Paper 2: with a GDC

How Paper 2 differs from Paper 1, how to decide when to use the GDC and when to use algebra, and how to write GDC answers that earn every mark.

IB Mathematics: Analysis and Approaches
Exam skills
SL and HL

10 min readLast reviewed 14 Oct 2026

Paper 2 covers the same course content as Paper 1, but a graphic display calculator (GDC) is allowed and expected. The questions use realistic numbers and contexts, many of them cannot be answered by hand at all, and statistics, probability distributions and modelling appear more often. The paper still rewards clear mathematical thinking: the GDC does the arithmetic, but choosing the method, setting up the equation and explaining the result remain the student's work.

Like Paper 1, it has five minutes of reading time, then Section A (short-response questions answered in the question paper) and Section B (long multi-part questions answered in an answer booklet). Every question is compulsory, and the time works out at a little more than one minute per mark.

What changes when a GDC is allowed

The GDC changes what can be asked rather than making the questions easier. Without a calculator, an equation such as $e^{x} = 4 - x^{2}$ cannot appear, because it has no algebraic solution. With one, it is a routine Section A part. Paper 2 therefore contains:

equations and inequalities with no algebraic method, solved graphically or with a numerical solver
probabilities from the binomial and normal distributions, including inverse normal calculations
statistics from data: means, standard deviations, regression lines and correlation coefficients
definite integrals of functions with no simple antiderivative, areas and volumes, and distances travelled
financial questions with the finance solver
modelling questions in context, where the answer must be interpreted.

Algebra and calculus by hand do not disappear. Paper 2 still asks for derivatives in general form, "show that" proofs, answers in terms of a parameter, and exact answers when they are asked for. The GDC cannot do these, because the approved GDCs have no computer algebra system: they work with numbers, not symbols.

Deciding: GDC or algebra?

Every Paper 2 question part falls into one of three groups. Deciding which group a part belongs to, quickly, saves time and avoids losing marks.

Type of part	Signs in the question	Best approach
GDC only	Mixed function types ( $e^{x}$ with $x^{2}$ , $\sin x$ with $x$ ); data; distributions; "find the value of the integral" with no antiderivative	GDC, with the set-up written down
Either	Quadratic or linear equations with numerical coefficients; definite integrals of polynomials	GDC is usually faster; write the equation first
Algebra only	"Show that"; "find $f^{'} (x)$ "; "in terms of $k$ "; "give your answer exactly"; "find the exact value"	Algebra by hand; the GDC can only check a numerical case

Questions only a GDC can answer

The key word in the question is "solve": it asks for every solution. A window that showed only the right-hand intersection would lose a mark. Before reading off solutions, zoom out far enough to be sure there are no more (see Using the GDC).

Questions where algebra is still needed

Let $f (x) = \frac{2 x}{x^{2} + 1}$ .

(a) Show that $f^{'} (x) = \frac{2 - 2 x^{2}}{(x^{2} + 1)^{2}}$ .

(b) Hence find the coordinates of the local maximum point of the graph of $f$ .

Show the solution

(a) The GDC cannot produce a derivative in general form, so use the quotient rule.

f^{'} (x) = \frac{(x^{2} + 1) (2) - 2 x (2 x)}{(x^{2} + 1)^{2}} = \frac{2 x^{2} + 2 - 4 x^{2}}{(x^{2} + 1)^{2}} = \frac{2 - 2 x^{2}}{(x^{2} + 1)^{2}}

This is the result given.

(b) "Hence" means use part (a). Set $f^{'} (x) = 0$ .

2 - 2 x^{2} = 0 ⟹ x = \pm 1

The derivative changes from positive to negative at $x = 1$ (for example $f^{'} (0) = 2 > 0$ and $f^{'} (2) = - \frac{6}{25} < 0$ ), so the maximum is at $x = 1$ , where $f (1) = 1$ .

The local maximum point is $(1, 1)$ .

A GDC maximum search confirms $(1, 1)$ , which is a sensible check. Reading the maximum only from the GDC would ignore "hence" and may not earn the marks.

