Casio fx-115ES Plus: Ten Tips
This blog entry covers both the original and the current 2nd Edition of the Casio fx-115 ES Plus. Here are ten things to help you know about some of the advanced features of the fx-115 ES Plus, including some things to watch out for.
I believe this also covers the fx-991 ES Plus 2nd Edition (NOT the Classwiz).
Tip 1: Integer Division and Modulus
Find the quotient and remainder of a division problem by pressing [ALPHA] [ []/[] ] (÷R). We can use this calculate the modulo of two positive numbers (use caution with negative numbers).
Example 1: 364 mod 20 = 4
364÷R20 returns 18, R = 4
(18 * 20 + 4 = 364)
Example 2: 178.5 mod 18.5 = 12
178.5÷R18.5 returns 9,R=12
(9 * 18.5 + 12 = 178.5)
Tip 2: Solving Quadratic Equations Also Calculates the Extrema Point
Solving quadratic equations in EQN mode will present the point of the parabola's extrema point (minimum or maximum). Keep on pressing [ ↓ ] or [ = ].
[ Mode ], 5: EQN, 3: aX^2+bX+c=0
Example 1: 4 * x^2 + 13 * x + 5 = 0
[ 4, 13, 5]
X1 = (-13+√89)/8 (MthIO mode)
X2 = (-13-√89)/8
X-Value Minimum = -13/8
Y-Value Minimum = -89/16
Example 2: -2 * x^2 + 5 * x + 10 = 0
[-2, 5, 10]
X1 = (5+√105)/4
X2 = (5-√105)/4
X-Value Maximum = 5/4
Y-Value Maximum = 105/8
Please note that results and coefficients are not stored in variables. This goes for all the equations in EQN mode, including finding roots of a polynomial and solving simultaneous equations.
Tip 3: Solving Quadratic Inequalities
The Inequality mode solves inequalities for quadratic and cubic equations.
[ MODE ], [ ↓ ], 1: INEQ, 1 for quadratic equation/2 for cubic equation, select inequality:
1: >0
2: <0
3: ≥0
4: ≤0
Example: Solve x^3 + 2 * x - 3 > 0
[1, 0, 2, -3], option 2
Result: 1<X
Tip 4: The Percent Function
The percent function ( [ SHIFT ] [ ( ] (%) ) just divides the argument by 100. This can lead to puzzling results when working addition and subtraction problems involving percent.
8 + 10% returns 8.1 (10% converts it to 0.1)
8 - 10% returns 7.9
To add and subtract percents properly, do this instead:
8(1 + 10%) returns 8.8
8(1 - 10%) returns 7.2
Tip 5: Limited Powers in Complex Mode
In complex mode (CMPLX), the only powers available to be calculated are x^2 and x^3. To take any complex number to any real power will require the use of De Moivre's formula:
(x + yi)^n = r^n * cos θ + i * r^n * sin θ
My suggestion to use COMP mode, with the Rec and Pol conversions. In CMPLX mode, rectangular/polar conversions do not store results. In COMP mode, rectangular/polar conversions store results in the following variables:
X: x, r
Y: y, θ
Tip 6: Solve Equations for Any Variable
We can use the general solver in COMP mode to solve for any variable. The syntax is:
equation, variable; press [ SHIFT ], [ CALC ] (SOLVE)
If variable is omitted, the variable to be solved for assumed to be X.
If the equation does not contain an equals sign (=), the solver finds the root for equation, assuming equation=0.
The entries and results are stored in variables.
In Radians mode:
Example 1: y = x * sin x with y =0.5
We are solving for x, so we can eliminate the variable argument.
Y=X*sin(X), [ SHIFT ], [ CALC ]
Enter 0.5 for Y
Enter a guess for X, I chose 1.
Result: X = 0.7408409551, L-R = 0
Example: 2 * a - b = 3 * c, solve for b when a = 2 and c = -1.
2A-B=3C, B, [ SHIFT ], [ CALC ]
Enter 2 for A
Enter -1 for C
Enter a guess for B, I chose 1 (again).
Result: B = 7, L-R = 0
Caution: Some equations can not be solved on the fx-115 ES Plus. In particular, involving integrals and derivatives.
Tip 7: The Repeating Decimal Bar
I think this may be only calculator (yet), that allows the use to easily type in a bar to represent repeating decimals.
Example:
1.45454545454545454545.... can be typed with 1.45 with the bar over the 45, or 1, [ . ], [ ALPHA ], [ √ ] ( bar ) 45
Pressing [ = ] returns 16/11 (assuming MthIO is set). Repeated uses of [ S←→D ] gives 1.(45), 1.454545455, 16/11.
Tip 8: Integer Part and Greatest Integer Function (Floor)
Int ( [ ALPHA ] [ + ] ): Returns the integer part of a number
Intg ( [ALPHA] [ - ] ): Returns the floor function of a number, the largest integer that does not exceed the given number.
Example 1:
Int(-12.96) returns -12
Intg(-12.96) returns -13
To find the (calculator) fractional part of a number, enter n - Int(n).
Tip 9: Use CALC to Formula Evaluation
In addition to the Table mode, using [ CALC ] in COMP mode allows the user to evaluate a formula using different expressions. As long as you keep pressing [ = ], the prompting for variables and calculations repeat. The latest values are updated in the memory registers.
Expressions may take the form of:
variable = expression
To results are stored in the designated variable.
Example: Evaluate for y when x = 0.2, x = 0.7, and x = 1.2 when y = x^3 + 15 * log x
Y=X^3+15*log(X)
[ CALC ]
Enter 0.2 for X, [ = ]
Result #1: -10.49255007, [ = ]
Enter 0.7 for X, [ = ]
Result #2: -2.6665294, [ = ]
Enter 1.2 for X, [ = ]
Result #3: -0.5402813093
Press [ AC ] to exit.
Tip 10: Previous Answers are Stored Two-Deep in COMP Mode
In COMP mode, we have both Ans and PreAns ([ALPHA], [ Ans ]). PreAns recalls the answer from two calculations ago.
Be careful, switching modes with most likely clear the PreAns register (zero). Also, PreAns is only available in COMP mode.
Bonus: Checking the fx-115ES Plus 2nd Edition's ID (2nd Edition only)
You can see the calculator's ID along with a bar code which allows to test whether the calculator is a genuine Casio calculator.
I hope you find these tips helpful,
Eddie
All original content copyright, © 2011-2021. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author
