SAT / SAT II Math Programs for Your Calculator

<p>Thanks for answer! Should I input everything as you showed it with 'X1", A ; “Y1”, B; etc for all of them?</p>

<p>Thanks again!</p>

<p>I am completely new to calculator programming, so forgive me if this sounds stupid. xD I’m trying to put the quadratic solver on the first page of this thread into my calculator. I named the variable and pressed enter; now I’m at the programming field, but the cursor is between two parantheses. Below this it says “:Prgm”. Underneath that there’s a colon. The last line says “:EndPrgm”. So where exactly am I supposed to type the program? Between the parentheses? In the second line that starts with “:Prgm”? Next to the colon on the third line? Thanks a lot.</p>

<p>Steps to make a program say for distance between 2 points.</p>

<ol>
<li>Press on.</li>
<li>Click PRGM</li>
<li>Scroll right to NEW</li>
<li>Click enter</li>
<li>Type in a name such as DISTANCE</li>
<li>Input what was above. Input, Disp, and Prompt can all be found by clicking PRGM again and scrolling over to I/O.</li>
<li>Exit out and enjoy.</li>
<li>To edit go click PRGM and click EDIT.</li>
</ol>

<p>Wow, this thread has been alive for awhile… anyone got any other useful programs?</p>

<p>Yuusss, I do. </p>

<p>Area of a regular polygon given side length:</p>

<p>Disp “Change mode to degrees, N = number of sides”
Prompt N
360/(2N) -> A
Disp “S = side length”
Prompt S
(S/2)/tan(A) -> H
.5(SH) -> B
BN -> Z
Disp “Area is”
Disp Z
Stop</p>

<p>Finding average rate given 2 rates:</p>

<p>Disp “A and B are 2 given rates”
Prompt A
Prompt B
2/((1/A)+(1/B)) -> R
Disp “Average rate is”
Disp R
Stop</p>

<p>1 version of Law of cosines (find an angle if 3 sides of any triangle are known)</p>

<p>Disp “A, B, and C are side lengths, C is side with desired angle, change mode to degrees”
Prompt A
Prompt B
Prompt C
cos^-1 ((C^2 - A^2 - B^2)/((-2)(A)(B)) -> E
Disp “Angle C is”
Disp E
Stop</p>

<p>Heron’s formula (finding area of any triangle given length of sides)</p>

<p>Disp “A, B, and C are side lengths”
Prompt A
Prompt B
Prompt C
(A+B+C)/2 -> S
sqroot(S(S-A)(S-B)(S-C)) -> D
Disp “Area is”
Disp D
Stop</p>

<p>Alternate form of Heron’s formula (finding area of any triangle given 3 coordinates)</p>

<p>Disp “(A,B), (C,D), and (E,F) are coordinates”
Prompt A,B,C,D,E,F
sqroot((A-C)^2 + (B-D)^2) -> X
sqroot((C-E)^2 + (D-F)^2) -> Y
sqroot((E-A)^2 + (F-B)^2) -> Z
(X+Y+Z)/2 -> S
sqroot((S)(S-X)(S-Y)(S-Z)) -> G
Disp “Area is”
Disp G
Stop </p>

<p>Not sure how much these will really help, but if you’re bored, might as well put them in. Who knows. They could end up helping you on the actual test.</p>

<p>Please create a program to find degrees of angles.</p>

<p>Does this work on TI-84 plus?</p>

<p>found an error in the Sphere program. when calculating surface area its 4PiR^2 not 4. here s the correct code</p>

<p>Program : Sphere</p>

<p>Disp “Radius=”
Input R
(4/3)PiR^3–>Z
4PiR^2–> Y
Disp “Volume=”
Disp Z
Disp “Surface Area=”
Disp Y
Stop</p>

<p>You could try the SAT Operating System. I used it and it helped me work some of the math questions faster.</p>

<p>Program : Quadratic Solver
when i use this program for 2x^2+4x-6, the program says D = 64 1 -3… but what does that mean?</p>

<p>Prompt A
Prompt B
Prompt C
B^2-4AC–> D
Disp “D=”
Disp D
(-B+Sqrt(D))/(2A)–>Q
(-B-Sqrt(D))/(2A)–>W
Disp Q
Disp W
Stop</p>

<p>Area of an Equilateral Triangle Based on an Altitude
Disp “Height”
Input H
(H/sqrt(3))*H -->A
Disp “AREA=”
Disp A
Stop</p>

<p>Sum of a Geometric Series
Disp “FIRST TERM”
Input A
Disp “COMMON RATIO”
Input R
Disp “TERMS AFTER A”
Input N
A*((1-R^(N+1))/(1-R))–>S
Disp “SUM OF A-N=”
Disp S
Stop</p>

Is this against the rules?

