For all who want the highest score with the least work:
(For the TI-89 Titanimum)
IN THE HOME SCREEN
1) Define:
Press F4, then enter, this gives the word, Define. This can be used to define functions that can then be used in other things.
E.g, enter:
Define f(x)=x^2 then;
Define g(x)=ln(x)
Entering f(g(x)) will give (ln(x))^2, and of course, more complex functions can be used.
Entering Define y1(x)=x^2 will put x^2 in the [ Y= ] window, which can be accessed by pressing diamond F1.
The function can then be used in all other operations, entering f(2) will give 4, and f(y+2) will give (y+2)^2.
2) Differentiating.
Differentiating can be achieved by pressing 2nd 8, typing a function and specifying parameters.
ie, entering d(f(x),x) will differentiate f(x) with respect to x. finding the 2nd derivitive can be done as follows:
d(f(x),x,2).
3) Integrating.
Press 2nd 7, and specify parameters:
integral(f(x),x) will give integral. lower and upper bounds for definite integrals can be placed as follows:
integral(f(x),x,lowerbound,upperbound)
4) Solving.
Easily the most useful tool. You MUST be able to use the "Given that" symbol to specify domain and restrictions, this is achieved by pressing the button with just a line that is 4 buttons up from the left.
ie, entering:
solve(sin(x)=1/2,x) will provide the general solution to the sinusoidal function. However, entering
solve(sin(x)=1/2,x)|0<x<2pi will give you the distinct solutions. Similarly, you can specify other restrictions.
solve(y=3x^4 + 2x^2 + x -11,x)|y=0 will give the x intercept,
solve(y=3x^4 + 2x^2 + x -11,x)|x=0 will give the y intercept.
with functions of several variables, more restrictions can be added.
solve(y+t=3x^4 + 2t^2 + x -11,x)|y=0 and t = 3
will give the value of x when y=0 and t=3. similarly, just typing
3x^2 + 2|x=2 will give the value of that function at x = 2.
solving simultaneous equations:
enter:
solve(y + 2 = x/3 and 3x-4y=5,x) to achieve the solution, (-9/5,-13/5).
If there are 2 functions in terms of 3 variables, you can specify which variable you want to solve for using curly brackets, by pressing 2nd ( or 2nd ).
solve(3x+2a - y/2 = 0 and -2x+y=a+2,{x,y}) will give x = -(3a - 2)/4 and y = -(a-6)/2. alternatively, entering
solve(3x+2a - y/2 = 0 and -2x+y=a+2,{x,a}) will give x and a in terms of y. again, using "given that" and substituting a known value of y will solve for x and a.
you can use previously defined functions within solve.
5) Expand
When given a fraction, you can split it up into partial fractions using F2 expand. Entering:
expand((3x^2+2x)/(x^2 + 5x + 6)) will give the partial fraction form, 33/(x+3) - 12/(x+2) + x - 5.
It can also expand more simple expressions, such as
expand((x+3)*(x+2)) will give x^2 + 5x + 6.
6) ComDenom
this will reverse the partial fractions back to its original form, sometimes useful and can be found in F2.
7) "Hidden" Keys.
Pressing diamond EE will display what each key will do if you press diamond before hand. eg, pressing 2nd 0 will give a less than sign. Pressing diamond 0 will give a less than or equal to sign, helpful in setting domain restrictions.
Matrices
You can enter matrices by pressing 2nd , and 2nd / to give square brackets. Entries in a row are separated by commas, and each row is separated by a semicolon. eg, the matrix with 1 2 3 4 as the four entries from top left to bottom right is entered:
[1,2;3,4]
you can use define to give matrices a letter and then actually use them in solve etc:
Define a = [1,2;3,4]
Define b = [x;y]
define c = [5;6]
now the equation AB = C
can be solved for x and y by entering solve(a*b = c,x)
Also, a^-1 will give the inverse matrix of a, and det(a) will give you the determinant.
