Category: TI 84 Plus techniques

How to sketch both cartesian and parametric graphs on the same diagram using GC

Example

Suppose we want to sketch the curve C and the line y=-2x+2 on the same graph

Note how the line y-2x+2 is entered.

Adjust the Tmax to 1% more so the graph displays correctly.

## Sketching Periodic functions with GC

Suppose we want to sketch the graph from -3 to 8.

- Enter by pressing “Math, Piecewise”.

2. Adjust the window setting to the required domain.

3. Trace the end point at -3 since it is not 1 complete cycle.

Functional differences between TI 84 Plus CE and TI 84 Plus C for h2 maths

The following comparison are based on

TI 84 CE: Operating system 5.3.0

TI 84 Plus C: Operating system 4.2

Singapore Approved Operating System

- Division of complex numbers in TI 84 Plus CE can be entered in fractions, whereas it must be entered using division in TI 84 Plus C

.

- Piecewise function is now available in TI 84 Plus CE. This command can be found under MATH B: piecewise ( . Piecewise function can also be created manually in TI 84 Plus C but slightly more tedious.

New CONDITIONS submenu in “2nd test” allows faster entry of intervals for the piecewise functions

- Inverse binomial distribution and inverse norm enhancement in TI 84 CE

- Store tangent and faster access to n/d template in TI 84 CE

Conclusion

There are no major functional differences between TI 84 Plus CE and TI 84 Plus C. For piecewise functions, students should learn how to sketch manually without using the GC.

Using GC to calculate Expectation and Variance of Discrete Random Variable

Example 1

Solution

Enter the data in the GC as follows:

Variance can also calculated using the GC as follows:

Example 2

## GC setting for faster graph plot

Method 1: Change Xres to 3

The Xres button refers to pixel resolution (1 through 8). At Xres = 1, functions are evaluated and graphed at each pixel on the x-axis. At Xres = 8, functions are evaluated and graphed at every eighth pixel along the x-axis. Small Xres values improve graph resolution but may cause the calculator to draw graphs more slowly. Setting Xres to 3 provides good balance between speed and resolution.

Example

Xres= 1

Time taken to plot= 23.4 s

Xres= 3

Time taken to plot= 3.6 s

Savings of almost 20 seconds! Which is crucial in exams

Method 2: Turn off “Detect Asymptotes”

## Using GC to find the Normal vector to planes

## Using GC in Differential Equations

The following example illustrates how we can use GC in Differential equations, and avoid the need to do integration to solve differential equation.

Solution for part ii

## Using GC in Complex Numbers

GC can be very helpful in solving certain problems in Complex Numbers.

Example 1

Use the GC to find the real value of k such that has a complex root 1-i.

Solution

Since 1-i is a root,

Using TI 84 Plus (OS 2.55) to evaluate the complex numbers, we have

2+k = 0

k=-2

Example 2

Solution

Since the equation is quadratic, we can use the quadratic formula.

Using the GC to evaulate the above,

z = 1+2i or -7i

## Challenging Permutation question 3

There are a total of 20 amusement rides in a theme park. A child insists on trying at least 5 of the amusement rides. Calculate the number of ways in which this can be done.

Answer: 1042380

Solution

Method 1

20 choose 5 + 20 choose 6 +… 20 choose 20

Using TI 84 OS (2.55)

sum (seq(20 nCr X, X, 5, 20, 1)

= 1042380

Method 2

2^20- (20 choose 0+ 20 choose 1+20 choose 2+20 choose 3+ 20 choose 4)

=1042380