratic function, the equation for the axis of symmetry is _________. (6.1)
x = -b/2a
Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of f(x) = x/(x - 2). (9.3)
x = 2
Solve 2x - 3 + (y - 4)i = 3 + 2i (5.9)
x = 3, y = 6
Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of f(x) = (x² - 1)/(x² - 6x + 5). (9.3)
x = 5 is a vertical asymptote, and x = 1 represents a hole in the graph
Equation of vertical lines (2.2)
x = C (they only have an x-intercept)
Solve 7x - 5 > 6x + 4. (1.5)
x > 4
What is the domain and range of y = √3x + 4? (7.9)
x >= -4/3 y >= 0
Solve |3x - 12| >= 6 (1.6)
x >= 6 or x <= 2
Simplify 4x³y² + 8xy² - 12x²y³ divided by 4xy. (5.3)
x(squared)y + 2y - 3xy(squared)
Write an equation for the line that passes through (-4, 3) and is perpendicular to the line with the equation y = -4x - 1. (2.4)
y = 1/4x + 4
Solve by substitution. x + 2y = 8 1/2x -y = 18 (3.2)
(22, -7)
Solve by elimination. 4a + 2b = 15 2a + 2b = 7 (3.2)
(4, -1/2)
Solve by substitution. 2x + y = 11 x + 3y = 13 (3.2)
(4, 3)
Simplify 7x/15y² + y/18xy (9.2)
(42x² + 5y²)/90xy²
Solve the following equal matrices for x and y: (rows one and two connect to their corresponding matrix parts) [ y ] = [ 6 - 2y ] [3x] [31 + 4y] (4.1)
(5, -4)
Solve by elimination. 3x - 7y = -14 5x + 2y = 45 (3.2)
(7, 5)
Find the LCM of a² - 6a + 9 and a² + a - 2. (9.2)
(a - 3)²(a + 4)
(ab)ᵐ (5.1)
(a to the power of m)(b to the power of m)
Factor a³ - 4a² + 3a - 12 by grouping. (5.4)
(a(squared) + 3)(a - 4)
(a/b)⁻ⁿ (5.1)
(b/a) to the power of n
Find the LCM of 6 and 4. (9.2)
12
If f(x) = x³ - 2x² - x + 1, find f(3) by using synthetic substitution. (7.4)
7
functional notation (2.1)
f(x) (or another letter besides f) replaces y in a relation
When adding two functions, (f + g)(x) is equal to... (7.7)
f(x) + g(x)
When subtracting two functions, (f - g)(x) is equal to... (7.7)
f(x) - g(x)
If the degree of a polynomial is EVEN and the leading coefficient is NEGATIVE then the end behavior of the graph is... (7.1)
f(x) -> negative infinity as x -> negative infinity, f(x) -> negative infinity as x -> positive infinity
If the degree of a polynomial is ODD and the leading coefficient is POSITIVE then the end behavior of the graph is... (7.1)
f(x) -> negative infinity as x -> negative infinity, f(x) -> positive infinity as x -> positive infinity
-0.25y >= 2 (1.5)
y <= -8
Simplify: 6 times the 3rd root of 9n² multiplied by 3 times the 3rd root of 24n (5.6)
108n
Solve (3 - 2i) - (5 - 4i) (5.9)
-2 + 2i
Find the slope of a the line that passes through A (2/p, 1/2) and B (1/3, 3/p) (9.2)
-3/2
Simplify: √-10 x √-15 (5.9) (Write out your answer in words.)
-5 times the square root of 6
If y varies directly as x and y = 12 when x = -3, find y when x = 16. (9.4)
-64
Josh and Pam have bought an older home that needs some repair. After budgeting a total of $1,685 for home improvements, they started spending $425 on small improvements. They would like to replace six interior doors next. What is the maximum amount they can afford to spend on each door? (1.3)
$210
division property of inequality (1.5)
(+c) If a > b, then a/c > b/c (-c) If a > b, then a/c < b/c
multiplication property of inequality (1.5)
(+c) If a > b, then ac > bc (-c) If a > b, then ac < bc
Solve y - 2 > -3 or y + 4 <= -3 (1.6)
(-infinity, -7] U (-1, +infinity)
Turn x² + 12x into a perfect square. (6.4) (Write out your answer in words.)
