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

Example 1

DHS 2018 J1 Aug test

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

DHS 1

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

Adjust the Tmax to 1%  more so the graph displays correctly.DHS 3

2011 GC12011 GC2

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

.complex number division using fraction

  • 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.

piecewise function compared with TI 84 plus C

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

piecewise logic

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

TI 84 CE inverse binomial and inverse norm

Ti 84 ce inverse norm

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

Store tangent and faster access to fraction template

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

1

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.

1

Example

2

Xres= 1

IMG_3962

Time taken to plot= 23.4 s

Xres= 3

IMG_3963

Time taken to plot= 3.6 s

Savings of almost 20 seconds! Which is crucial in exams

Method 2: Turn off “Detect Asymptotes”

detect asymptotoes 1.jpg

detect asymptotoes 2

detect asymptotoes

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  Tex2Img_1404187817 has a complex root 1-i.

Solution

Since 1-i is a root,

Tex2Img_1404188152

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 Tex2Img_1404188506

Solution

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

Tex2Img_1404188717

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

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