# CASIO fx-991 EX/ES Tips and Tricks for A Level

The CASIO fx-991 ES series is around £16-18 on Amazon.co.uk. The fx-991 ES PLUS version is slightly newer but without any major differences other than the design and a few tweaks to the software.

The CASIO fx-991 EX ClassWiz is the new version of this calculator. Some of its major new features include:
- 4×4 matrices, 4-variable polynomials and simultaneous equations
- Much higher resolution display
- Can hold a maximum of 200 digits/signs on the screen at once, vs 100 on the 991 ES series (very useful for the Statistics modules and Numerical Methods)
- 2, 3 and 4 degree inequality solving
- Input SI prefixes (e.g. type 100 and then enter the M prefix from the OPTN menu to use 100,000,000)
- Graph functions by pressing the QR button and scanning the screen with the calculator's smartphone app
- Much faster CPU and more memory, so it calculates solutions 3-10× faster than the 991 ES series
- Nicer design

Both models are allowed in all GCSE and A-level maths and science exams where calculators are permitted.

# Solving equations

## Quadratics and cubics:

• fx-991 ES:
- mode → 5
- Option 3 for a quadratic, option 4 for a cubic
- Enter the values for a, b, c (and d for a cubic) and press = to cycle through the solutions
- View complex number solutions in mod-arg form with shift-mode → down → COMPLX → 2
• fx-991 EX:
- mode → (-) → 2
- Press 2 for a quadratic, 3 for a cubic, 4 for a quartic
- Enter the values for a, b, c, etc and press = to cycle through the solutions
- The coordinates of the maximum point is also given
- View complex number solutions in mod-arg form with shift-mode → down → Complex → 2

## Simultaneous equations:

• fx-991 ES:
- mode → 5
- Option 1 for 2 variables (x and y)
- Option 2 for 3 variables (x, y and z)
- Enter the values for x, y, (z) and RHS, use = to cycle through solutions
• fx-991 EX:
- mode → (-) → 2
- Enter the number of unknowns (2 is for 2 variables, x and y. 3 is for 3 variables, etc)
- Enter the values for x, y, etc and RHS, use = to cycle through solutions
- If there are no solutions or infinite solutions, this will be shown

## Equations in any form:

• Use mode 1
• Enter the equation in terms of x, where x is the unknown, with the = sign
• Press shift-calc
• Press =
• Wait up to 60 seconds (the fx-991 EX is 3-5x faster than the fx-991 ES for this)
• A single solution is output. Only one solution is shown, even if there are multiple
• If L-R= on the display is equal to 0, this means that the solution is accurate to 9+ sig figs. If it is very large, it indicates that the calculator could not solve the equation and the provided solution is very innacurate
• To find more solutions if the equation has multiple, press shift-calc, enter a value near to where you think the solution is, and press = (fx-991 EX only: press = twice). This approximation does not need to be very accurate (the calculator uses the Newton-Raphson method)
• All solutions are provided in decimal form (not surd form, fractions etc). If you save the solution to a memory slot (instructions on this are further down) and then recall it, the calculator will try to display it in fraction form. This will only work for more simple fractions (e.g. 5/8) and not surds
• To convert a solution to surd form, square the solution. If it is indeed a surd, this will be an integer and you can write this under a square root sign

# Calculating function values

• e.g. to find y when x = 5 for the equation y = 5x2 + 6:
- Enter the equation in terms of x (y may also be used) in mode 1 (5X2 in this case)
- Press CALC

# Matrices

## Creating:

• fx-991 ES:
- Add the first matrix with mode → 6 and then 1 for slot 1 (up to 3 matrices can be saved)
- Select the size (it's in rows × columns, up to 3×3)
- Enter the elements and press = after each to save it
- AC to finish adding the matrix
- Add additional matrices with shift-4 → Dim
• fx-991 EX:
- Add the first matrix with mode → 4 and then 1 for slot 1 (up to 4 matrices can be saved)
- Enter the number of rows (up to 4)
- Enter the number of columns (up to 4)
- AC to finish adding the matrix
- Add additional matrices with OPTN → Define Matrix

## Operations:

• e.g. to multiply:
- fx-991 ES: shift-4 → (the first matrix to multiply) → shift-4 → (the second matrix) → =
- fx-991 EX: OPTN → (the first matrix to multiply) → OPTN → (the second matrix) → =
• Use the x-1 button to find the inverse
• Use det to find the determinant

# Numerical differentiation and integration

The calculator supports numerical calculus. This means that it can accurately differentiate and integrate to 8+ decimal places if given the x-coordinate (differentiation) or bounds (integration). However, it does not do this with algebraic manipulation so it can't give answers in exact form (e.g. square roots and fractions) or in terms of x.

## Differentiation:

• e.g. to find the gradient when x = 2 for y = 2x2
- Press the d/dx button (shift and integral button)
- Enter the equation without the y
- In the x= box to the right, enter the x value (2 in this case)
- Press =
- This only outputs approximations, accurate to ~9 d.p at most
- This doesn't output values in terms of π etc

## Integration:

• Use the integral button and again input in terms of x

# Conversions

## Radians to degrees:

• Set the calc to degrees mode (fx-991 ES: shift-mode → 3; fx-991 EX: shift-mode → 2 → 1)
• Enter the value in radians
• fx-991 ES: Shift-ans → 2
• fx-991 EX: OPTN → 2 → 2
• =

## Degrees to radians:

• Set the calc to radians mode (fx-991 ES: shift-mode → 4; fx-991 EX: shift-mode → 2 → 2)
• Enter the value in degrees
• fx-991 ES: Shift-ans → 1
• fx-991 EX: OPTN → 2 → 1
• =

## Metric and imperial:

• fx-991 ES: shift-8 → conversion number (on calculator cover) → left → number to convert → =
• fx-991 EX: shift-8 → select conversion from the menus → left → number to convert → =

# Memory

## Saving:

• Enter the number to save/calculation
• fx-991 ES: shift-RCL→ one of the third row buttons (there are 6 slots, A to F)
• fx-991 EX: STO→ one of the third row buttons (there are 6 slots, A to F)

## Recalling:

• Use the saved numbers in algebraic expressions by adding the letters with ALPHA or use RCL to view them in one less keystroke

# Summation

• Use the sum button (shift-top right button)
• This requires mode 1
• Enter the equation in terms of X
• Y cannot be used here, it must be single-variable

# Complex numbers

## Inputting:

• Use CMPLX mode
• Enter in terms of i (ENG button)
• Use shift-2 to find the arg and conjugate, and to convert to mod-arg form
• When finding the argument, remember to be in radians mode
• Use shift-hyp to find the modulus
• Note (ignore if using the fx-991 EX): in where n > 3 results in a MATH ERROR, use iiii (i multiplied by itself 4 times) for i4 instead, iiiii for i5 etc to bypass this restriction
• CALC mode can be used in CMPLX mode