GDC guide

The single most common source of lost marks in trig - your answer is only correct if the angle mode matches the question. AA usually uses radians; AI usually uses degrees.

1. Check the question: are angles in degrees (°) or radians (π, rad)?
2. Press MODE, highlight RADIAN or DEGREE on the angle row and press ENTER, then 2nd → MODE to quit.
3. Press ctrl → menu → Settings (or doc Settings) → Angle, and choose Degree or Radian.
4. Press SHIFT → MENU (SET UP) → Angle, then choose Deg or Rad and EXIT.
5. Re-enter the calculation after switching - the mode only affects new work.

Tip: If a sin/cos/tan answer looks wildly wrong, the angle mode is almost always the cause.

Get exact fractions and surds instead of long decimals, or convert a decimal answer back to a tidy fraction to check it.

1. After a calculation press MATH → 1:▶Frac then ENTER to turn the last answer into a fraction.
2. Press ctrl → ENTER (instead of ENTER) for the exact form; or menu → Number → Approximate to Fraction.
3. Press the F↔D key to toggle the answer between fraction and decimal; Math input mode (SET UP) shows surds and stacked fractions.
4. Use this to confirm a messy decimal is really a nice value like 7/8 or √2.

Tip: Convert to a decimal only at the very end - keep exact values through the working.

A classic error: the negative key and the subtraction key are different. Mixing them gives a syntax error or the wrong sign.

1. Use (−) (grey key, bottom row) for a negative number; use − (blue, right column) only between two numbers.
2. Use the (−) key for a negative value and the − key for subtraction - negatives show as a shorter dash.
3. Use (−) for a negative number and − for subtraction; entering −3 needs the (−) key.
4. Example: −5 + 2 needs (−)5 + 2, not −5 + 2.

Tip: A SYNTAX or MA ERROR near a minus sign usually means the wrong key was used.

IB exams require cleared memory - and a reset also fixes a calculator that's behaving strangely.

1. 2nd → + (MEM) → 7:Reset → 1:All RAM → 2:Reset clears all data and resets settings.
2. Use Press-to-Test for a clean exam state (hold ESC + ON, or via the documents menu).
3. From the main menu open MEMORY (or System) → Reset and choose what to clear.
4. Do this before the exam, not during - you'll lose any stored lists and programs.

Tip: After a reset, re-check the angle mode (degrees/radians) before you start.

Faster and safer than algebra for messy equations - and essential in AI, where many equations can't be solved by hand.

1. Rearrange so everything is on one side: f(x) = 0.
2. Press MATH → Solver, enter the expression, give a starting guess, then press ALPHA + ENTER.
3. menu → Algebra → Numerical Solve, then type nSolve(f(x)=0, x).
4. From the main menu choose Equation, or in Run-Matrix use SolveN(f(x), x).
5. Read off the solution, then re-run with a different starting guess to find any other roots.

Tip: Always sketch or graph first so you know how many solutions to expect and roughly where they are.

Solves 'line meets curve' and simultaneous problems visually, with no algebra.

1. Enter both functions as Y1 and Y2 and graph them.
2. 2nd → CALC → 5:intersect, move near the crossing, then press ENTER three times.
3. menu → Analyze Graph → Intersection.
4. Press G-Solve (SHIFT F5) → Intersection (ISCT).
5. Repeat for each crossing point.

Tip: Adjust the window/zoom so every intersection point is visible before using the tool.

Tip: Adjust the window so the crossing point is on screen first - the solver looks near the part of the graph you can see.

Find every root of a quadratic, cubic or quartic in one step - including roots that don’t factorise nicely.

1. Write the polynomial in standard form, e.g. 2x^3 − 3x^2 − 11x + 6 = 0.
2. Use the PlySmlt2 app: APPS → PlySmlt2 → Polynomial Root Finder. Set the degree, enter the coefficients, then SOLVE.
3. menu → Algebra → Polynomial Tools → Find Roots of a Polynomial, or type polyRoots(expr, x).
4. Main menu → Equation → Polynomial, choose the degree, enter the coefficients, then SOLVE.

Tip: Set the degree to match the highest power. Complex roots show as a ± bi on models that support them; real roots are where the graph crosses the x-axis.

