Math 7 - 12 TEXES Content Exam

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derivative of a^u

(a^u)(u')(lna)

Rotate 180 degrees about the origin

(x,y) -> (-x,-y)

Rotate 90 degrees counterclockwise

(x,y) -> (-y,x)

Rotate 270 degrees counterclockwise

(x,y) -> (y, -x)

derivative of cosx

-sinx

standard deviation (steps)

1. Calculate the mean 2. Calculate each variable (x) minus the mean. (x-x̄) 3. Square each value left over 4. Add them all together 5. Divide by n 6. Take the square root

How to calculate variance

1. find mean 2. Subtract each score from the mean 2. Square every deviation of the mean 3. Find mean again

What makes a function not differentiable?

1. has a cusp 2. has a hole 3. limit is not the same approaching both sides 4. not a funct (vert line test)

Calculate Regression line in calc

1. stat - edit 2. enter lists in L1 and L2 3. 2nd - y= - plot 1 ON - L1, L2 5) stat - calc - linreg - enter

binary system notation

2^n

Empirical Rule (stats)

68%, 95%, 99.7%

response variable

A variable that measures an outcome of a study. (dependent)

Area of equilateral triangle

A=s² (√3)/4

inverse

If not p, then not q

Contrapositive

If not q, then not p

converse

If q, then p

How to make the center of a circle

find the perpendicular bisectors of two chords

deductive reasoning

general to specific

Is a matrix invertible?

if ad - bc = 0

odd function

left half is reflected and flipped upside down perfectly! graph is symmetrical with respect to the origin; f(-x)=-f(x)

even function

left half reflects the line of the right halfgraph is symmetrical with respect to the y-axis; f(x) = f(-x)

Special Right Triangle 45-45-90

leg1 = leg2; hypotenuse = leg√2

point of inflection

point where concavity changes

Ordinal survey items

refers to oder (ranking in order)

derivative of tanx

sec^2(x)

inductive reasoning

specific to general

z-score

tells us how many standard deviations from the mean an observation falls, and in what direction (pos/neg)

null hypothesis

the hypothesis a researcher or experimenter will try to disprove or discredit.

Law of Large Numbers

the larger the number of individuals that are randomly drawn from a population, the more representative the resulting group will be of the entire population

incenter of a triangle

the point of concurrency of the angle bisectors of a triangle

orthocenter of a triangle

the point of concurrency of the three altitudes of a triangle

Product Rule

uv' + vu'

Mean of Discrete Distribution

weights each outcome xi according to its probability, pi

unit circle cos

x

Quadratic Formula

x = -b ± √(b² - 4ac)/2a

Circle Function

x^2 + y^2 = r^2

point slope form

y - y1 = m(x - x1)

unit circle tan

y / x

log function derivative

d/dx ln(u) = 1 / u

monotone non-linear function

data is always positive or negative

Derivative of e^u

e^u du

one-to-one function

every output has exactly one input and vice versa (horiz and vert line test!)

Chain Rule f(g(x))

f'(g(x)) x g'(x)

Trig Function Equation

f(x) = Atrig(Bx - C) + D

vertex form of a quadratic function

f(x) = a(x-h)^2 + k

standard form of a linear equation

Ax+By=C

Pascal's Triangle (used for)

Easy way to show combinations

Fundamental Theorem of Arithmetic

Every composite number can be expressed as a unique product of prime numbers.

Combination Formula

ORDER DOES NOT MATTER (Read as n choose r)

Permutation Formula

ORDER MATTERS (Read it as n choose r)

"at Least one" rule

P(L) = 1 - P(not L)

alternative hypothesis

The hypothesis stating what the researcher is seeking evidence of. Directly contradicts the null hypothesis.

centroid of a triangle

The point of concurrency of the medians of a triangle (median is vertex to midpoint of opposite side)

Special Right Triangle 30-60-90

X:x/3:2x

unit circle sin

Y

removable discontinuity

a "hole" in a graph

What do each of the constants stand for? f(x) = Atrig(Bx - C) + D

a = amplitude, period = 2pi/b, c/b = phase shift, d = vertical shift

corrollary

a secondary inference or deduction from a main theorem

conjecture

a statement that has not been proved: an educated guess

correlation coefficient

a statistical measure of the extent to which two factors vary together, and thus of how well either factor predicts the other. Will b between -1 and 1. Closer to the extremes - stronger the correlation

Closed number system

a system is closed under an operation if performing that operation on two elements of the system results in another element of that system

axiom

a universal truth; an established rule (don't have to prove)

explanatory variable

a variable that we think explains or causes changes in the response variable (independent)

Additive Inverse

a+(-a)=0

multiplicative inverse of a complex number

a/(a^2 + b^2) - b(a^2 + b^2)i

Exponential Derivative Rule d/dx a^x

a^x * x' * ln(a)

determinant of a 2x2 matrix IAI

ad - bc

standard form of a quadratic equation

ax² + bx + c = 0

Nominal survey items

categorical survey items (think school, food)

derivative of sinx

cosx


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