(x + 6)(squared)
Simplify (1/x - 1/y)/(1 + 1/x) (9.2)
(y - x)/(xy + y)
List all possible rational zeros. f(x) = x³ - 9x² - x + 105 (7.6)
+-1, +-3, +-5, +-7, +-15, +-21, +-35, +-105
List all possible rational zeros. f(x) = 2x³ - 11x² + 12x + 9 (7.6)
+-1, +-3, +-9, +-1/2, +-3/2, +-9/2
Simplify (w + 12)/(4w - 16) - (w + 4)/(2w - 8) (9.2)
-1/4
What is the slope of the line parallel to x + 4y = -4? (2.3)
-1/4
Simplify (z²w - z²)/(z³ - z³w). (9.1)
-1/z
Names for number of terms in a polynomial. (5.2)
1 - Monomial, 2 - Binomial, 3 - Trinomial, n - Polynomial with n terms
a⁻ⁿ = ______ and 1/a⁻ⁿ = _____ (5.1)
1 / a to the nth power, a to the nth power
If the value of the discriminant is equal to 0, than there is/are __ _____, ________ root(s). (6.5)
1 real, rational
According to the table, what is the marginal relative frequency of left handed people? (L.T. P.4)
12/121 or 9.9%
How to determine if a piece of data is an outlier: Determine the lower and upper bands of the data set. Use the formulas LB = Q(____) + 1.5(IQR) and UB = Q(____) + 1.5(IQR) to determine the bands. If the undecided outlier does not fit in the constraints set by the two bands, it is an outlier. (Unit S)
1, 3
What are the three steps to simplify a radical? (5.6)
1. Factor the radicand into as many squares as possible 2. Use the product property to isolate the perfect squares 3. Simplify each radical
Use log³ 5 = 1.465 and log³ 20 = 2.7268 to find the value of log³ 4. (10.3)
1.2618
What is the probability of getting a 6 and a 1 when two dice are rolled? (L.T. P.1)
1/18 or 6%
Solve In 5x = 4 (10.5)
10.9196
Simplify (-2x³ⁿ) (the difference in intent means it is a fraction). (5.1) (x²ⁿy³)
16 times x to the 4nth power over y to the 12th power
If the value of the discriminant is less than 0, than there is/are __ ________ root(s). (6.5)
2 complex
If the value of the discriminant is greater than 0 and not a perfect square, than there is/are __ _____, ________ root(s). (6.5)
2 real, irrational
If the value of the discriminant is greater than 0 and a perfect square, than there is/are __ _____, ________ root(s). (6.5)
2 real, rational
Simplify 2(5m + n) + 3(2m - 4n) (1.2)
2(5m) + 2(n) + 3(2m) - 3(4n) (Distributive Property) 10m + 2n + 6m - 12n (Multiply) 10m + 6m + 2n - 12n (Commutative Property) (10 + 6)m + (2 - 12)n (Distributive Property) 16m + 10n (Simplify)
Express log⁴ 25 in terms of common logarithms, then approximate its value. (10.4)
2.3219
Given log⁴ 6 = 1.2925, what is the value of log⁴ 36? (10.3)
2.585
1.4 + |5y - 7| if y = -3 (1.4)
23.4
If f(x) = 2x⁴ - 5x² + 8x - 7, find f(6) by using synthetic substitution. (7.4)
2453
MUSIC Travis and his band are planning to record their first CD. The initial start-up cost is $1500 and each CD will cost $4 to produce. They plan to sell their CDs for $10 each. How many CDs must the band sell before they make a profit? (3.1)
250
Write in standard form and identify A, B, and C: y = -2x + 3 (2.2)
2x + y = 3; A = 2, B = 1, C = 3
Find the inverse of f(x) = (x + 6)/2 (7.8)
2x - 6
Simplify the following equation: ⁵√32x¹⁵y²⁰ (5.5)
2x(cubed)y(to the 4th power)
Simplify (4x²y/15a³b³)/(2x²y/5ab³). (9.1)
2x/3a²y
Simplify (2x(x - 5))/((x-5)(x² - 2)) (9.1)
2x/x² - 1
Factor 6x²y² - 2xy² + 6x³y by finding the GCF. (5.4)
2xy(3xy - y + 3x(squared))
(3x² - 2x + 3) - (x² + 4x - 2) (5.2)
2x² - 6x + 5
Solve √(x + 1) + 2 = 4 (5.8)
3
if 3 + -8 equals 9/5, what is the value of 3 + -3? (1.3)
3 + -3 equals 34 / 5
Solve (8x⁴ - 4x² + x + 4) divided by (2x + 1) by using synthetic division. (5.3)
4x(cubed) - 2x(squared) - x - 1
What is the index? (5.5)
5
Use log² 3 = 1.585 to find the value of log² 48. (10.3)
5.585
What is the slope of the line parallel to 2x + 5y = 10? (2.3)
5/2
Solve (5x³ - 13x² + 10x - 8) divided by (x - 2) by synthetic division. (5.3)
5x(squared) - 3x + 4
Simplify: √-125x⁵ (5.9) (Write out your answer in words.)
