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SAT II: Math 2 > Vocabulary > Flashcards

Vocabulary Flashcards

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SAT® Prep flashcards
1
Q

domain of a function

A

the input numbers, the x-values, domain of a function is all real numbers for which the equation produces outputs that are real numbers

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2
Q

range of function

A

the output values, the y-values or f(x) values

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3
Q

typically, a value of x that must be excluded from the domain of a function makes the denominator _____

A

zero

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4
Q

in place of an equation, a function with a small finite domain can also be described by _____

A

a set of ordered pairs

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5
Q

in a function, every x-value has _____ y-values

A

exactly one y-value. if an x-value has more than one y-value than it is not a function

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6
Q

relation

A

describes association between two variables. a function is a type of relation

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7
Q

in terms of functions and relations, a circle is ___

A

a relation that is not a function

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8
Q

relations that are not functions are ___

A

ellipses, hyperbolas, and parabolas that open side ways

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9
Q

combining functions f(x) and g(x)

A

…

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10
Q

composition of functions f(x) and g(x)

A

…

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11
Q

inverse of a function f, denoted by f^(-1)

A

switch y and x. putting y’s in place of the x’s and x’s in place of the y’s than solve for y

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12
Q

what is something to remember about inverses?

A

inverses don’t have to be a function

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13
Q

the graphs of inverses are ___

A

reflection of the original function about the line y=x

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14
Q

if the point with coordinates (a,b) belongs to a function f, then the point with coordinates ___ belongs to the inverse of f

A

(b,a)

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15
Q

the inverse of any function f can always be made a function by ___

A

limiting the domain of f. cutting out the parts that keep it from being a function

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16
Q

properties of an even function

A

f(x)=f(-x)

an even function is symmetric about the y-axis

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17
Q

properties of an odd function

A

f(-x) = -f(x), an odd function is symmetric about the origin

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18
Q

the sum of even functions is ___

A

even

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19
Q

the sum of odd functions is ___

A

odd

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20
Q

the product of an even function and an odd function is ___

A

odd

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21
Q

linear functions

A

polynomials in which the largest exponent is 1

graphs of linear equations are always a straight line

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22
Q

general form of the equation for a linear function

A

Ax + By + C = 0

  • A/B = slope of line
  • C/B = y intercept
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23
Q

slope intercept

A 
y = mx + b
m = slope of line
b = y intercept
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24
Q

formula for slope

A

(y1 -y2)/(x1-x2)

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25
Q

point slope

A

y - y1 = m( x - x1 )

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26
Q

parallel lines have ___ slopes.

A

same

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27
Q

the slopes of 2 perpendicular lines are ___

A

negative reciprocals of one another

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28
Q

distance formula for x-y plane

A

…

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29
Q

midpoint formula

A

…

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30
Q

properties of quadratic functions

A

polynomials where the largest exponent is 2

graph is always a parabola

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31
Q

general form of equation for quadratic functions

A

y = ax^2 + bx + c
if a is positive, then graph opens up
if a is negative graph opens down

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32
Q

how to calculate x value of vertex of parabola

A

-b / 2a

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33
Q

zeroes of a quadratic function are ___

A

the points where the the graph crosses the x-axis, and y = 0

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34
Q

quadratic formula

A

…

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35
Q

sum of the zeroes of a quadratic equations is ___

A

-b / a

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36
Q

determinant of a quadratic equation

A

(b^2) - 4ac

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37
Q

if determinant of quadratic equation equals 0

A

the two roots equal zero and the graph is tangent to the x-axis

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38
Q

if the determinant of quadratic equation is less than 0

A

the roots are two complex numbers because there is a negative under the radical and the graph never touches the x-axis

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39
Q

if the determinant of quadratic equation is more than zero

A

two different real roots and the graph intersects the x-axis in two places

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40
Q

the graphs of polynomial functions are always ________

A

continuous curves

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41
Q

if the largest exponent of a polynomial function is even then the ends of its graph

A

point in the same direction ( a parabola or a W)

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42
Q

if the largest exponent of a polynomial function is odd then the ends of its graph

A

point in opposite directions ( an S or snake graph)

