How do you?: Find the minimum of a function

Example: Minimum of x^3+6X-15

How to get to it: Math button, Math menu, fMin (6)

What to type: fMin(expression)

Example: fMin(x^3+6X-15)

How do you?: Find the maximum of a function

Example: Maximum of x^3+6X-15 

How to get to it: Math button, Math menu, fMax (7)

What to type: fMax(expression)

Example: fMax(x^3+6X-15)

How do you?: Find a numerical derivative at a specific x value

Example: Derivative of f(x)=x^2+3 at x=1

How to get to it: Math button, Math menu, nDeriv (8)

What to type: nDeriv(expression,variable,x value)

Example: nDeriv(x^2+3,x,1)

How do you?: Find the integral of a function

Example: Integral of X^2+10 from x=4 to x=5

How to get to it: Math button, Math menu, fnInt (9)

What to type: fnInt(expression,variable,lower,upper)

Example: fnInt(expression,variable,lower,upper)

How do you?: Find the coefficients in a binomial expansion (without Pascal’s triangle)

Example: (⁶₁) 

How to get to it: Math button, Prb Menu, nCr (3)

What to type: top number Cr bottom number

Example: 6 Cr 1

Notes: Can also be used to find combinations, with the first number being the number of items in the combination and the second one is the number of items in each combination (for example, 7 baseballs in the maximum possible combinations of two).

How do you?: Find the area under a section of a normal distribution curve

Example: What % of trees are between the heights of 38 and 40 (u=30 o=4)?

How to get to it: Distr (2nd Vars) Button, Distr Menu, normalcdf( (2)

What to type: normalcdf(lower bound,upper bound,mean, standard deviation)

Example: normalcdf(38,40,30,4) Notes: When you have only one bound, use like -99999 for no lower bound or 99999 for no upper bound.

How do you?: Find what part of a normal distribution curve is under.

Example: 40% of trees are less than what height (u=30, o=4)?

How to get to it: Distr (2nd Vars) Button, Distr Menu, invNorm( (3)

What to type: invNorm(area,mean,standard deviation) Example: invNorm(.4,30,4)

Notes: If the question asks for greater than some %, use 1-that percent. For example, if the given example had instead been greater than, you would have used 0.6 instead of 0.4.

How do you?: Find the probability of a single outcome with replacement

Example: 30% chance a blue marble is drawn, if a marble is drawn twice, what is the probability that a blue one is drawn exactly once?

How to get to it: Distr (2nd Vars) Button, Distr Menu, binompdf( (A)

What to type: binompdf(trials,probability,desired number of trials with certain outcome)

Example: binompdf(2,0.3,1)

How do you?: Find the probability of a range of outcomes with replacement

Example: 30% chance a blue marble is drawn, if a marble is drawn twice, what is the probability that a blue one is less than or equal to once?

How to get to it: Distr (2nd Vars) Button, Distr Menu, binomcdf( (B)

What to type: binomcdf(trials,probability, upper desired number of trials with certain outcome)

Notes: If the question asks for less than or equal to, find the probability that it's not the numbers you’re looking for (if it’s greater than or equal to 3, find less than or equal to 2) and then do 1-that number. Also, if the question just says something like less than instead of less than or equal, go down one number (or up if it’s greater than) so that the new number is less than or equal to (if you have less than 5, it’s the same thing as less than or equal to 4, so use four in your calculations instead 

How do you?: Enter stuff into a data table

Example: 4,5,6 into the first column; 3,5,7 into the second

How to get to it: Stat button, Edit Menu, Edit… (1)

What to type: First column in L1, second in L2

Example: 4,5,6 in L1; 3,5,7 in L2

Notes: Click clear and then enter when the actual column header is selected (like L1) to clear everything in that’s in that column. Also, if you want to use this as a frequency list, use the first column for your x value and the second one for the frequency of each x value.

How do you?: Find a bunch of statistics information about a frequency list

Example: Find the mean and standard deviation and Q3 of a data set

How to get to it: Stat button, Calc Menu, 1-Var Stats (1)

What to type: Just have your frequency list already entered

Notes: Just look over everything in this, because a lot of this stuff seems like it could turn out to be useful.