Solve two or three simultaneous equations (linear systems) without elimination by hand.

1. Write each equation in the form ax + by (+ cz) = d.
2. APPS → PlySmlt2 → Simultaneous Eqn Solver; set the number of equations/unknowns and enter the coefficients.
3. menu → Algebra → Solve System of Equations, or use linSolve.
4. Main menu → Equation → Simultaneous, set the number of unknowns, enter the coefficients, SOLVE.

Tip: No solution or infinitely many? The calculator will flag it - that means the lines/planes are parallel or coincident.

Optimisation and root questions become a couple of button presses.

1. Graph the function with a window that shows the feature you want.
2. 2nd → CALC → 2:zero, 3:minimum or 4:maximum; set a left bound, right bound, then guess.
3. menu → Analyze Graph → Zero, Minimum or Maximum.
4. G-Solve (SHIFT F5) → ROOT, MIN or MAX.
5. Note the coordinates shown at the bottom of the screen.

Tip: For a turning point, minimum/maximum gives both the x and y values you usually need.

If a graph looks blank or flat, the window is wrong - not the function. Choosing the window well is half of most graphing questions.

1. Decide the x-range from the question (e.g. 0 ≤ t ≤ 10) and a sensible y-range.
2. Press WINDOW to set Xmin/Xmax/Ymin/Ymax; ZOOM → 0:ZoomFit auto-fits y to the x-range; ZOOM → 6:ZStandard resets to −10…10.
3. menu → Window/Zoom → Window Settings, or Zoom-Fit / Zoom-Standard.
4. Press SHIFT → F3 (V-Window) to set the range, or Zoom (F2) → Auto.
5. Re-graph after changing the window.

Tip: For a real-world model, set Xmin/Xmax to the domain in the question and let the y-range auto-fit.

Read off coordinates, spot where a function changes sign, or check a value without algebra.

1. Enter the function in the Y= / graph editor.
2. 2nd → WINDOW (TBLSET) to set the start and step, then 2nd → GRAPH (TABLE) to view it.
3. Add a Graphs or Lists & Spreadsheet page, then menu → Table (or ctrl+T).
4. Enter the function in Table mode, set the range, then TABL (F6).
5. A sign change between two rows means a root lies between those x-values.

Tip: Use a small step (e.g. 0.1) to pin down a root or a maximum more precisely.

Get the gradient at a point - and the tangent's equation - straight off the graph.

1. Graph the function with the point on screen.
2. 2nd → PRGM (DRAW) → 5:Tangent(, type the x-value (or move the cursor), ENTER - the tangent and its equation appear.
3. Use the derivative template to evaluate f′(a), or draw a tangent with the Geometry tools.
4. With the graph shown, SHIFT → F4 (Sketch) → Tangent, then enter the x-value.
5. The displayed line gives both the gradient and the tangent's equation.

Tip: The gradient shown equals the derivative at that point - a fast check on your differentiation.

Instant summary statistics from a list - no formulas to compute by hand.

1. Enter the data into a list.
2. STAT → Edit → type values into L1. Then STAT → CALC → 1:1-Var Stats, choose L1, Calculate.
3. Add a Lists & Spreadsheet page, name a column and enter data; then a Calculator page → menu → Statistics → Stat Calculations → One-Variable Statistics.
4. Statistics menu → enter data in List 1 → CALC (F2) → 1-VAR.
5. Read x̄ (mean), Sx (sample sd) or σx (population sd), and the five-number summary (min, Q1, median, Q3, max).
6. For frequency data, put values in one list and frequencies in another and set the frequency list.

Tip: Sx vs σx: use σx (population) for a complete data set, Sx (sample) for a sample. IB usually wants σx.

Core AI skill - gives the regression line and the correlation coefficient in one step.

1. Enter x-values in one list and y-values in another.
2. Turn on DiagnosticOn once (2nd → CATALOG) so r appears; then STAT → CALC → 4:LinReg(ax+b), set Xlist and Ylist, Calculate.
3. Calculator page → menu → Statistics → Stat Calculations → Linear Regression (mx+b).
4. Statistics menu → CALC (F2) → REG (F3) → X (linear); r shows automatically.
5. Read a (gradient), b (intercept), r (correlation) and r² (coefficient of determination).
6. Use the equation to predict - but only within the data range (interpolation).