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43
Q

if all the exponents of a polynomial function are even then the polynomial is an ______

A

even function and symmetric about the y-axis

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44
Q

if all the exponents of a polynomial function are odd then the polynomial is an _______________

A

odd function and symmetric about the origin

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45
Q

a polynomial of degree n has ___ zeroes

A

n, same number as degree

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46
Q

when it comes to the zeroes of polynomial functions, imaginary ezroes must ______

A

occur in pairs

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47
Q

with polynomial functions, real zeroes can occur ____

A

more than once

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48
Q

Remainder theorem

A

if a polynomial P(x) is divided by x-r (where r is any constant), then the remainder is P(r)

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49
Q

factor theorem

A

r is a zero of the polynomial P(x) if and only if x-r is a divisor of P(x)

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50
Q

rational zero (root) theorem

A

if p/q is a rational zero (reduced to lowest terms) of a polynomial P(x) with integral coefficients, then p is a factor of the constant term and q is is a factor of the leading coefficient

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51
Q

if P(x) is a polynomial with real coefficients, then complex zeroes occur as _____

A

conjugate pairs ( if p + qi is a zero then p - qi is also a zero)

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52
Q

angles measured in a counter clockwise direction from the initial side to the terminal side is said to have a _____ value

A

positive

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53
Q

angles measured in a clockwise direction from the initial side to the terminal side is said to have a _____ value

A

negative

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54
Q

sin and cos are always between ___ and ___

A

-1 and 1

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55
Q

the six trig definitions

A

…

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56
Q

complimentary angles

A

add to 90 degrees

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57
Q

sumplementary angles

A

add to 180 degrees

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58
Q

cofunctions of complementary angles are ___

A

equal

if a and b are complimentary, then the sina=cosb

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59
Q

radian

A

the measure of one radius length

one radian equal 360/2pie

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60
Q

arc length equation

A

radius times angle (in radians)

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61
Q

area of a sector of a circle

A

(1/2)(radius ^2)( angle in radians)

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62
Q

special triangles

A

…

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63
Q

periodic functions

A

where the values eventually repeat over regular intervals

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64
Q

period

A

smallest positive value in which a periodic function repeats

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65
Q

periods of six trig functions

A

sin, cos, csc, sec have periods of 2pie

tan and cot have periods of pie

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66
Q

the vertical asymptotes of sec, csc, tan and cot

A

sec and tan’s occur on pie/2

csc and cot’s occur on pie

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67
Q

general form of a trig function

A

y = A * trig(Bx + C) + D
amplitude = abs(A)
horizontal translation is -C/B and is called phase shift
period is period of original trig func divided by B
D is amount of vertical translation

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68
Q

reciprocal identities

A 
csc = 1/sin
sec = 1/cos
cot = 1/ tan
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69
Q

cofunction identities

A

…

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70
Q

pythagorean identities

A

…

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71
Q

double angle formulas

A

…

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72
Q

law of sines

A

…

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73
Q

law of cosines

A

…

74
Q

area of triangle (using sine)

A

…

75
Q

basic exponential properties

A

…

76
Q

basic log properties

A

…

77
Q

logbN is only defined for

A

positive N

78
Q

the graphs of all exponential function y = b^x

A

have roughly the same shape and pass through the point (0,1)

79
Q

the graphs of all logarithmic functions y = logbX

A

have roughly same shape and pass through point (1, 0)

80
Q

the function f is a rational function if and only if

A

f(x) = p(x)/q(x) , where p(x) and q(x) are both polynomial functions and q(x) is not zero
if p and q are both zero, there is a whole at that x
if only q is zero than there is an asymptote

81
Q

a point of discontinuities occurs at any value of X that ___

A

would cause q(x) to become zero

82
Q

parametric equations

A

x = x(t) and y = y(t)

83
Q

piecewise functions

A

defined by different equations on different parts of the domain

84
Q

general absolute value function

A 
f(x) = a * abs(x-h) +k
vertex at (h,k)
85
Q

translation of graph

A

moves graph around plane

accomplished by addition

86
Q

stretching and shrinking graph

A

changing scale of graph

accomplished by multiplication

87
Q

ellipses

A

the oval graphs, the set of points whose distances from two given points (foci) sum to a constant