5x(squared) i times the square root of 5x
According to the table, what is the joint relative frequency of left handed females? (L.T. P.4)
7/121 or 5.8%
Solve 3(5n - 1)¹/³ - 2 = 0 (5.8)
7/27
According to the table, out of all females, what is the conditional frequency of those that are left handed? (L.T. P.4)
7/53 or 13.2%
Solve where a=2, b=-4, and c=-3: a³+2bc over c²-5 (1.1)
8
dashed boundary line (2.7)
<; the points in the boundary line are not included in the inequality set
filled in boundary line (2.7)
<=; the points in the boundary line are included in the inequality set
Examples of linear equations or not? 5x - 3y = 7 x = 9 6s = -3t - 15 y = 1/2x (2.2)
Examples of Linear Equations
subtraction property of inequality (1.5)
If a > b, then a - c > b - c
vertical asymptote (9.3)
If a function is undefined for x = a, the x = a is a vertical asymptote
Transitive Property (1.3)
If a=b and b=c, then a=c
Substitution Property (1.3)
If a=b, then a can be substituted for b in any equation or expression, or vice versa
Property of Equality for Exponential Functions (10.1)
If b is a positive number other than 1, then bˣ = bʸ if and only if x = y
modified box plot (Unit S)
Outliers are given a dot and the second highest/lowest number becomes the new max/min.
BUSINESS A mail order company is hiring temporary employees to help in their packing and shipping departments during their peak season. Write and choose which side to fill in on a graph for the inequality to describe the number of employees that can be assigned to each department if the company has 20 temporary employees available. (2.7)
P + s <= 20; left
Formula for probability (L.T. P.1)
P(E) = number of ways the event can occur (over) number of possible outcomes
Order of Operations (1.1)
PEMDAS (Grouping symbols, powers, mult/div left to right, add/sub left to right)
What do you call a inconsistent system of equations? (3.1)
Parallel lines
_____ in an interval notation means that an endpoint is not included in the set. (1.5)
Parenthesis
System of inequalities solution (3.3)
The intersecting shaded area.
scalar multiplication (4.2)
The product of a scalar and a m x n matrix is an m x n matrix in which each element equals k times the corresponding elements of the original matrix.
Synthetic substitution is almost the same as synthetic division but... (7.4)
The upper left hand corner divisor is the number you are substituting for.
Determine whether f(x) = 5x + 10 and g(x) = 1/5x - 2 are inverse functions. (7.8)
Their compositions form the identity function, so they are inverse functions.