Probability and statistics

Statistics and probability are a large share of Paper 2, because the calculations behind them (standard deviations, normal probabilities, binomial sums, regression) are long by hand. The marks for these questions depend on writing the set-up clearly: the distribution, its parameters, and the probability being found.

Writing distribution answers

A good line of working for a distribution question names the distribution and the probability, then gives the value: " $X \sim B (12, 0.3)$ , $P (X \leq 4) = 0.724$ ". This line earns the method mark even if a slip in the GDC gives the wrong number, and it makes clear which calculation was done. Avoid writing calculator syntax such as `binomcdf(12, 0.3, 4)` as the only working: it is not mathematical notation, and some examiners may not recognise it.

Modelling and context questions

Paper 2 Section B questions are often built around a context: a particle moving along a line, a population, a loan, a water tank. Contexts add three demands: translate the words into mathematics, keep track of units, and interpret the answers back in the context.

A particle moves in a straight line. Its velocity, in metres per second, after $t$ seconds is

v (t) = 10 e^{- 0.5 t} \sin t, 0 \leq t \leq 5.

(a) Find the velocity of the particle when $t = 2$ .

(b) Find the time at which the particle first changes direction.

(d) Find the total distance travelled by the particle in the first 5 seconds.

Show the solution

(a) Substitute, with the GDC in radian mode.

v (2) = 10 e^{- 1} \sin 2 = 3.35 {m s}^{- 1} (3 s.f.)

(b) The particle changes direction when $v (t)$ changes sign. Since $e^{- 0.5 t} > 0$ , this happens when $\sin t = 0$ and changes sign, first at $t = π$ .

The particle first changes direction at $t = π \approx 3.14$ s.

v(t)

The velocity is positive until t = π and negative after it. The distance is the area between the graph and the t-axis, counting both parts as positive.

The maximum velocity is $5.14$ m s $^{- 1}$ , at $t = 1.11$ s.

(d) Distance is the integral of speed, $∣ v (t) ∣$ , not of velocity.

distance = \int_{0}^{5} ∣ v (t) ∣ d t = 11.2 m (3 s.f.)

Part (d) is a typical trap: $\int_{0}^{5} v (t) d t = 8.13$ is the displacement, because the part of the motion below the $t$ -axis cancels some of the part above. Writing the integral with the modulus shows the method and earns the method mark.

Working with unrounded values

Paper 2 answers are usually given to three significant figures, but values carried forward must not be rounded. A rounded intermediate value can change the final answer in the third significant figure and lose the accuracy mark. Store intermediate results in the GDC's memory (or use the previous-answer key) and round only at the end.

Write the intermediate values in the working to more figures than the final answer, for example " $a = 7.4209 \dots$ ", so the examiner can see the method and the accuracy is kept. The rounding rules are covered fully in Accuracy, notation and setting out.

Using a table to answer "first" questions

"Find the smallest $n$ such that…" questions appear often on Paper 2, for sequences, series and financial growth. They can be solved with an inequality and logarithms, but a table of values on the GDC is often quicker and gives the integer directly.

Writing the two table values on either side of the target is the clearest way to justify an integer answer. It shows both that $n = 25$ works and that $n = 24$ does not.

Time traps on Paper 2

The GDC saves time on hard calculations but can waste it on easy ones. Some common traps:

Typing long expressions. Entering a complicated expression in one go invites bracket errors. Break it into stored parts, or check it against an easy value.
Hunting through menus. If the correct function is not found within a few seconds, work by hand or move on and come back. Menu practice belongs before the paper.
Searching for algebra the question does not want. If a part only asks for a numerical answer and the equation looks difficult, the GDC is probably intended.
Ignoring the GDC for a check. A quick graph or substitution confirms an algebraic answer in seconds.

Checklist

To do:
I can tell quickly whether a part needs the GDC, algebra or either.
To do:
I write the equation, distribution or integral I am evaluating before giving the GDC result.
To do:
I sketch any graph I use to find a solution, and check the window shows every solution.
To do:
I write distributions in mathematical notation, not calculator syntax.
To do:
I store intermediate values unrounded and round only the final answer.
To do:
I give units and interpret answers in context questions.
To do:
I check that the GDC is in radian mode for calculus and trigonometric functions.

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