IB Maths calculator guide: GDC skills that save marks in Paper 2

Which IB Maths papers allow a GDC

Rules differ by course, so start here. This table is my summary of how the papers are set up. Confirm it against the subject guide your school gives you, because the IB can change arrangements.

Two points to take from it. In AA, Paper 1 is a calculator-free paper, so exact values and algebra matter there, and your GDC skills are tested on Paper 2 and Paper 3. In AI, technology is part of every paper, so GDC fluency is not an extra, it is the course. If you are still choosing, our sister-site comparison of AA versus AI in IB Maths goes through the trade-offs. Even on a GDC paper, not every question needs it, so judge each one.

Graphing and window setting

Most GDC marks start from a good graph. A graph in a bad window hides the very feature you need, such as a second root or a turning point.

1. Enter the functionUse brackets freely. A missing bracket around a numerator or exponent is the most common entry error.
2. Set a sensible windowThink first: where do you expect the roots and the turning point? Start with a standard window, then use the zoom or fit option, then adjust by hand.
3. Check the shapeDoes the picture match what you know? A cubic with a positive leading coefficient should rise to the right. If it does not, you entered it wrongly.
4. Look for all the featuresThe question may need two intersections, but the first window shows one. Widen the window before you trust the picture.

Intersections, zeros, max and min, and solving numerically

These four tools solve most Paper 2 questions. Every GDC has them under a menu such as the graph analysis or G-Solve menu (on a TI-84, the CALC menu has zero, minimum, maximum and intersect).

• Zeros. Where a graph crosses the axis. Use this to solve f(x) = 0, and plot the left side minus the right side if the equation has two sides.
• Intersections. Plot each side of an equation as its own function and find where they meet. This solves equations that cannot be rearranged, for example 2^x = 5 − x.
• Maximum and minimum. Gives the turning point, and so the best value in an optimisation question. Read both coordinates, then decide which one the question wants.
• Numerical equation solver. Fast for polynomials, but it gives one root at a time unless you set a starting guess, so check against the graph that you have all roots in the interval.

A tip from our classes at Photon Academy: the mark students lose most often here is not the keystrokes, it is the interval. The question says "for 0 ≤ x ≤ 10" and the student reports a root at x = 12 because it was the one on screen.

The numerical derivative and integral

Your GDC can give the gradient of a function at a point and the area under a curve between two limits. These are quick and accurate, and often a good way to check an algebraic answer.

• Gradient at a point. Use the dy/dx option on the graph, or the numerical derivative function in the maths menu, with the x-value. It returns a number, not a formula.
• Definite integral. Enter the function, then the limits. Use it for areas, and for volumes of revolution if you set up the integrand yourself.
• Area between curves. Find the intersections first, store them, then integrate the difference. Storing avoids rounding the limits.

Be careful: the numerical derivative can mislead at a sharp point such as that of y = |x|, and a numerical integral does not tell you whether the area is above or below the axis. Write the integral you set up, not just the number. In AA, the exam often wants you to write the expression before the value, because that is where the method mark sits.

Statistics: lists, regression, normal and binomial distributions

The statistics menu is where AI students spend the most time, and it is also tested in AA.

Lists and one-variable statistics

Enter data in a list, then run the one-variable option for mean, standard deviation, median and quartiles. Check the sample size shown on screen matches the data you typed, because a missing entry is easy to miss. Remember which standard deviation the question needs: population or sample.

Regression

Run linear regression for a line of best fit and read r, the correlation coefficient. Use the other regression types (quadratic, exponential, power) only when the question names a model or the data clearly bends. Write the equation with the coefficients to 3 s.f. and, in AI, comment on r.

Normal and binomial

• Normal distribution. The cumulative option gives a probability between two values, and the inverse option gives the value for a given probability. Sketch the bell curve with the shaded area before you enter anything. That sketch is the examiner's evidence that you chose the right area.
• Binomial. Use the probability option for "exactly r" and the cumulative option for "at most r". For "at least r", subtract the cumulative value for r − 1 from 1. This is a very common slip.

Matrices and the finance solver in AI

These are for AI students, and the matrices topic is HL only.

• Matrices (AI HL). Enter the matrix, then multiply, invert or raise to a power. For a transition matrix, repeated powers show the long-run behaviour. Check dimensions before multiplying, and write the matrix equation you set up.
• Finance solver (AI). The time-value-of-money screen has N, I%, PV, PMT, FV, P/Y and C/Y. Fill in what you know and solve for the one you need. The two classic errors are the sign of PV against FV (money paid out is negative) and forgetting to set payments per year and compounding periods per year.

Practise the finance solver with a loan or savings question where you can check the result by hand, then trust it on harder ones.

Writing GDC working that earns method marks

A GDC gives answers, but the IB awards marks for method. The rule I teach is: show what you did, show what you saw, and then give the answer to the right accuracy.

• State the method in words. "Using the GDC to find the intersection of y = 2^x and y = 5 − x" earns more than a bare x = 1.7.
• Sketch it. A small graph, labelled, is usually enough for a mark that would otherwise be lost to a wrong answer.
• Write the setup. The integral, the equation, the distribution, such as X ~ N(50, 4²).
• Give 3 s.f. unless told otherwise. Do not round in the middle, store full values, and round once at the end.
• Never write calculator syntax. Writing "normalcdf(40,60,50,4)" is not mathematics. Write P(40 < X < 60) = 0.988 instead.

In our classes, the commonest loss is a wrong answer with no working. A right setup with a slip in the last number can still earn most of the marks, but a bare wrong number earns none. Practise this habit on free practice questions and mark yourself on the working, not just the answer. For more on what each question wants, read our guide to IB command terms.

Approved models, exam mode and home practice

The IB sets rules on which calculators are allowed, and they change between sessions, so do not rely on a blog, including this one. Ask your IB coordinator for the current list and rules, and check whether your model must be put into an exam mode (sometimes called press-to-test) that locks features and clears memory before the paper.

Models that students commonly use include the TI-84 Plus CE, the TI-Nspire CX in a non-CAS version, and the Casio fx-CG50. Whether a particular unit is acceptable can depend on its software version and your school's rules, so confirm it before you buy. For manufacturers' own information, see the TI-84 Plus CE page, the TI exam mode page and Casio's article on preparing for exams with the fx-CG50.

Desmos is excellent for home practice: it draws graphs fast, so you can see the shape before you meet it on your GDC. I do not know of an IB policy that lets it replace your approved GDC in an exam, so treat it as a practice tool unless your coordinator tells you otherwise.

Find the topics that lean on technology most in the AA HL and AI HL past-paper analysis, and see our full course pages for AA HL and AI HL.