piecewise function (2.6)
a function that us written using two or more expressions; different Ray's, segments, and curves
absolute value inequalities (1.6)
True: 1. If |a| < b, then -b < a <b 2. If |a| > b, then a > b or a < -b
one-to-one function (2.1)
a function where every coordinate of the domain only has one coordinate of the range, and vice versa
"And" Compound Inequalities (1.6)
a compound inequality containing the word "and" is true if and only if both inequalities are true
"Or" Compound Inequalities (1.6)
a compound inequality containing the word "or" is true if and only if one or more of the inequalities is true
Factor each polynomial: a. 5x² - 13x + 6 b. 3xy² - 48x c. c³d³ + 27 d. m⁶ - n⁶ (answer is with square roots) (5.4)
a. (5x - 3)(x - 2) b. 3x(y- 4)(y + 4) c. (cd + 3)(c²d² - 3cd + 9) d. (m + n)(m² - mn + n²)(m - n)(m² + mn + n²)
Write the following in exponential form: a. log⁸ 1 = 0 b. log² 1/16 = -4 (10.2)
a. 1 = 8⁰ b. 1/16 = 2⁻⁴
Solve (a.) In 4 and (b.) In 0.05 with a calculator. (10.5)
a. 1.3863 b. -2.9957
Simplify: a. 16⁻¹/⁴ b. 243³/⁵ (5.7)
a. 1/2 b. 27
Simplify: a. ⁸√81/ ⁶√3 b. ⁴√9z² (5.7)
a. 3 to the 3rd root b. (m - 2m(to the 1/2 power) + 1) / m - 1
Solve: a. (4a/5b)(15b²/16a³) b. (8t²s/5r²)(15sr/12t³s²) (9.1)
a. 3b/4a² b. 2/rt
If f(x) = x² + 5x - 1 and g(x) = 3x - 2, solve the following equations. a. (f x g)(x) b. (f/g)(x) (7.7)
a. 3x(cubed) + 13x(squared) - 13x + 2 b. x(squared) + 5x - 1 (over) 3x - 2
Solve (a.) e² and (b.) e⁻¹³ by using a calculator. (10.5)
a. 7.3891 b. 0.2725
Solve by remembering that exponential and logarithmic functions are inverses: a. log⁶ 6⁸ b. 3ˡᵒᵍ³ ⁽⁴ˣ ⁻ ¹⁾ (10.2)
a. 8 b. 4x - 1
Write an equivalent exponential or logarithmic equation: a. eˣ = 5 b. In x = 0.6931
a. In 5 = x b. x = y⁰.⁶⁹³¹
Solve: a. 3 log⁵ x - log⁵ 4 = log⁵ 16 b. log⁴ x + log⁴ (x - 6) = 2
a. x = 4 b. x = 8
For f(x) = x + 3 and g(x) = x(squared) + x - 1, find the following compositions: a. [f ° g](x) b. [g ° f](x) c. [f ° g](x) for x = 2 d. [g ° f](x) for x = 2 (7.7)
a. x(squared) + x + 2 b. x(squared) + 7x + 11 c. 8 d. 29
If f(x) = x² - 3x + 1 and g(x) = 4x + 5, solve the following equations. a. (f + g)(x) b. (f - g)(x) (7.7)
a. x(squared) + x + 6 b. x(squared) - 7x - 4
Find f ° g (a.) and g ° f (b.) if f(x) = {(7, 8), (5, 3), (9, 8), (11, 4)} and g(x) = {(5, 7), (3, 5), (7, 9), (9, 11)} (7.7)
a. {(5, 8), (3, 3), (7, 9), (9, 4)} b. {(5, 5)}
Solve each equation. State the number and type of roots. a. x + 3 = 0 b. x² - 8x + 16 c. x³ + 2x = 0 d. x⁴ - 1 = 0 (7.5)
a. {-3}, 1 real root b. {4}, 2 real roots (double root) c. {0, i times the square root of 2, -i times the square root of 2}, 1 real root and 2 imaginary roots d. {1, -1, i, -i} 2 real roots and 2 imaginary roots
Solve |a| > 4 (1.6)
a>4 or a<-4
exponential growth range for b (10.1)
b > 1
b¹/ⁿ = _____ (5.7)
b to the nth root
end behavior of a polynomial (7.1)
behavior of a graph as it approaches positive infinity or negative infinity
Normal distribution shape (12.7)
bell curve
like radical expressions (5.6)
both the indices and the radicands are alike
y = logᵇx is equal to x = _____ (10.2)
bʸ
In a quadratic function, the y-intercept is represented by _. (6.1)
c
Solve radical equations be raising each side of the equation by the ______ that eliminates the radical. (5.8)
power
vertical line test (2.1)
determines whether a relation is a function (a vertical line only intersects once if and only if it is a function)
conditional relative frequency (L.T. P.4)
distribution of one variable given something true about the other variable
