IB Maths: Sketching Graphs by Hand (AA Paper 1) — FAQ

Sketching graphs by hand means drawing a function's key features — intercepts, asymptotes, turning points, symmetry, behaviour as x tends to infinity — without a GDC to plot it for you. It's examined in Paper 1 (no calculator), usually worth 3-6 marks, and marked on features shown, not artistic accuracy.

"Sketch" means represent the general shape and key features without exact scale or plotted coordinates — a smooth curve showing intercepts and asymptotes is enough. "Draw" (used mainly in Paper 2 with a GDC) means an accurate, to-scale diagram, often plotted from a table of values.

Sketching by hand shows up across Topic 2 (functions), Topic 3 (geometry and trig graphs), and Topic 5 (calculus, especially curve sketching from derivatives). Expect it with quadratics, rational and reciprocal functions, trig functions, exponentials/logarithms, and functions analysed using $f^{\prime }(x)$ and $f^{\prime \prime }(x)$.

No — Paper 1 is the non-calculator paper for both SL and HL, so any sketching question there must be done from algebraic reasoning alone. Paper 2 and Paper 3 (HL only) allow a GDC, where graphing is usually about interpreting a calculator-generated graph rather than sketching from scratch.

Work through the function systematically rather than guessing the shape. Find intercepts, asymptotes and domain restrictions first, then check behaviour at the extremes and symmetry, and only then draw — a smooth curve joining the dots you've already worked out logically, not one you're hoping looks right.

Examiners mark against a specific list: axis intercepts, asymptotes (drawn as dashed lines and labelled with their equations), turning points with coordinates where relevant, and correct end behaviour. Miss an asymptote label or an intercept coordinate and you lose the mark even if the overall shape is right.

For a rational function like $f(x)=\frac{2x+1}{x-3}$, find the vertical asymptote from the value that makes the denominator zero (x = 3), and the horizontal asymptote by comparing degrees or dividing through (here, y = 2 as x tends to infinity). Plot intercepts, then sketch each branch approaching both asymptotes.

The three I see every mock season: forgetting to label asymptotes with their actual equations, drawing a curve that crosses a vertical asymptote, and ignoring domain restrictions (like a square root or logarithm graph starting where the function stops existing). All three cost marks even when the general shape is fine.

A standalone graph-sketching question typically carries 3-6 marks out of Paper 1's 80 or 110 (SL/HL), often as one part of a longer question on functions or calculus. Marks are usually split roughly one per correctly identified feature — intercept, asymptote, turning point, shape.

The core skill is the same at SL and HL, but HL questions go further — expecting sketches derived from second derivatives, points of inflexion, or composite/inverse functions, and sometimes combined with calculus proof. SL sketching questions stay closer to standard functions: quadratics, exponentials, simple rational functions.

Yes — a common Paper 1 question gives you $f(x)$ and asks for a sketch of $f^{\prime }(x)$ (or vice versa), testing whether you understand that turning points on $f(x)$ correspond to zeros on $f^{\prime }(x)$, and inflexion points on $f(x)$ correspond to turning points on $f^{\prime \prime }(x)$.

Yes, generally — AA's non-calculator Paper 1 demands algebraic sketching from first principles, while AI leans more on GDC-generated graphs interpreted rather than hand-drawn from scratch. AA students need stronger command of asymptotes, symmetry and calculus-based curve features without a screen to check their work against.

Past paper Paper 1 questions are the best practice — get your child sketching from algebra alone, then checking against a GDC afterwards rather than while sketching. Topical worksheets grouped by function type (rational, trig, calculus-based) build the pattern-recognition that timed exams reward.