# 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