Identify the domain and range of of f(x) = {x - 4 if x < 2 1 if x >= 2} (2.6)
domain = all real numbers, range = {y|y < -2 or y = 1}
What is the domain and range of f(x) = aˣ? (10.1)
domain: all real numbers range: all positive numbers
element (in a matrix) (4.1)
each value in a matrix
variance equation (12.6)
each value in the data set subtracted by the mean and squared added up and divided by the number of data in the set
elimination method (3.2)
eliminate one of the variables by adding or subtracting the equations
After you find the intersection for two lines, you must check it by inserting it back into the ______. (3.1)
equation
It is appropriate to use absolute value in you answer when the root is an _____ power and the result is an _____ power. (5.5)
even, odd
Exponential functions are the _______ of logarithmic functions. (10.2)
inverse
eᴵⁿ ˣ = x and In eˣ = x are _________. (10.5)
inverses
change of base formula
logᵃ n = (logᵇ n)/(logᵇ a)
quotient property of logarithms (10.3)
logᵇ m/n = logᵇ m - logᵇ n
product property of logarithms (10.3)
logᵇ mn = logᵇ m + logᵇ n
power property of logarithms (10.3)
logᵇ mᵖ = p logᵇ m
Property of Equality for Logarithmic Functions (10.2)
logᵇ x = logᵇ y if and only if x = y
In x = (10.5)
logᵉ x
slope formula (2.3)
m = y** - y* over x** - x*
-m <= (m + 4) ÷ 9 (1.5)
m >= -2/5
five number summary (Unit S)
minimum, Q1, median, Q3, maximum
terms (5.2)
monomials that make up the polynomial
In inequalities, division or multiplication by a _____ number stays true. Division or multiplication by a _____ number requires the ordered be reversed. (1.5)
positive, negative
A radical is in simplified form when: 1. The index n is as _______ as possible 2. The radicand contains no _______ (other than 1) that are nth powers of an integer or polynomial 3. The radicand contains no __________ 4. No radicals appear in the ____________ (5.6)
small, factors, fractions, denominator
roots (6.2)
solution of a quadratic equation
degree of a polynomial (5.2)
the degree of the monomial with the greatest degree
product property of radicals (5.6)
the nth root of ab is equal to the nth root of a multiplied by the nth root of b (a and b are real numbers, n is greater than one, and if n s odd, then a and b are both non negative)
Descartes' Rule of Signs (7.5)
the number of positive (or negative) real zeros of y = P(x) is the same as the number of changes in sign of the coefficients of the terms (of P(-x)), or is less than this by an even number
Slope (2.3)
the ratio of the change in y coordinates to the corresponding change in x coordinates in a line
joint relative frequency (L.T. P.4)
the ratio of the frequency in a particular category (box) divided by the total number of data values (finding the inside number)
domain (2.1)
the set of all first coordinates (x) from the ordered pairs
range (2.1)
the set of all second coordinates (y) from the ordered pairs
compound inequality (1.6)
two inequalities joined by the words "and" or "or"
equal matrices (4.1)
two matrices with the same dimensions and equal corresponding elements
system of equations (3.1)
two or more equations with the same variables
Find the dimensions: A(1×3) and B(4×3) (4.3)
undefined
A quadratic function goes _____ when the x coordinate of the vertex is x > 0, and it goes ______ when x < 0. (6.1)
up, down
leading coefficient of a polynomial (7.1)
what is in the front of the polynomial with the largest degree
empty set (1.4)
when an absolute value equation is equal to a negative number (the equation is not equal)
inverse relation (7.8)
