Download Algebra II Intervention Helps

Algebra II Intervention Helps
Chapter 1 – Equations, Formulas, Inequalities
Vocabulary – Informal Definitions
whole numbers: 0, 1, 2, 3, 4, 5, …
integers: all whole numbers and their opposites
rational number: any number that can be expressed as a fraction
commutative property: an operation is commutative if you can change the order
and get the same answer (ex: 3 + 4 = 4 + 3 )
associative property: an operation is associative if you can change the grouping
and get the same answer (ex: (3 + 4) + 5 = 3 + (4 + 5) )
distributive property: there are several variations of the distributive property
3(4 + 5) = 3 • 4 + 3 • 5 ; also true with subtraction
46 4 6
 
; also true with subtraction
2
2 2
mean: average
median: middle number
mode: most frequent
simplifying expressions: using properties and collecting like terms
solving equations: finding a replacement for a variable that makes the
statement (equation) true
Key Concepts
order of operations (pp. 7 – 8)
solving equations and formulas by isolating the variable (pp. 28 – 29)
solving absolute value equations (pp. 39 – 40)
using graphing calculators to evaluate numerical expressions (p. 6)
Chapter 2 – Graphing Linear Functions
Vocabulary – Informal Definitions
relation: any set of ordered pairs
function: a set of ordered pairs no two of which have the same first coordinate
domain: the set of all first coordinates of a relation or function
range: the set of all second coordinates of a relation or function
slope: the ratio of vertical change to horizontal change of a line (rise over run)
linear: pertaining to a line
slope-intercept equation of a line: y = mx + b
prediction line/line of regression: a linear equation that most closely aligns to a
set of given points
absolute value: the distance from zero; always positive
greatest integer function: round down to the nearest integer
Key Concepts
slope-intercept method of graphing (ex. 4, p. 82)
intercept method of graphing (p. 75)
parallel lines (p. 83)
perpendicular lines (pp. 83-84)
writing linear equations (ex. 1, p. 89)
using graphing calculators to: graph lines (p. 79)
find prediction lines (pp. 101-102)
Chapter 3 – Linear Systems
and
Chapter 4 - Matrices
Vocabulary – Informal Definitions
system of equations: 2 or more equations to be solved simultaneously
inconsistent system: a system with no solution
consistent system: a system with at least one set of solutions
matrix: a rectangular array of numbers
row: horizontal
column: vertical
Key Concepts
solving systems by: graphing (p. 128)
elimination (p. 135)
substitution (p. 134)
using graphing calculators and matrices (p. 221)
matrix operations: scalar multiplication (p. 190)
addition (p. 195)
multiplication (p. 200)
division (p. 185)
Chapter 5 – Exponents, Polynomials, Radicals
Vocabulary – Informal Definitions
monomial: a single term
binomial: 2 terms
trinomial: 3 terms
degree: the highest exponent in an expression
scientific notation: expressing very large or very small numbers as a product of a
number between 1 and 10 and a power of 10: for large numbers
use a positive exponent; for small numbers, a negative exponent
factoring an expression: separating into a product
imaginary unit: i = √ (– 1)
complex numbers: any number in the form a + bi , where a and b are real numbers
Key Concepts
exponent rules (pp. 255-257)
FOIL (p. 263)
dividing polynomials (pp. 267-268)
factoring polynomials (p. 276)
simplifying radical expressions (p. 289)
rational exponents (p. 298)
solving equations with roots or radicals (p. 303, 305)
operating with complex numbers (pp. 311-313)
Chapter 6 – Quadratic Equations
Vocabulary – Informal Definitions
standard quadratic equation: ax² + bx + c , where a, b, and c are real numbers
quadratic term: ax²
quadratic coefficient: a
linear term: bx
linear coefficient: b
constant term: c
vertex of a parabola: the highest or lowest point on the graph of a parabola
axis of symmetry of a parabola: a vertical line that contains the vertex
zeros of a function: values of x that make the function equal zero; on the graph
of the function, the zeros give the x-intercepts
discriminant of a quadratic equation: the value of b² – 4ac
Key Concepts
graphing quadratic functions (p. 335)
solving quadratic equations by: factoring (pp. 342-343)
completing the square (p. 347)
using the quadratic formula (pp354-355)
analyzing solutions to a quadratic equation using the discriminant (p. 356)
solving quadratic inequalities (p. 379)
recognizing normal distribution (p. 393)
using graphing calculators to: graph parabolas, finding the x-intercepts and vertex
find standard deviation
Chapter 8 – Inverse Functions
and
Chapter 9 – Rational Expressions
Vocabulary – Informal Definitions
composition of functions: substituting one function into another
inverse function: a function that “undoes” another function (ex: f(x) = x² and
g(x) = √x are inverse functions)
rational expression: a fraction
asymptote: a line that a graph gets closer and closer to but never touches; vertical
and horizontal asymptotes provide “boundaries” for the graph of a
rational equation
direct variation: when one variable changes the same way as another variable; the
general equation is y = kx (k is called the constant of variation)
inverse variation: when one variable changes the opposite way as another variable;
the general equation is y = k/x
joint variation: when one variable changes the same way as two or more other
variables
Key Concepts
finding vertical and horizontal asymptotes for rational functions (p. 551)
solving variation problems (pp. 557-558)
operating with rational expressions (pp. 562-623, pp. 569-570)
solving rational equations (p. 577)
using graphing calculators to graph rational functions (pp. 548-549)
Chapter 10 – Exponential and Logarithmic Functions
Vocabulary – Informal Definitions
exponential function: a function with the variable in the exponent
logarithmic function: the inverse of an exponential function
logarithmic scale: a scale based on powers; the Richter Scale and the pH scale
are examples of logarithmic scales (pp. 605-606)
common logarithm: a base 10 logarithm
natural logarithm: a base e logarithm (p. 622)
Key Concepts
analyzing logarithmic scales (p. 606)
solving logarithmic equations (p. 606, 608)
using properties of logarithms (pp.611-613)
solving exponential equations (pp. 626-627, 632)
Chapter 11 – Sequence and Series
and
Chapter 12 – Probability
and
Chapter 13 – Right Triangle Trigonometry
Vocabulary – Informal Definitions
arithmetic sequence: a set of numbers with a common difference (ex: 2, 4, 6, 8, 10, …)
geometric sequence: a set of numbers with a common ratio (ex: 2, 4, 8, 16, 32, …)
series: the sum of a sequence
permutation: an orderly arrangement
combination: an arrangement in which order doesn’t matter
probability: the ratio of favorable outcomes to total outcomes; could be expressed as
a fraction, a ratio, or a percent
odds: the ratio of favorable outcomes to unfavorable outcomes; usually expressed as a
ratio
sine function: in a right triangle, the sine of an angle is the ratio of the opposite side
to the hypotenuse
cosine function: the ratio of the adjacent side to the hypotenuse
tangent function: the ratio of the opposite side to the hypotenuse
Key Concepts
evaluating arithmetic sequences and series (pp. 649-650, 656-657)
evaluating geometric sequences and series (pp. 663-664, 671-672)
using the Fundamental Counting Principle (p. 713)
solving linear permutations (p. 719)
solving combination problems (p. 727)
evaluating probability and odds (pp, 732-734)
knowing the 6 basic right angle trigonometry functions (p. 772)
solving right triangles (pp. 773-776)