math 2 - 2nd semester exam review

true or false : a function is when x repeats.

FALSE. example of a function : (5,-7)(8,-9)(2,6)(3,11) example of NOT a function : (0,-3)(5,-7)(0,-5)(8,-6)

secant (cosine)

H/A or R/X

cosecant (sine)

H/O or R/Y

tangent

TOA : O/A or Y/X

true or false : in a function, y can repeat.

TRUE example : (5,-7)(-9,-2)(1,-2)(-8,9)

TRUE or FALSE : you can't take the log of a negative number

TRUE : log(-1000) has no solution ¡BUT! log(10^-3) = -3 >>> NOT TO BE CONFUSED: 10^-3 (no log) = 0.001

when is the only time pythagorean theorem is used?

for right triangles. with this theorem, you can find either legs or the hypotenuse.

when solving a system ...

graph the equations, it is very helpful!

give an example of two events that are NOT independent :

height and gender

H is...

hypotenuse

how to find the shortest distance in a angle-side-side Δ

k = shortest length b = hypotenuse/top side k/b = sinθ k = b x sinθ = shortest distance

what are independent events?

knowing the outcome of one doesn't change the outcome of the other

skewed right

majority of the data is on the LEFT SIDE of the graph

skewed left

majority of the data is on the RIGHT SIDE of the graph

O is...

opposite

fair price

prize ----- = probability x prize chances

expected value

prize x probability

1-P when P = success...

probability of failure

domain

x-axis

range

y-axis

on a domain and range graph the arrow means...

∞ (infinite / all numbers)

or means _______ in a probability problem.

+ (to add)

practice problem: log(10^-3)

-3

when a graph intersects at no points there are __ solutions.

0

practice problem: 10^-3

0.001

when a graph intersects at one point there are __ solutions.

1

what does probability always add to?

1 (¡ALWAYS!)

expected wait time

1 / P (P = probability)

on a chart where number of trials is on the left and probability is on the right, what does 1 equal?

1 = p for ONLY trial 1

how many answers for the equation x^2 - 25 = 0 ? (also, how/steps to solve)

1 answer : x^2 - 25 = 0 x^2 = 25 √25 = 5 FINAL ANSWER : x = +- 5

how to solve ax^2 + b^2 + c = mx +d

1. set to 0 2. see if the equation factors 3. if yes it factors, put into (x+m)(x+n) form 3a. if doesn't factor, than use the quadratic formula QUAD FORM: -b +- √b^2-4ac ---------------- 2

when a graph intersects at two points there are __ solutions.

2

how many answers for the equation -4x^2 + 10x = 0 ? (also, how/steps to solve)

2 answers : -4x^2 + 10 = 0 2x (-2x + 5) = 0 2x = 0 and -2x + 5 = 0 FINAL ANSWER : x = 0 or x = 5/2

how many answers for the equation x^2 - 12x + 20 = 0 (also, how/steps to solve)

2 answers : multiply to 20 and add to -12 (x - 2)(x - 10) opposite sign : - to + FINAL ANSWER : x = 2 or x = 10

what commands are entered to find an unknown angle?

2ND SIN or TAN or COS = SIN-1 = angle measure example: tan^-1(4-3) = 53.13

point ending / beginning

( on value

on a chart where number of trails is on the left and probability is on the right, what is the formula to find out 2+ is?

(1-p)^x-1 * P 1 = total probability P = probability x = number of trials (on trial #3/ x = 3 and so on) example: @ 1 = .67 @ 2 = (.33) (.67) @ 3 = (.33) (.67)^2 and so on....

cotangent (tangent)

A/O or X/Y

cosine

CAH : A/H or X/R

what is the formula to find the rule for independent events?

P (A and B) to solve : >>>> P(A) x P(B)

what is the formula to find the rule for conditional probability?

P(A I B) or P(B I A)

sine

SOH : O/H or Y/R

what type of triangle theorem does NOT prove congruence?

SSA (the donkey theory)

what types of triangle theorems prove congruence?

SSS, SAS, ASA, AAS or HL

when A and B are supplements ...

Sin A = Sin B

arrow ending

[ on value

2 Δs when...

a is between bsinθ and b -- bsinθ < a < b

1 Δ when...

a is bigger or = to b

0 Δs when...

a is smaller than b x sinθ

pythagorean theorem is...

a^2 + b^2 = c^2

law of cosines :

a^2 = b^2 + c^2 - 2bc COS A b^2 = a^2 + c^2 - 2ac COS B c^2 = b^2 + a^2 - 2ba COS C

A is...

adjacent

in order to use the law of sines, you need to know :

an angle, the side opposite, and one other detail.

why is tan(45) = 1?

because 2 45º angles make an isosceles triangle, which means the 2 side lengths are the same length

why are sine and cosine always less than 1?

because they use a side length and they hypotenuse. sine = O/H and cosine = A/H. the hypotenuse of a triangle is ALWAYS the longest side, making it so that the outcome will ALWAYS be less than 1.

inverse

curved symmetrical graph line opening down

quadratic

curved symmetrical graph line opening up

what does taking the log of a number do?

finds the power on ten example: log(1000)=3 log(10^-4.2) = -4.2

practice problem : how to find missing side length find : length of x (opposite) info - angle A = 35 hypotenuse = 7 adjacent and opposite = unknown

sin = O/H (finding O and we know H) sin(35)=x/7 7 x sin35 = x x = 4.015

law of sines is...

sinA / a = sinB/b = sinC/c

linear

straight line in any direction

why can tangent be more than 1?

tangent = O/A. because there are 2 side lengths, they can equal more than 1. example: O = 14 A = 7 14/7 = 2

what is probability?

the likelihood of an event to occur

what is a rare event?

the lower 5% at the point where the probability column adds to 95% or more, anything under that point on the chart is considered a rare event.

what is conditional probability?

the probability of an even occurring, when you already know the outcome of one event

θ

theta = any unkown angle

give an example of two events that ARE independent :

weight and eye color

and means _______ in a probability problem.

x (to multiply)