Sketching Periodic functions with GC

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

1. 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.

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 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

Find the 2 roots of

Solution

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.

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