Master IB Exam Review

y-y₁ = m(x-x₁), where m is the slope and (x₁, y₁) is a point on the line.

point-gradient form

ax+by+c=0

standard form

polyhedron

A three-dimensional geometric figure with flat polygonal faces, straight edges, and vertices.

function

each input has only one output

R

rational number (number that can be written as a fraction

natural numbers

counting numbers

Whole numbers

all natural numbers and zero

integers

all whole numbers and their negative counterparts

Irrational numbers

numbers that cannot be expressed as a fraction of two integers. They have non-terminating, non-repeating decimal expansions

t(n)=Cn+t₀

a function that represents a linear sequence, where C is the common difference and t0 is the first term.

Un=C(n-1)+U₁

is a formula that defines the nth term of an arithmetic sequence, where U1 is the first term and C is the common difference.

S_n=(n/2)(U₁+U_n)

the formula for the sum of the first n terms of an arithmetic sequence, where U1 is the first term and Un is the nth term.

I=Crn

simple interest calculated on the principal amount over a specified period, where I is the interest earned, C is the principal amount, r is the rate of interest, and n is the time in years.

extrapolation

estimating a value outside the range of the given data interp

interpolation

estimating a value within the range of the given data f

functional relationship

variables are related to each other through an exact equation statis

statistical relationship

variables have no direct relationship, but tend to fit a pattern

= (x₁+x₂₎/2

axis of symmetry equation

y=a(x-h)²+k

the vertex form of a quadratic equation that represents a parabola, where (h,k) is the vertex.

U_n=u₁r^n-1

the general term of a geometric sequence, where u1 is the first term and r is the common ratio.

log₃9=y → 3^y=9

how to roll the log

logarithms

the inverse functions of exponential functions

y=log(x)

the inverse of f(x)=10^x

1

natural log times exponent or ln*e always equals

|a|

in y=a*sin(bx)+d how to find amplitude

360/b

y=a*sin(bx)+d how to find period

y=d

y=a*sin(bx)+d how find principal axis

(high point-low point)/2

how to find a in y=a*sin(bx)+d

(y₁+y₂)/2

how to find d in y=a*sin(bx)+d_2-2

(x₂-x₁)2

how to find b in y=a*sin(bx)+d

opposite reciproccal

how to find perpendicular lines (slope)

normal

line perpendicular to the tangent

1) graph original function

2) trace # fro intersection point

3) calc dy/dx # for slope

4) use y=mx+b, plugging in intersection point coordinate and slope from previous steps

5) solve

steps for finding tangent

take tangent - change current slope for -1/m

how to solve for normal

2nd → trace →7

calculator steps for definite integral (finding the area under the curve between two x values)

gradient = m = y/x

constant of proportionality

angle of elevation

horizon and observer’s line of sight angle when looking upwards

angle of depression

horizon and observer’s line of sight angle when looking downwards

discrete

data that can be counted (natural numbers)conin

continuous

data than can be measured (height, weight)

univariate data

data that has only 1 variableqa

mode

the value that occurs most frequentlym

median

the value that lies in the middle when the data is arranged in sizemean

mean

sum of all values divided by the Humber of values

calc →1-var stats

calculator steps to find mean median mode

stat, sortA L1

steps for sorting data sets

(Q1-1.5(IQR)) and (Q3+1.5(IQR))

equations to calculate outliers

Q3-Q1

IQR equation

standard deviation

the spread of values in relation to the mean ( σ )

varience

the measure of spread that there is in the spread between the numbers in a list σ²

simple random sampling

selecting a sample completely at random sys

systmeatic sampling

for example, taking every fifth entry starting at a random place

convenience sampling

getting data by selecting people who are easy to reach

stratified sampling

selecting a random sample where numbers in certain categories are proportional to their numbers in the poulaiontqu

quota sampling

setting certain quotas for your sample

histogram

bar chart without space

box

teh iqr is represented by a ____ in a box and whisker plot

box’s center line

the median si represented by a ___ in a box and whisker plot

minimm and maximum

the whiskers extend to the ____ and _____ values in a box and whisker plot

cululative frequency

all of the total data points that are at or under the parameter

Q1

the 25% of highest values in cumulative frequency

median

cumulative frequency time .5

functional relationship

there is a formula or function that relates one variable to the other, so that all Data points lie on the same line or curves

statistical relationship

not such a direct relationship, but the data points, when plotted, may indicate a tendency to be close to a line or curve

r-value

correlation strength

line of best fit

line or scatter diagram showing trend followed by data points

mean point

found through mean of x-values and mean of y-values, always on line of best fit

cosecant

reciprocal sine function

secant

reciprocal cosine function

cotangent

reciprocal tangent function

x x*square root of 2

a 45 45 90 special right triangle have two sides of equal length _ and a hypotenuse of ____

x 2x x*square root of 3

on a 30 60 90 special right triangle - the side across from 30 degrees is length __, the hypotenuse is ___, nad the side across from 60 degrees (long side) is ____