when one relation has (a, b), the other has (b, a) (they have each other's opposing domain and range)
negative correlation (2.5)
when the data in a scatter plot consistently has a decreasing y value; it goes down
positive correlation (2.5)
when the data in a scatter plot consistently has an increasing y value; it goes up
no correlation (2.5)
when the data in a scatter plot has no relationship
You can graph a line with any equation by finding the y-intercept (put 0 in for ____) and the x-intercept (put 0 in for ____) (2.2)
x, y
In a quadratic function, the equation for the axis of symmetry is the same as the _-_____________ __ ____ _______. (6.1)
x-coordinate of the vertex
Solve 2(2x+3)-3(4x-5)=22 (1.3)
x=-1/8
point-slope form (2.4)
y - y* = m (x - x*); (x*, y*) are coordinates of a point on the line and m is the slope of the line
What is the equation of the line through (-1, 4) and (-4, 5)? (2.4)
y = -1/3x + 11/3
Write an equation in slope-intercept form for the line that has a slope -3/2 and passes through (-4,1). (2.4)
y = -3/2x - 5
FARMING In 1983, there were 102,000 farms in Minnesota, but by 1998, this number had dropped to 80,000. Write an exponential function in the form of y = abˣ that could be used to model the farm population y of Minnesota. Write the function in terms of x, the number of years since 1983. (10.1)
y = 102,000(0.98)ˣ
Evaluate log² 64. (10.2)
y = 6
Equation of horizontal lines (2.2)
y = C (they only have an y-intercept)
vertex form (6.2)
y = a (x - h) squared + k; (h, k) is a vertex of the parabola
Exponential function (10.1)
y = abˣ (a and b do not equal 0, b > 0)
slope-intercept form (2.4)
y = mx + b; m - slope, y - intercept
Use the graph of _______ to check that the graph of an inverse function is true. (7.8)
y = x
When solving |y| >= 3, change the equation into these two parts. (3.3)
y >= 3 and y <= -3
|5x - 6| + 9 = 0 (1.4)
{ }
Solve x² - 22x + 121 = 0 by using the quadratic formula. (6.5)
{-11}
Solve x² + 4x + 11 = 0 by completing the square. (6.4) (Write out your answer in words.)
{-2 + i times the square root of 7, -2 - i times the square root of 7}
Solve 2x² - 4x - 5 = 0 by using the quadratic formula. (6.5) (Write out your answer in words.)
{-2 - the square root of 14 / 2, -2 + the square root of 14 / 2}
Solve x² - 12x = 28 by using the quadratic formula. (6.5)
{-2, 14}
Solve 3x² - 3x - 60 = 0 by factoring. (6.3)
{-4, 5}
Solve by factoring: 2x² + 7x = 15 (6.3)
{-5, 3/2}
Solve x² + 8x + 16 = 9 by using the Square Root Property. (L.T. 5.6)
{-7, -1}
Solve x² = 49 by factoring. (6.3)
{-7, 7}
Solve by factoring: x² = 6x (6.3)
{0, 6}
Solve 2x² - 5x + 3 = 0 by completing the square. (6.4)
{1, 3/2}
Solve |x - 18| = 5 and check solutions. (1.4)
{13, 23}
Solve x² - 4x + 13 = 0 by using the quadratic formula. (6.5)
{2 + 3i, 2 - 3i}
Find all zeros of f(x) = x³ - 4x² + 6x - 4. (7.5)
{2, (1 + i), (1 - i)}
Solve x² + 8x - 20 = 0 by completing the square. (6.4)
{2, -10}
Solve x² + 10x + 25 = 49 using the square root property. (6.4)
{2, -12}
Solve 3x² - 7 = 5 by using the Square Root Property. (L.T. 5.6)
{2, -2}
Solve (x + 3)² = 25 by using the Square Root Property. (L.T. 5.6)
{2, -8}
Solve x² - 6x + 9 = 32 using the square root property. (6.4) (Write out your answer in words.)
{3 + 4 times the square root of 2, 3 - 4 times the square root of 2}
3x² + 48 = 0
{4i, -4i}
Solve |x + 6| = 3x - 2 and check. (1.4)
{4}
Find all zeros of f(x) = 2x⁴ - 13x³ + 23x² - 52x + 60 (7.6)
{5, 3/2, 2i, -2i}
Solve 2x² + 3 = 75 by using the Square Root Property. (L.T. 5.6)
{6, -6}
Solve x² - 16x + 64 = 0 by factoring. (6.3)
{8}
