Graphing calculators

Contents

• Approved calculators
• Use of calculator on exams
• Settings
• Storage
• Be careful entering expressions
• Be careful interpreting answers
• What to know?
  • graphing
  • solver
  • statistics
  • probability
  • financial
  • sequences (lists)
  • storage and general use
  • arithmetics
• Further reading

Approved calculators

Here is a mirror of Use of calculators in IB DP Examinations 2022  hosted on NumWorks website. This document is published annually by IB, but not released publicly.

All approved calculators are sufficient for any IB exam that requires a graphing calculator. However, advanced models are faster, and have better (newer) user interfaces. Though, it is sometimes your speed of keying in the question and using the right tools that determines speed, not the calculator itself.

Only a few undergraduate math classes allow graphing calculators on exams.

Use of calculator on exams

You may not bring a scientific calculator to IB exams that require a graphing calculator. IB recommends bringing extra batteries instead of extra calculators. Your school may provide a few backup calculators. If so, be sure to use them a few times during revision.

Calculator manuals, including lids with hot-keys, cannot be brought into the exam room.

Settings

After your calculator is reset, or set to exam mode. You should change the following settings, or at least know how to change them.

1. Change so the input wraps across lines. It is typically easier to have the math wrap (continue to the next line). This often comes at a cost of additional parentheses.

2. Change between radians and degrees. First answer the questions requiring degrees. Then stick with radians for the rest of the exam.

3. Change function plotting from continuous/connected to dotted. This can speed up most graphing, but not graphing of definite integrals with a variable in the limits of integration, so that should always use solver. The change can be set in mode or at a per-function level.

Storage

Graphing calculators allow you to store values, functions, lists, and other data, so you can recall and reuse them, rather than repeatedly keying the same values.

This is particularly helpful to keep all decimal places for intermediate answers, so you don’t have to worry about rounding errors. IB typically requires at least three correct significant figures for accuracy marks.

Be careful entering expressions

Check the following when entering expressions or pretty much whenever using the calculator

• It is often preferable to have your longer functions wrap as opposed to going off the screen. Be able to change the view as necessary.
• If an operator takes an expression, eg $\ln$, be sure to use brackets if there are operators in the expression, eg $\ln (3x + 5)$
• The negative sign is not the minus sign.
• Check all brackets are manually closed.
• Check if your exponents are in fact exponents.
• Check if your denominators are in fact denominators.
• Unless specified, use radians mode for all trigonometric functions
• If you are modifying the equation before entering into the calculator, it’s a good idea to write down on the answer booklet what equations you are entering.
• If you need to enter the same expression multiple times, consider store it as a function, then call the function.
• If you need to enter the same value multiple times, consider store it under a letter (typically ALPHA + letter), then use the letter instead of retyping the value.

Be careful interpreting answers

A few extra seconds of sanity checks can help you catch mistakes and save you a few marks!

• Did you get the same number of solutions as you were expecting?
• Do the values make sense and are around what you were expecting?
• Are the solutions in the domain given in the question? Are any solutions extraneous?
• If you modified the equations prior to solving them, did you solve for the original variables?

What to know?

This is a general list of calculator procedures to know.

graphing

• Graph functions of $x$, ie $y = f(x)$ involving operators, built-in functions, including but not limited to absolute values, square root, derivative functions, probability and cumulative probability density functions.
• Reuse definitions to graph composite functions.
• Change graph style for different functions on the same graph.
• Hide functions from a graph.
• Graph inverse functions.
• Graph piece-wise functions.
• Graph multiple branches of a relation.
• Find zeros of a function.
• Find local and global extrema of a function.
• Find intersection of two functions.
• Zoom in and zoom out on the graph, and changing the zoom factors.
• Graph over a specific domain.
• Generate a table of values.
• Evaluate a function over a list of values.

solver

• Find multiple roots of an equation involving operators and built-in functions (see graphing, above).
• Solve systems of linear equations, up to 2 variables at SL, and up to 3 variables at HL.

statistics

• Report sample mean, median, mode (or modal class), range, standard deviation, variance, quartiles, interquartile range for a list of values or estimates for grouped values for equal-sized classes by using one-variable statistics.
• For HL, also be able to use the $\sum x^2$ property, for finding variance of linear transformations of a random variable or some data.
• Find $y$ on $x$ and $x$ on $y$ regression lines.
• Find the intersection of regression lines using two-variable statistics.
• Report Pearson’s correlation coefficient $r$ for a linear regression.

probability

• Find $\text{P}(X = x)$ and $\text{P}(X \leq x)$ for discrete random variables (eg binomial distributions) and continuous random variables (eg normal distributions).
• Use graphing or solver with unknown parameters, such as $n$, $p$, $\mu$, $\sigma^2$, and known endpoint(s).
• Report mean, median, mode … (see statistics for list) of a discrete random variable.
• Find $z$-score for a given cumulative probability in normal distributions.

financial

• Calculate compound interest or depreciation, include finding quantities other than the future value.

sequences (lists)

The same calculator can have sequence, list, recursion, table, and even spreadsheet modes. These have different features, but the central theme is working with a discrete set of inputs or values.

• Generate a table of values using sequence or recursion mode.
• Plot sequences.
• Generate sequences both from explicit formulas and recursive formulas.

For HL candidates

• Solve a differential equation using Euler’s method

storage and general use

• Save and reuse values.
• Copy and paste expressions.
• Modify and rerun a previous computation.
• Understand the order of operations used by the calculator, and where closing brackets are inserted.

arithmetics

This is a non-exhaustive list of calculations.

• Use $\pi$, $e$ and other values.
• Convert to and from scientific notation.
• Convert between exact values and decimals, and between improper fractions and mixed numbers.
• Use the negative symbol, which is different from the minus sign.
• Evaluate trigonometric functions and their inverses.
• Evaluate exponential and logarithmic functions at any base $b > 0$, and use $^2$, and $^{-1}$ (and be aware of differences between $f^{-1}(x)$ and $f(x)^{-1}$).
• Evaluate the binomial coefficient.
• Evaluate derivative at a point.
• Evaluate definite integrals.

Here are additional calculations for HL students.

• Enter complex numbers in rectangular and polar forms.
• Convert between the forms.
• Perform arithmetics of complex numbers.
• Evaluate expressions involving factorials and permutations.

Further reading

Some additional calculator tips are mentioned in solve equations and inequalities by graphing, find zeros and extrema by graphing, and Euler’s method to solve an ODE (HL).