COMPLEX NUMBERS:
The i used in complex numbers is found by pressing 2nd catalog
to solve equations using complex numbers, enter:
csolve(z^2 + 2iz + 6 =0,z) gives z = +/-(root(7)+1)i
simliarly, using cfactor will give the factors of a complex polynomial.
to find the Argument of a complex number, enter:
abs(a+bi) to get the magnitude, and angle(a+bi) to get the Argument.
WITHING THE GRAPHING SCREEN:
in the y= screen, enter:
y1(x) = x^2.
Obviously, this graphs x^2. But if you enter:
y1(x) = x^2|-2<x<2 will only draw the graph over [-2,2]. *Sorry, I cant get a less than or equal to sign on this thing!*
you can also enter things like y1(x) = f(x) if you have previously defined some function f.
obviously, you can set your desired window with diamond F2.
Whilst in the actual graph, pressing F5 enter and then entering a value for x will give the corresponding value for y.
eg, entering (for y1(x) = x^2|-2<x<2) within the graphing screen:
F5
Enter
1.5
Enter
will give you (in the bottom right hand corner) y = 2.25
If you have two graphs drawn, you can toggle between graphs by pressing up or down.
IN THE GRAPHING SCREEN:
F5 Value - this does what i just said above! Enter x = 0 for the y intercept.
F5 Zero - Placing an upper and lower bound will give you the x intercepts
F5 Minimum - Placing a lower and upper bound will give you the coordinates of the local minimum
F5 Maximum - Placing a lower and upper bound will give you the coordinates of the local maximum (you can scroll through quicker by holding 2nd and pressing left and right)
F5 Intersection will give the intersecting point between two graphs. When prompted for "1st Curve" toggle the graphs using up and down arrows until the cursor is on the graph you're working with, then press enter on the second graph, and enter a lower and upper bound for the intersection on this second graph.
F5 Derivitives will give dy/dx at the input point.
F6 Integrate will give the area under the graph you select for the upper and lower bounds you input.
F5 Inflection will look for a point of inflection between the lower and upper bound you input. If no p.o.i is present, the calculator will say "No Solutions found"
F5 Distance will give the distance between two points inputted (these can be on two separate graphs)
F5 Tangent will draw and give the equation of the tangent at a given point
So as you can see, the graphing screen does pretty much everything.
And now, to blow your mind. METHODS ONLY
Probability. Input this EXACTLY, and you can get capital letters by pressing the button with an arrow pointing up (its next to 2nd).
Define noc(l,u,m,s)=TI.Stat.normCdf(l,u,m,s)
Then press enter. Then press 2nd - ( to get to VAR-LINK), then find "noc", select it and press F1 and archive this variable.
Now in the homescreen, if you want to find the probability in a normal distribution that X lies between l and m, with a mean of m and standard deviation of n, then you input:
noc(l,u,m,s)
eg, for a normal distribution with mean 5, standard deviation 2, and you want to find Pr(3<X<6), you input
noc(3,6,5,2) and it will give you the answer of 0.532807
I chose l for lower bound, u for upper bound, m for mean and s for standard deviation. For the rest of these, p will be probability, n will be number of trials, x will be number of successes (for binomial probability)
After each input, Archive the variable to avoid losing it later!
Define ino(p,m,s)=TI.Stat.invNorm(p,m,s)
This is the inverse normal function.
Define bip(n,p,x)=TI.Stat.binomPdf(n,p,x)
This is for binomial probability.
Define bic(n,p,x1,x2)=TI.Stat.binomCdf(n,p,x1,x2)
This is for cumulative binomial probability, ie, if x does not take a single value, but a range of values.
My french exam is tomorrow, so yeah, i'll post worked specialist and methods exams for the 2009 exam to show you all how easy it is with a calculator at a later date (within a week)! if you know what youre doing, these exams can be done in about 40 minutes - thats how long it was taking me when i did methods!
So i'll walk you all through it step by step, and trust me, you dont need to know any maths. you just need to know how to use a calculator!
Happy studying everyone
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