Casio Calculator Classwiz fx-991CW

Casio has released a major redesign of its scientific calculator, probably the biggest change in physical design since 1994.

Welcome, Casio fx-991CW Classwiz! We'll look at what functions it has that are useful for A-Level students.

You can find a complete manual on the Casio website.

General

"ANS" refers back to the previous answer, so you can re-use it for calculations.
"Shift" is for accessing secondary functions - written in yellow next to each button.

Memory (Variable Store/Recall)

There is a new 'VARIABLE' button, immediately showing you the values of nine variables, and allowing you to update them on the same screen. You can immediately see what you have saved and what letters you are using.

Errors

It's useful to know the difference between Math Error and Syntax Error:

Syntax Error

Syntax Error means you typed something wrong, so the calculator can't understand what you mean.
$\sin(90($ , with an extra open bracket, gives a syntax error.

Math Error

Math Error means your calculator understands what you mean, but the maths doesn't make sense.
$\tan(90)$ gives a math error (in Degrees mode), since $\tan(90^{\circ })$ is mathematically undefined.

A-Level Mathematics

There are many functions in the calculator to help you with A-Level Mathematics and Further Mathematics - don't miss them!

Pure

Angle Units (Radians/Degrees)

Settings > Calc Settings > Angle Unit >

Once you have chosen Degrees or Radians, press AC to escape back to the calculation screen.

If you haven't used Radians yet, this is still important: you need to make sure your calculator is in Degrees for any angle questions.

The Casio calculation screen always has a handy 'D' or 'R' in a black box, telling you whether you are working in Degrees or Radians. Being able to see immediately if you're working in the right units is super-useful, as using the wrong one can be a hidden disaster.

Prime Factorisation

Format > Prime Factor >

It can occasionally be handy for questions to have the prime factorisation of an integer. Type the number and press EXE before choosing the format.

Integration (Numerical Integration with Limits)

Catalog > Func Analaysis > Integration >

A calculator that can do algebraic/indefinite integration is not allowed in an A-Level exam, but a calculator that does numerical integration with limits is allowed. Usually, this won't give you an exact answer, being calculated by a numerical method - Casio is using the Gauss-Kronrod method. This should allow you to check your working.

Make sure your calculator is in Radians if using sin/cos/tan
Press Catalog > Func Analaysis > Integration >
Fill in the body of the integral using $x$
Make sure you also close any brackets
Press down-arrow and up-arrow to reach and fill in the limits

As a check, $\int \limits _{0}^{\pi }\sin {x}\ dx=2$

Equation Solver

Home > Equation >

Simultaneous Equation Solver

Home > Equation > Simul Equation >

You can pick between 2 unknowns $(x,y)$ , 3 unknowns $(x,y,z)$ , 4 unknowns $(x,y,z,t)$

Your equations have to be arranged in the correct format, with $x$ always before $y$ :

$2x-3y=5$
$3x+2y=-4$

Don't forget to type any minus signs in the coefficients! For the first equation, you will type 2, -3, and 5 into the available spaces.

Once you are done, Pressing EXE will give you the value of $x$ , and pressing EXE again will give you the value of $y$ .

As a check, the above equations give you:

$x=-{\frac {2}{13}}$
$y=-{\frac {23}{13}}$

Instead of giving you $x$ and $y$ , the Casio screen can read Infinite solution or No solution. This becomes more important at Further Maths.

Infinite solution with 2 unknowns means you have put in the same equation twice (perhaps one is a multiple of the other). On a graph, you have gone over the same line twice - there are infinite points where the lines cross - infinite solutions.

No solution means you have put in two equations representing parallel lines - there are no points where these cross, so there are no solutions.

Polynomial Equation Solver

Note: This is a key skill at A-Level. "Show all stages of working" or similar means you are being tested on showing how to solve by hand. Otherwise, you can rely on a calculator to solve these for you.

Home > Equation > Polynomial >

You can solve quadratic, cubic, and quartic equations here.

At A-Level, it's expected that you will use your calculator, so take advantage of this.

The polynomial must be written in standard form, equalling zero, e.g. $2x^{2}+3x+1=0$

Equation Solver (Numerical)

Note: Risky to use for A-Level exams, not recommended.

Home > Equation > Solver >

This uses a numerical method to solve any equation of your choice, typed out with $x$ and $=$ (equals sign). Casio uses "Newton's method" which is likely to be the same as Newton–Raphson method calculated with tolerances. Unfortunately, this probably won't help you to get marks for the Newton-Raphson method.

This may give unexpected results and I don't recommend using this, except perhaps as a check. If there are multiple solutions, it will only find one (or none).

Inequality Solver

Note: This is a key skill at A-Level. I recommend solving these by hand and using a calculator to check.

Home > Inequality >

You can solve quadratic, cubic, and quartic inequalities here.

The calculator returns the structure of the solution at the top of the screen, and the complete solution at the bottom of the screen - you may need to scroll to the right.

The format of the solution may be unexpected. For example, a calculator may give $1\leq x$ , which should preferably be written as $x\geq 1$ .