88
Q

ellipse equation

A

…

89
Q

how to figure out wither ellipse is x or y orientated

A

which ever has the bigger constant underneath, usually defined as a while smaller constant is b

90
Q

center of ellipse

A

h,k

91
Q

vertices of ellipse

A

endpoints of major axis
(h-a, k) (h +a, k) if on x axis
(h, k-a) (h, k +a) if on y axis

92
Q

foci of ellipse

A

on major axis, at distance of c from center, c = sqr( a^2 -b^2)

93
Q

if the constants in the denominators equal each other in an ellipse equation, then

A

its the equation of a circle

94
Q

equation of circle

A

(x-h)^2 + (y-k)^2 = r^2

95
Q

hyberbola

A

set of points whose distances from two fixed points (focci) differ by a constant, the twin parabola graph

96
Q

equation of hyberbola

A

…

97
Q

how to figure out which directions the graph of a hyperbola points

A

if its x - y, its on the x-axis

if its y - x, than its on the y-axis

98
Q

vertices of hyperbola

A

(h-a, k) (h+a,k)

or (h, k-a) (h, k+a) if on y axis

99
Q

transverse axis

A

segment joining vertices of hyperbola

100
Q

conjugate axis

A

segment with length 2b, perpendicular to transverse axis , intersects it at midpoint

101
Q

equation of asymptotes of hyperbola

A

y-k = +or - (b/a)(x-h) if on x axis

if on y axis, its a/b instead of b/a

102
Q

eccentricity of ellipse or hyperbola

A

c/a

c^2 = a^2 + b^2

103
Q

polar cordinates

A

distance from origin and angle between x axis and ray

r, angle

104
Q

relationships between polar and regular coordinates

A

x = r * cos(ang)
y = r * sin(ang)
x^2 + y^2 = r^2

105
Q

volume of prism

A

v = Bh

106
Q

surface area of prism

A

(perimeter of base)h + 2B

107
Q

vol of rectangular prism

A

lwh

108
Q

SA of rect solid

A

2lw + 2lh + 2wh

109
Q

vol of cube

A

s^3

110
Q

SA of cube

A

6s^2

111
Q

vol of pyramid

A

(1/3)Bh

112
Q

SA of pyramid

A

(1/2)(base perimeter)(slant height) + B

113
Q

vol of cylinder

A

(r^2)(h)(pie)

114
Q

SA of cylinder

A

2(pie)(r)(h) + 2(pie)(r^2)

115
Q

vol of cone

A

(1/3)(pie)(r^2)(h)

116
Q

SA of cone

A

(pie)(r)(slant height) + (pie)(r^2)

117
Q

vol of sphere

A

(4/3)(pie)(r^3)

118
Q

SA of sphere

A

4(pie)(r^2)

119
Q

formula for length of diagonal of rectangular solid

A

sqroot of ((l^2)(w^2)(h^2))

120
Q

distance formula for 3D plane

A

…

121
Q

equation for sphere in 3D plane

A

…

122
Q

know how to use venn diagram for counting problems

A

…

123
Q

factorial

A

n!
ex: 5! = 5 * 4 * 3 * 2 *1 = 120
use to find number of ways objects can be ordered

124
Q

permutations

A

(n!) / ((n-r)!)
use when having to only find partial number of ways to order objects out of the total set
Ex: ways to order first second and third out of set of 20, in this case n=20 and r=3

125
Q

combinations

A

(n!) / (n-r)!(r!)

number of ways of choosing r of n objects

126
Q

value of i

A

i = sqroot (-1)

127
Q

powers of i

A 
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i
pattern repeats from there
128
Q

imaginary numbers

A

form of bi, where b= real number

129
Q

sq root of negative number

A

i times the sqroot of the abs val of the number

130
Q

complex number

A

a + bi, where a and b are real numbers

131
Q

to find the quotient of 2 complex numbers….

