GDC guide

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.

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.

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.

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'.

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.

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.

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.

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.

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.

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.