Tip: r near ±1 means a strong linear fit; near 0 means weak. r² is the proportion of variation explained.

Read the median, quartiles, range and any outliers - and draw the box plot a question asks for.

1. Enter the data in a list (and frequencies in a second list if grouped).
2. 2nd → Y= (STAT PLOT) → choose the box-plot icon, then ZOOM → 9:ZoomStat. 1-Var Stats also lists Q1, Med, Q3.
3. On a Data & Statistics page add the variable to the x-axis, then menu → Plot Type → Box Plot.
4. In Statistics set GRPH → SET to MedBox, then DRAW; 1-VAR also lists the quartiles.
5. IQR = Q3 − Q1. Outliers lie beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR.

Tip: Box plots make comparing the spread of two data sets very quick.

See the relationship between two variables before fitting a regression line.

1. Enter the x-values in one list and the y-values in another (equal lengths).
2. 2nd → Y= (STAT PLOT) → Plot1 On → scatter icon → set Xlist and Ylist, then ZOOM → 9:ZoomStat.
3. On a Data & Statistics page click the x- and y-axis labels to assign the two variables.
4. In Statistics set GRPH → SET to Scatter, assign XList and YList, then DRAW.
5. Describe the correlation (positive/negative, strong/weak, linear or not) from the shape.

Tip: The scatter shape tells you whether a linear, quadratic or exponential model is sensible.

No need for z-tables or standardising - the GDC works straight from μ and σ.

1. Decide what you need: P(a < X < b), a tail, or a value from a probability.
2. 2nd → DISTR → normalcdf(lower, upper, μ, σ). For inverse, invNorm(area-to-left, μ, σ).
3. menu → Statistics → Distributions → Normal Cdf (or Inverse Normal).
4. Statistics menu → DIST (F5) → NORM (F1) → Ncd (or InvN for inverse).
5. For a left tail use a very small lower bound (e.g. −1E99); for a right tail use 1E99 as the upper bound.

Tip: Sketch the bell curve and shade the region first - it stops you mixing up 'less than' and 'greater than'.

Tip: For "more than", use the lower bound and a very large upper bound (e.g. 1E99); for "less than", use a very negative lower bound.

Handles 'exactly', 'at most' and 'at least' for B(n, p) without expanding anything.

1. Translate the words: exactly r → pdf; at most r → cdf; at least r → 1 − cdf(r−1).
2. 2nd → DISTR → binompdf(n, p, r) or binomcdf(n, p, r).
3. menu → Statistics → Distributions → Binomial Pdf / Binomial Cdf.
4. Statistics menu → DIST (F5) → BINM (F5) → Bpd or Bcd.

Tip: ‘Fewer than 3’ means X ≤ 2, so use the cdf at 2, not 3.

The reverse of a normal probability: given a percentage, find the cut-off value (e.g. the mark for the top 10%).

1. Work out the area to the LEFT of the value you want.
2. 2nd → VARS (DISTR) → invNorm(area, μ, σ). Newer OS lets you pick the tail.
3. menu → Probability → Distributions → Inverse Normal; enter the area, μ and σ.
4. Main menu → Statistics → DIST → NORM → InvN; set the tail and enter area, σ, μ.

Tip: invNorm needs the area to the LEFT. For "top 10%", use area = 0.90; for "bottom 25%", use area = 0.25.

Counts of random events at a mean rate λ - calls per hour, flaws per metre - without the e^(−λ) formula.

1. Identify λ for the interval in the question (scale it if the interval changes).
2. 2nd → DISTR → poissonpdf(λ, r) for exactly r; poissoncdf(λ, r) for at most r.
3. menu → Statistics → Distributions → Poisson Pdf / Poisson Cdf.
4. Statistics → DIST (F5) → Poissn → Ppd (exactly) or Pcd (at most).
5. ‘At least r’ = 1 − cdf(r−1). Independent Poissons add: λ_total = λ₁ + λ₂.

Tip: Scale λ to the interval: 3 per hour over 20 minutes means λ = 1.