How do you?: Find the data points for a cumulative sum graph

Example: x data is (1,3,6, 7,20)

How to get to it: List (2nd Stat) Button, Ops Menu, cumSum( (6)

What to type: cumSum(L1) (Your data should be in L1)

Example: cumSum(1,3,6,7,20)

Notes: This basically adds up all the previous terms for each term. So, for term 2 of the cumulative sum, it term1 + term 2. Term three is term 1 + term 2 +term 3, and so on.

How do you?: Find certain terms in a sequence

Example: If your sequence is defined by x+2, then what are terms when x equals from 8 to 12

How to get to it: List (2nd Stat) Button, Ops Menu, seq( (5)

What to type: seq(expression,variable,first term,last term, step (just put 1))

Example: seq(x+2,x,8,12,1) Notes: This will probably will be most helpful when just finding one term (I can’t think of a time we’ve had to find a range of terms), so you can just put the first and last terms as the same thing if that’s the case.

How do you?: Graph a table of x and y values as a stat plot, bar graph, or box and whiskers plot

Example: x=(1,2,3,4) y=(3,18,42,89), graph box and whiskers plot

How to get to it: Stat Plot (Y= 2nd) Button, Plot 1

What to select: After your data is already in L1 and L2 (your x and y values), turn stat plot on, select your desired graph under type, and make sure you x list and y list are using the correct data (probably L1 and L2)

Notes: When you’re under type, to get to the second row of graph types, don’t scroll down, as this will send you all the way down to x list. Instead, just keep scrolling right (I don’t know if this is just a problem only I had, but I thought it was worth mentioning).

How do you?: Change the window to a preset option

Example: Zoom to the preset for trigonometric equations

How to get to it: Zoom Button

What to select: Whichever preset fits you graph

Example: ZTrig (7) Notes: If you want to tweak any of these presets for your specific graph, you can use the Window button to do so.

How do you?: Calculate the y value at a certain x value from a graph

Example: x^2+3, y when x=4

How to get to it: Calc (2nd Trace) Button, value (1)

What to type: The x value

Notes: If you need to find the y value, you can enter another function of y=whatever value you’re looking for, then finding the intersection of the two graphs with the Calc button

How do you?: Calculate the zeros of a graph

Example: Zeros of x^2+3

How to get to it: Calc (2nd Trace) Button, zero (2)

What to select: First, pick some point on the graph to the left of the zero, and then one to the right, and then guess where you think the point actually is

Notes: You’ll have to do this multiple times for multiple zeros

How do you?: Calculate a local minimum of a graph

Example: Minimum of x^2+3

How to get to it: Calc (2nd Trace) Button, maximum (4)

What to type: First, pick some point on the graph to the left of the maximum, and then one to the right, and then guess where you think the point actually is

How do you?: Calculate point of intersection between two graphs

Example: Intersection between x^2+3 and x+2

How to get to it: Calc (2nd Trace) Button, intersect (5)

What to type: First, pick a point close to the intersection on the first graph, and then do the same for the second, then try to select the actual point the third time

How do you?: Calculate the derivative of a graph at a specific x value

Example: Derivative of x^2+3 when x=4

How to get to it: Calc (2nd Trace) Button, dy/dx (6)

What to type: The x value

How do you?: Calculate the integral of a graph between two x values

Example: Integral of x^2+3 between x=0 and x=2

How to get to it: Calc (2nd Trace) Button, ∫f(x)dx (7)

What to type: The value of the lower x value, then the higher one

Example: Type 0 then 2

How do you?: Enter numbers into a matrix

Example: l3 2l

               l4 1l

How to get to it: Matrix (2nd x^-1) Button, Edit Menu

What to type: Select a matrix, type in the dimensions, then type in the numbers

Notes: The only way to get out of editing a matrix is to use the Quit (2nd mode) button

How do you?: Use matrices with mathematical operations

Example: [A]x[B]

How to get to it: Matrix (2nd x^-1) Button, Names Menu

What to select: Here you can select different matrices you have already entered