Finding range of composite functions using GC
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
Find the 2 roots of 
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
H2 Maths Tuition 
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