Given a probability and one parameter, work back to the missing μ or σ - a standard exam twist.

1. Turn the probability into a z-value using the inverse normal with μ = 0, σ = 1.
2. invNorm(area-to-left, 0, 1) gives z; then solve z = (x − μ)/σ for the unknown.
3. Use Inverse Normal with μ = 0, σ = 1 to get z, then solve the standardising equation for μ or σ.
4. DIST → NORM → InvN with μ = 0, σ = 1 gives z; substitute into z = (x − μ)/σ.
5. If two probabilities are given, form two equations and solve them simultaneously for μ and σ.

Tip: Sketch the curve and shade the area on the correct side before using invNorm.

The fastest way to do compound interest, loan repayments and investments - central to AI.

1. APPS → Finance → 1:TVM Solver.
2. Calculator page → menu → Finance → Finance Solver.
3. From the main menu choose Financial → Compound Interest (or TVM).
4. Enter N (number of payments), I% (annual rate), PV (present value), PMT (payment), FV (future value), and P/Y & C/Y (payments/compounds per year).
5. Use the sign convention: money you pay out is negative, money you receive is positive.
6. Put the cursor on the unknown and solve.

Tip: Set P/Y and C/Y to match the compounding (12 for monthly). Leave PMT = 0 for a simple lump-sum investment.

Find every solution of e.g. 2 sin x = 1 on 0 ≤ x ≤ 2π - the calculator finds them all, not just one.

1. Set the correct angle mode first (radians for AA, usually degrees for AI).
2. Graph each side as Y1 and Y2 over the required interval (or rearrange to f(x) = 0).
3. Graph, then 2nd → CALC → 5:intersect (or 2:zero) for each solution in the interval.
4. menu → Analyze Graph → Intersection (or Zero) for each crossing in the interval.
5. Draw the graphs, then G-Solv (SHIFT F5) → ISCT (or ROOT) for each solution.
6. Set the window to exactly the interval so you don't miss or double-count solutions.

Tip: Trig equations have several solutions per period - work out how many the interval should contain and check you have them all.

Gives a gradient instantly to check your differentiation or when a function is awkward.

1. MATH → 8:nDeriv(, then enter nDeriv(f(x), x, a). Or graph and use 2nd → CALC → 6:dy/dx.
2. menu → Calculus → Numerical Derivative at a Point.
3. Run-Matrix → MATH (F4) → d/dx, then enter the function and the x-value.
4. Read off the gradient - useful for tangent slopes without algebra.

Tip: Handy for checking the gradient at a point or finding a tangent's slope.

Evaluates areas and accumulated change, including integrals you can't do by hand.

1. MATH → 9:fnInt(f(x), x, a, b). Or graph and use 2nd → CALC → 7:∫f(x)dx.
2. menu → Calculus → Numerical Integral, or use the ∫ template.
3. Run-Matrix → MATH (F4) → ∫dx, then enter the function and limits.
4. Enter the lower and upper limits to get the value.

Tip: Area below the x-axis is negative - take the absolute value if the question asks for area.

Tip: A definite integral can return a negative value where the curve is below the x-axis - for total area, integrate the parts separately.

Locate maxima and minima - the basis of optimisation questions.

1. Graph the function so you can see how many turning points there are.
2. Graph, then 2nd → CALC → 3:minimum / 4:maximum (set left bound, right bound, guess). To solve f′(x)=0, enter nDeriv(Y1,X,X) as Y2 and find its zeros.
3. menu → Analyze Graph → Minimum / Maximum; or define f′ with the derivative template and solve f′(x)=0.
4. Graph then G-Solv → MIN / MAX; or solve d/dx(f(x))=0 with SolveN in Run-Matrix.
5. Substitute each x back into f(x) for the y-coordinate.

Tip: Max/min on the graph gives both coordinates at once - usually faster than solving f′(x)=0 by hand.

Find the area enclosed between two graphs - a common Paper 2 integral.

1. Find where the curves meet (intersection) - these x-values are the limits.
2. Integrate top minus bottom: MATH → 9:fnInt(Y1 − Y2, X, a, b).
3. Use the ∫ template: ∫(f(x) − g(x)) dx from a to b (upper curve minus lower).
4. Run-Matrix → ∫dx of (upper − lower) between the intersection x-values.
5. Integrate (upper − lower) so the area is positive.