Yup. But most proctor are so lazy or don’t know how to do their job (clear calculators before starting a test) that students can get away with doing this.

I don’t think that you are required to clear anything from your calculator on the SAT.

But even so, I’ve yet to see a program that is worth the trouble. The time spent learning to enter the program and then to apply it in the right context (which will no doubt be slightly different than what you expect) would be better spent practicing the math content and techniques.

With a TI-Nspire CS CAS, instead of programs, you can create multivariable functions with the Define command. You don’t have to know anything about programming.

For example, for the distance between two points,

Define r(a,b,c,d)=√((a-c)^2+(b-d)^2 ) (returns) Done

Then to find the distance between, say, (-1.8,6) and (-5,7.2)

r(-1.8,6,-5.7,2) (returns) 5.58659108939

I also like to have a discriminant function in memory. I have noticed quite a few discriminant questions on the new test.

Define q(a,b,c) = b^2 – 4a·c

You can store as many of these as you like in memory. You just have to remember what letter is defined as what function, and not to use the same letter as a variable in other problems. The calculator shows letters that have been defined in boldface, so this helps to avoid issues.

OK, but I’m saying that the cognitive load to create and use even that first function is more than what it takes to draw a diagram and apply the pythag thm directly. And the numbers are never that hard.

And while I’ve seen a couple of questions where you COULD use the discriminant, I don’t recall one where you have to. But I may be overlooking one. Can you give me an example from released tests 1 - 6?

I know from earlier posts that you are a big fan of nspire. Maybe when I am more familiar with it, I’ll come around to your way of thinking. But for now, I am not convinced that it’s the right path for anyone whose math background has not already led them to a comfort level with the nspire.

You should create the functions before the test, not during the test. The only cognitive load during the test is remembering that “r(a,b,c,d)” gives the distance between points (a,b) and (c,d). Before the test, you can also create a note file on the calculator with a list of the defined functions, just in case you forget.

I am not saying that everyone should use this method. My experience has shown that is a good method for some people, especially people who have trouble remembering or using a particular formula.

I agree it is essential to be comfortable with calculator, and to do only those operations with which one is comfortable. This varies greatly. More advanced students can do more advanced operations, and less advanced students should stick to simple operations. Plugging values into a distance function is pretty simple, but even this skill should be practiced.

As far as I can remember, I found most of the discriminant problems on Khan Academy, and put the q function into memory because of these.

Looking through my notes, I found these. I think they were on Khan Academy, but I am not sure.

What is the least integer value k such that x^2(3k+1)-6x+2=0 has no real roots?
CAS solution:
solve (q(3k+1,-6,2)<0,k) returns k>7/6 so Answer=2.

For what value of k will the equation 5x^2+6x=-3k have exactly one real solution?
CAS solution
solve(q(5,6,3k)=0,k) returns k=3/5

Looking over the official tests, I found this:

Practice Test 2, Section 4, question 29.
y=3
y = ax^2 + b
In the system of equations above, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions?
A) a=−2,b=2 B) a=−2,b=4 C) a=2,b=4 D) a=4,b=3

Clearly, this one is a lot easier than the two previous (Khan Academy?) problems, so the q function makes less sense. But you can use the q function if worried about sign mistakes.

Right. So your post raises an interesting question. One of my main objections to third-party practice tests is that they often have material that is outside of the scope and/or level of difficulty of the real thing. So a student – a busy student – who uses that material ends up wasting time better spent immersed in more realistic material. Are we sure that Khan Academy is any better? I’m still telling my students to spend their time mastering the material on released tests 1 - 6.

I just put another one onto my calculator that I think is super useful for geometric series as that’s one of my weak points… here it is if anyone wants to use it:

NOTE this program finds either the sum of n terms OR the sum of an infinite geometric series. To do the first one, just input values as prompted and to do the second one, enter 0 for the value of n.

Disp “firstterm=”
Input A
Disp “ratio=”
Input R
Disp “numofterms=”
Input N
If N>1
Then
A*((1-R^N)/(1-R)) -> S
Disp S
Else
A/(1-R) -> S
Disp S
Stop

Random Side Note:

Here are the programs I found most useful when looking through SAT Math II material (having taken all 5 Barron’s practice tests)…

Equation Given Imaginary Roots
Exact Value for Given Angle
Triangle Solver (Law of Sines / Cosines)
Double & Half Angle Formulas
Linear Equation Given Two Points
Area of Sector Given Angle/Radius
Sum / Difference Identity Formulas
Formulas for Sums / Terms of Infinite / Finite Geometric / Arithmetic Series / Sequences
Area / Volume of Sphere / Cone / Rhombus / Cylinder / Triangle

Good luck!