An A-Level exam may ask you to write your exam in set notation here - a calculator will not typically help you with this.

Statistics

Binomial Distribution

P(X=x)

Home > Distribution > Binomial PD > Variable >

Suppose you have the Binomial Distribution $X\sim Bin(50,{\frac {1}{3}})$ , so $n=50$ and $p={\frac {1}{3}}$

You can work out $P(X=10)$ from "Binomial PD", the Probability Distribution.

Input $x=10,N=50,p={\frac {1}{3}}$ .

Press EXE and you'll find the answer $P(X=10)=0.01573...$

You can use the Variable button to store this answer for ongoing calculation.

P(X<=x)

Home > Distribution > Binomial CD > Variable >

Suppose you have the Binomial Distribution $X\sim Bin(17,0.8)$

You can work out $P(X\leq 15)$ from "Binomial CD", the Cumulative Distribution

Input $x=15,N=17,p=0.8$ .

Press EXE and you'll find the answer $P(X\leq 15)=0.88178...$

You can use the Variable button to store this answer for ongoing calculation.

Note: You will also need to know how to use this to calculate $P(X<x),P(X>x),P(X\geq x)$ , which the calculator will not give you directly.

Normal Distribution

Note that Normal PD, the Normal Probability Density, is not generally useful to calculate.

Normal CD

Home > Distribution > Normal CD >

Suppose you have the Normal Distribution $X\sim N(182,220)$ , so $\mu =182$ and $\sigma ={\sqrt {220}}$

You can work out $P(175<X<180)$ from "Normal CD", the Cumulative Distribution.

Input ${\text{Lower}}=175,{\text{Upper}}=180,\mu =182,\sigma ={\sqrt {220}}$

Press EXE and you'll find the answer $P(175<X<180)=0.12788...$

You can also calculate probabilities on the tails directly here.

For example, You can work out $P(X<185)$ . Treat this as $P(-\infty <X<185)$ . Although you can't type exactly $-\infty$ , you will get plenty of accuracy by using a large negative number in place of $-\infty$ :

Input ${\text{Lower}}=-10^{99},{\text{Upper}}=185,\mu =182,\sigma ={\sqrt {220}}$

Press EXE and you'll find the answer $P(X<185)=0.58014...$

Inverse Normal

Home > Distribution > (scroll down) Inverse Normal >

If you know the Probability/Area on a Normal curve and want to reverse this to find the value on the x-axis, you can do this here.

Suppose you have distribution $Y\sim N(50,50)$ and you want to find $c$ such that P(Y<c)=0.3.

Input ${\text{Area}}=0.3,\mu =50,\sigma ={\sqrt {50}}$

You'll get the result $xInv=46.29...$ , telling you that $P(Y<46.29...)=0.3$

Note: This tells you the x-value based on the probability on the left-hand tail. You will also need to calculate from the probability of the right-hand tail or from symmetry around the centre of the distribution, which the calculator will not tell you directly.

Summary Statistics

Home > Statistics > 1-Variable >

If you have a list of raw data, you can use the Statistics mode to get key summary statistics.

For example, say you have the raw data:

$2\quad 3\quad 3\quad 5\quad 5\quad 7\quad 8\quad 11\quad 13\quad 15$

You can type these numbers directly into the column provided in Statistics mode.
You can see how many items there as as a useful quick-check that you haven't missed anything.

When you are done, press EXE on a blank line.

Home > Statistics > 1-Variable > 1-Var Results >

Once you have input the data, you can get a list of summary statistics, including the mean, standard deviation, median and quartiles: ${\bar {x}}=7.2,\sum x=72,\sum x^{2}=700,\sigma _{x}^{2}=18.16,\sigma _{x}=4.261...,s_{x}^{2}=20.1777...,s_{x}=4.4491...,n=10,Q_{1}=3,{\text{Med}}=6,Q_{3}=11,...$

$\sigma$ or $s$ both represent standard deviation. Technically, you should take the value of $\sigma$ in cases where you have listed data from the whole population, and $s$ when you only have a sample of data.

Home > Statistics > 1-Variable > Statistics Calc > Catalog > Statistics >

Alternatively, you can reach a statistical calculation screen. All the summary statistics above are available to do regular calculations with. Press the "Catalog" button to access these numbers, or press "Tools" to see the whole list again.

A-Level Further Mathematics

Pure

Hyperbolic Functions

Catalog > (scroll down) Hyperblog/Trig >

Hyperbolic functions, $sinh,tanh,cosh$ , and their inverses $sinh^{-1},cosh^{-1},tanh^{-1}$ are hidden away but can be found!

Matrices

Home > Matrix >

Press TOOLS to define Matrices, then press CATALOG to access them for calculation.

Complex Numbers

Home > Complex >

Looks like the usual calculation screen, but allows complex numbers to be input and output. $i$ itself can then be found in the CATALOG menu.

FORMAT > Polar Coord

You can convert complex numbers into $(r,\theta )$ format by selecting Polar Coordinates. The output will then look like $r\angle \theta$ .
This can also be set as default in Settings > Calc Settings > Complex Result >