Tip: Find the intersection points first - they are the limits of the integral.

Inverses, determinants and solving linear systems are quick and reliable on the GDC.

1. Enter a matrix with 2nd → MATRX → EDIT. Determinant: det([A]); inverse: [A] then the x⁻¹ key.
2. Use the matrix template (or menu → Matrix & Vector). det(), and ^-1 for the inverse.
3. Run-Matrix → MAT/VCT (F3) to enter a matrix; use Det and the x⁻¹ key.
4. Solve A x = b by computing [A]⁻¹[b].
5. For eigenvalues/eigenvectors (AI HL) use the matrix menu's eigVl / eigVc functions where available.

Tip: If det(A) = 0 there is no unique solution - the system has no solution or infinitely many.

Find the state after n steps, or the long-run steady state, by raising the transition matrix to a power.

1. Enter the transition matrix and the initial state vector.
2. Enter [A] in 2nd → MATRX → EDIT, then compute [A]^n × [B] on the home screen.
3. Enter the matrix, then type matrix ^ n × the state vector.
4. Run-Matrix → MAT to enter the matrix; compute Mat A ^ n × the state vector.
5. For the long-run state, raise the matrix to a large power (e.g. ^50) and read the stabilising column.

Tip: Columns of a high power of a regular transition matrix converge to the steady-state distribution.

Work with a + bi directly - get the modulus, argument and polar/Euler form in one step.

1. Switch the calculator into complex (a + bi) mode.
2. MODE → a+bi. Enter i with 2nd → . ; MATH → CPX gives abs( (modulus), angle( (argument) and ▶Polar.
3. Settings → set Complex (Rectangular/Polar). Use abs() for modulus, angle() for argument; type i with the dedicated key.
4. In Run-Matrix use SHIFT → 0 for i; OPTN → CPLX gives Abs, Arg and ▶r∠θ (polar form).
5. Check the argument is in the range the question wants (−π < θ ≤ π, or 0 to 2π).

Tip: Use radian mode for arguments in AA HL unless the question asks for degrees.

Lengths, dot/cross products and the angle between vectors without coordinate algebra.

1. Enter each vector's components (as a list or a 3×1 matrix).
2. Store components in lists; magnitude = √(sum of squares); dot product = sum(L1×L2).
3. Type vectors with the matrix template; use dotP(), crossP() and norm() from menu → Matrix & Vector → Vector.
4. Run-Matrix → MAT/VCT to enter vectors; OPTN gives DotP, CrossP and the norm (magnitude).
5. Angle between: cos θ = (a·b)/(|a||b|), then inverse cosine.

Tip: A dot product of 0 means the vectors are perpendicular - the quickest perpendicularity check.

Evaluate sigma (Σ) notation, list the terms of a sequence, or total a series without adding by hand.

1. Write the general term, e.g. uₙ = 3n − 1, and the range of n.
2. List terms with 2nd → STAT (LIST) → OPS → 5:seq(expr, n, start, end); total with 2nd → STAT → MATH → 5:sum(seq(...)).
3. Type seq(expr, n, start, end) to list and sum(seq(...)) to total, or use the Σ template from the maths templates.
4. OPTN → LIST → Seq( builds the list; OPTN → LIST → Sum totals it.
5. For Σ notation the lower and upper limits are the start and end values of n.

Tip: Many calculators have a Σ( template - enter the term, the variable, and the two limits directly.

Advance a recurrence - a loan balance each month, a population each year - without retyping the previous value.

1. Write the rule, e.g. nextBalance = balance × 1.02 − 200, and the starting value.
2. Type the start value, ENTER; then the rule using 2nd → (−) (ANS), e.g. Ans×1.02−200, and press ENTER repeatedly.
3. Enter the first value, then a formula referring to the previous answer; press ENTER repeatedly (or use a recursive spreadsheet column).
4. In Run-Matrix enter the start value, then the rule using Ans, and press EXE repeatedly; Recursion mode also tabulates aₙ₊₁.
5. Each ENTER/EXE gives the next term - count the presses to reach the term you need.