A

multiply the denominator and numerator by the conjugate of the denominator

132
Q

how to graphically represent complex numbers

A 
x = real part (a)
y = imaginary part (bi)
133
Q

the modulus of a complex number is

A

the sq of its distance to the origin

134
Q

the product of an imaginary number and its conjugate is

A

the square of the modulus

135
Q

distance of complex number

A

sq root of ((a^2) + (b^2))

136
Q

two matrices are equal if

A

they are the same size and their corresponding entries are equal

137
Q

row matrix

A

a matrix with only one row

138
Q

column matrix

A

a matrix with only one column

139
Q

square matrix

A

a matrix with equal amount of rows and columns

140
Q

scalar multiplication

A

when each number in a matrix is multiplied by a constant

141
Q

two matrices can be subtracted or added together

A

if they are the same size

142
Q

matrices A and B can be multiplied if

A

the # of rows of A = # pf columns of B

or vice versa

143
Q

how to multiply matrices

A

multiply rows of A times columns of B and add values

144
Q

determinant of 2 by 2 matrix

A

…

145
Q

determinant of 3 by 3

A

…

146
Q

sequence

A

a function with a domain consisting of natural numbers
the one with comas
ex: 1, 2, 3, 4, 5

147
Q

series

A

sum of the terms of a sequence
the one with addition or subtraction marks
ex: 1 + 2 + 3 + 4 + 5

148
Q

infinite series or sequence

A

has …. at the end

idea is that it goes on forever

149
Q

finite series or sequence

A

only goes to a specific term

150
Q

recursion formula

A

formula of a sequence/ series where every term is expressed with respect of the term before it
ex: insert picture pg153

151
Q

series can be abbreviated by

A 
using Greek letter sigma
# on bottom the start
# on top the end
152
Q

arithmetic sequences

A

each term differs from previous term by a constant value

addition/subtraction sequence

153
Q

formula for arithmetic sequence

A

…

154
Q

formula of sum of arithmetic series

A

…

155
Q

arithmetic mean

A

one term falling between two given terms of an arithmetic sequence

156
Q

geometric sequence

A

ration of any two consecutive terms is constant r

multiply/ divide sequence

157
Q

formula for geometric sequence

A

…

158
Q

formula for sum of geometric series

A

…

159
Q

geometric mean

A

one term falling between two given terms of a geometric sequence

160
Q

if r is less than 1, than sum of geometric series as it approaches infinity equals

A

…

161
Q

vector

A

a vector in a plane is defined to be an ordered pair of real numbers
vector in space defined as an ordered triple of real numbers

162
Q

resultant vector

A

when two vectors are added together

Ex: vector U plus vector V has resultant of (u1 +v1, u2 + v2)

163
Q

vector - V has ____ magnitude and _______ direction of vector V

A

equal , opposite

164
Q

dot product

A

insert picture

dot product is a real number

165
Q

2 vectors are perpendicular, their dot product equal

A

zero

166
Q

measures of center

A

summarize a data set using a single “typical” value

the 3 on the SAT: mean, median, mode

167
Q

mean

A

sum of all data values divided by number of values

168
Q

median

A

order values from greatest to lest and find one in the middle

169
Q

mode

A

value that repeats the most in the set

170
Q

range

A

measure of the spread of the value set

highest value - lowest value

171
Q

standard deviation

A

the average difference between individual data values and their mean

172
Q

formula for standard deviation

A

…

173
Q

regression

A

a technique for analyzing the relationship between two variables

174
Q

probability of an event happening is a number defined to be the

A

number of ways the event can happen successfully divided by the total number of ways the event can happen

175
Q

sample space of experiment

A

set of all outcomes of an experiment

176
Q

odds in favor of an event happening are defined to be

A

the probability of the event happening divided by the probability of the event not happening

177
Q

independent events

A

events that have no effect on one another

the probability of both events A and B happening is the same as the Probability of A times the probability of B

178
Q

dependent events

A

events that are not dependent so

probability of both does not equal probability of A times probability of B

179
Q

to find probability of “at least one”

A

find 1 - probability of “none”

180
Q

mutually exclusive events

A

events where the probability of both happening is zero

181
Q

probability of event A happening or event B happening or both happening equals

A

P(A) + P(B) - P(both)

182
Q

generally in probability, “and” means ______ and “or” means _________

A

and means multiply and or means add

SAT II: Math 2 (1 decks)

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