TI 84 Plus techniques – Page 2 – JC A Level H2 Math Tuition Singapore

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.

2016 RI MCT

Solution for part ii

Using GC in DE

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

Quick Maclaurin’s series expansion using GC

In Maclaurin’s series expansion, where up to f”(0) need to be evaluated, can be done quickly using the GC.

Example

Expand up to powers of 2.

Using TI 84 Plus (OS 2.55)

From G.C,

f(0)= 3/2

f'(0) = -3/4

f”(0)= 5/4

Therefore using Maclaurin’s series expansion,

If powers higher than 2 such as 3 are required, then do differentiation to find the first derivative. Then enter into Y1. Y2 and Y3 will then give the second and third derivative.