Tip: This Ans-recursion trick (rule using the last answer, then repeated ENTER) works for any step-by-step process.

Work out log to any base directly - useful for solving exponential equations and for logarithmic scales.

1. Decide the base b and the value x you want log_b(x) for.
2. Press MATH → logBASE( and enter logBASE(x, b). (Older OS: use log(x)/log(b).)
3. Type log(x, b) directly - the base goes after the comma.
4. Use the log_□□ template (math templates) or type log(b, x) via OPTN → CALC.

Tip: Change of base always works on any calculator: log_b(x) = ln(x) / ln(b) = log(x) / log(b).

Count arrangements and selections quickly - and get the coefficients used in the binomial theorem.

1. Type n, then MATH → PROB → nCr (or nPr), then r, then ENTER.
2. Use nCr(n, r) or nPr(n, r) from the catalog.
3. Type n, then OPTN → PROB → nCr (or nPr), then r.

Tip: nCr ignores order (choosing a team); nPr counts order (ranking places). nCr(n, r) is the binomial coefficient.

The core AI hypothesis test: check whether data fit a distribution, or whether two variables are independent.

1. State H₀ and H₁ and the significance level first.
2. Goodness of fit: STAT → TESTS → χ²GOF-Test. Independence: put the data in a matrix (2nd → x⁻¹ → EDIT), then STAT → TESTS → χ²-Test.
3. menu → Statistics → Stat Tests → χ² GOF, or χ² 2-way Test (enter the observed matrix).
4. Main menu → Statistics → TEST → CHI → GOF, or 2WAY for a contingency table.

Tip: Compare the p-value to the significance level: p < level ⇒ reject H₀. Check every expected frequency is ≥ 5; the degrees of freedom are (rows−1)(cols−1) for independence.

Test a claim about a population mean (one sample) or compare two means, when the population is roughly normal.

1. State H₀, H₁ (one- or two-tailed) and the significance level.
2. STAT → TESTS → T-Test (one sample) or 2-SampTTest; enter the hypothesised mean and either the data list or the summary stats.
3. menu → Statistics → Stat Tests → t Test (or 2-Sample t Test).
4. Main menu → Statistics → TEST → t → 1-SAMPLE (or 2-SAMPLE).

Tip: Match the tail (≠, <, >) to H₁. Read off t and the p-value, then write your conclusion in context comparing p to the significance level.

The heart of AI modelling - find the best-fitting curve for a data set, not just a straight line.

1. Enter the data in two lists (x and y).
2. STAT → EDIT to enter L1/L2, then STAT → CALC → QuadReg / CubicReg / ExpReg / PwrReg / SinReg.
3. In a Lists & Spreadsheet page enter the data, then menu → Statistics → Stat Calculations → choose the regression type.
4. Main menu → Statistics, enter the data in lists, then CALC → REG and pick X² / X³ / Exp / Power / Sin.

Tip: Turn DiagnosticOn (TI-84: 2nd → 0 → DiagnosticOn) to see R². Choose the model with the best R² that also makes sense for the context.

After fitting a regression curve, use it to predict a value or to solve for when something happens.

1. Fit the model so its equation is available to reuse.
2. Paste the equation into Y1 (VARS → Statistics → EQ → RegEQ), then use a table or solve Y1 = value.
3. Store the regression equation to f1(x), then evaluate f1(a) or solve f1(x) = value.
4. Copy the regression equation to the graph (Y=), then use G-Solv or a table to read predictions.
5. Predict within the data range (interpolation); extrapolating beyond it is unreliable.

Tip: Solve model = target to find when a quantity reaches a given level (e.g. when sales hit 1000).

Avoids rounding errors - keep full accuracy and only round the final answer.

1. Compute a value.
2. Press STO→ then a letter (e.g. ALPHA, A) to save it; recall the last answer with 2nd → ANS.
3. Type the value then ctrl + var and a name to store it; use ans for the last answer.
4. Press → (the store key) then ALPHA and a letter to save it.
5. Use the stored letter in later calculations instead of retyping a rounded number.

Tip: Rounding too early is one of the most common ways to lose marks - store, don't round.