MathsNet: AS/A2 Modular Mathematics

Are graphic calculators allowed?

Yes, in all modules except C1.

In C1 you are allowed no calculating aids at all.

You are not allowed to use a graphic calculator with any of these facilities: data banks, dictionaries, language translators, retrieval of text or formulae, QWERTY keyboards, built-in symbolic algebra manipulations, symbolic differentiation or integration, capability of remote communication with other machines or the World Wide Web

Graph sketching | Differentiation | Statistics | A graphic calculator gallery

Whilst it may be true that you are not "programming" your calculator when you enter any of the equations mentioned below, it may constitute a significant advantage when going into the examination room.

This will not be allowed!

The best advice would be to clear everything from your calculator before entering the examination room. In fact, regulations state that you have to take responsibility for doing this. Once you have been told that the exam has begun, then you can enter these equations - or any programs - into the calculator.

These notes summarise some of the most useful functions provided by a graphic calculator, particularly for pure mathematics and statistics. They refer specifically to the TI-83 or TI-84 models. Other graphic calculators do offer similar functions but you will need to check.

Graph sketching

Select the Y= screen: For a general cubic graph, enter Y1 = AX^3+BX+CX+D Then select the GRAPH screen. You can then choose different values for the constants A, B, C and D. Alternatively, enter Y1 = X-A X-B X-C Then select the GRAPH screen. You can then choose different values for the constants A, B and C.
For a general modulus graph, enter Y1 = absMX+C (Find abs in the CATALOG menu) Then select the GRAPH screen. You can then choose different values for the constants M and C. To change the value of any of the constants, for example to make M = 1, press 1 ALPHA M.

Differentiation

The TI 82/3 can display the "gradient function" or derivative of a curve. In other words, given the curve y=f(x), the curve dy/dx=f'(x) (where f'(x) is the derivative of f(x) with respect to x) can be displayed on the same screen.
To set this up, go to the Y= screen. Against Y1= enter a simple curve, 3x²+1 for example. Against Y2= you should make the following selections:

MATH 8 VARS Y-VARS 1 1 then type in ,X,X)

The result should be that the Y= screen shows Y1=3x²+1 and Y2=nDerive(Y1,X,X).

Go to the GRAPH screen, to see the graphs of y=3x²+1 and the gradient function. In this case the gradient function displayed will be that of y=6x. The calculator cannot tell you this though. You will have to work that out for yourself.
If now you change the equation against Y1, the calculator will automatically show its derivative.

Statistics

The special statistical functions on a TI-83 are most easily found by using the CATALOG function (2nd 0).

Normal probabilities
Suppose that X ~ N(0,1), the standard normal distribution:
P(X < 0.2) is given by normalcdf(-1E99,0.2) =.5792596878
P(-0.1 < X < 0.3) is given by normalcdf(-0.1,0.2) =.119087584
If P(X < z) = 0.7, then z is given by invNorm(0.7) = .5244005101

shadenorm Suppose this question was asked: IQ scores are assumed to be normally distributed with mean 100 and standard deviation 15. Find the percentage of people expected to have an IQ between 80 and 120.
X ~ N(100,15²), so P(80<X<120) is given by:
normalcdf(80,120,100,15) = .8175774363.
ShadeNorm(80,120,100,15) displays the distribution and the probability too

Binomial probabilities
Suppose that X ~ B(12,0.2):
P(X=4) is given by binompdf(12,0.2,4)=.1328755507
P(X £ 4) is given by binomcdf(12,0.2,4)=.9274445005
A list of all the probabilites for the distribution B(12,0.2) is given by binompdf(12,0.2)

Poisson probabilities
Suppose that X ~ P(5):
P(X=2) is given by poissonpdf(5,2)=.0842243375
P(X £ 2) is given by poissoncdf(5,2)=.1246520195

Using STAT LIST
stat edit A complete set of probabilities can be calculated at once and displayed in a list format. For example: Suppose that X ~ B(5,0.5). Select the STAT LIST option and enter the numbers 0,1,2,3,4,5 in list L1. Next enter binompdf(5,0.5,L1) L2 and you will find all the probabilities P(X=0) to P(X=5) displayed in list L2.

A "Goodness of Fit" test
As part of ASA2 module S3, you are required to carry out a Goodness of fit, or c², test.
The following data is thought to from a Poisson distribution. Carry out a c² test to test this hypothesis.

X	0	1	2	3	4	5	6
O	17	31	64	43	16	11	10

Enter the above data into the first two lists, and select STAT CALC 1. Enter L1, L2 so that the display shows 1-Var Stats L1,L2. The display will tell you that the mean, l, of the distribution is 2.432291667. The total frequency is 192. Now enter poissonpdf(2.43229, L1) L3 to get the first display shown opposite.
Next enter L3 x 192 L4 and (L2-L4)²/L4 L5 to get the second display. Finally, LIST MATH 5 will put sum( in the display. sum(L5) gives 15.15279386, which is the c² test statistic to compare with the relevant critical value.

Contingency tables
As part of ASA2 module S3, you are required to carry out a Goodness of fit, or c², test for a two-way Contingency table. The whole process can be perfomed on the calculator.
The manager of a leasure centre collected data on the usage of facilities in the centre by its members. Test if there is any association between gender and type of facility used.

	Pool	Jacuzzi	Gym	TOTALS
Male	35	31	54	120
Female	68	32	30	130
TOTALS	103	63	84	250

1. Select MATRX EDIT, enter 2 x 3 and the data from the above table - not including the totals.
2. Select STAT TESTS C. this will bring up the c²-Test display showing the Observed data in matrix A and Expected data in matrix B. Confirm by pressing enter and you will get the results screen, showing the c² test statistic and the degrees of freedom:
3. The expected data is displayed by selecting MATRX EDIT 2. In this case the 5% critical value would be 5.991, meaning we have a significant result and there is evidence of an association between gender and type of facility used.

It is easy to forget where these special functions are on you calculator. Check this before your exam.