TI-84 Skills for the IB Maths SL

▶ Essential Setup & Navigation

First-Time Setup

Upgrade to OS 2.55MP: check via 2nd MEM → 1:About.

Install PlySmlt2 (Polynomial & Simultaneous Equation Solver).

Reuse previous entry: scroll ▲, press ENTER.

Jump to start/end of expression: 2nd ◄ or 2nd ►.

Sending / Receiving an App

Receive: LINK → RECEIVE → 1:Receive ENTER.

Send: LINK → SEND → C:Apps → select app → TRANSMIT → 1:Transmit ENTER.

Common Errors & Fixes

ERR: DIM MISMATCH — a STATPLOT is on.

Go to Y=; if a Plot is highlighted, press ENTER to un-highlight.

ERR: WINDOW RANGE — Xmin ≥ Xmax. Fix in WINDOW.

X = 5.67E-12 means the TI is reporting $X = 0$.

Hard Reset

2nd MEM → 5:Reset → 2:Defaults → 2:Reset.

Always works — but clears everything. After reset re-enable DiagnosticOn.

MODE Settings (Check Every Exam)

Angle mode: IB SL uses radians for most trig. Always check MODE.

Float vs Fixed: Keep on Float; round manually in final answer.

Function mode (default): MODE → FUNC.

a+bi mode: Not needed for SL — leave off.

WINDOW Quick Presets

ZOOM 6 — ZStandard: $[-10,10]^2$.

ZOOM 7 — ZTrig: ideal for trig in radians.

ZOOM 5 — ZSquare: equal axes (use for inverse).

ZOOM 0 — ZoomFit: auto-fits $y$-range.

Speed up slow graphs: set Xres = 4 in WINDOW.

Fractions, Exact Values & Storing

MATH 1: ►Frac — decimal to fraction.

$0.375 \Rightarrow \tfrac{3}{8}$; $1371/3656 \Rightarrow \tfrac{3}{8}$.

F1 fraction template (OS 2.55MP): press ALPHA F1 → select $\frac{n}{d}$ template. Eliminates bracket errors in complex fractions.

Storing & Recalling Results

After any CALC result, press ENTER → stores coordinates into $X$ and $Y$.

Recall $x$: X,T,θ,n or ALPHA X.

Recall $y$: ALPHA Y.

Store manually: value STO► A (any letter A–Z).

Ans = last result. Chain: √(Ans), Ans².

F4 accesses Y1, Y2, … variables directly on home screen.

▶ Functions & Graphs

2nd CALC Menu — Core Tools

2:Zero	Roots of $f(x)=0$. Set Left Bound → ENTER, Right Bound → ENTER, ENTER.
3:Minimum	Local min. Set left & right bounds.
4:Maximum	Local max. Set left & right bounds.
5:Intersect	Solve $f(x)=g(x)$. Press ENTER × 3 (first curve, second curve, guess).
6:dy/dx	Numerical derivative at typed $x$-value.
7:∫f(x)dx	Definite integral; set lower and upper bounds on graph.

NEVER use TRACE or ZOOM to read off intercepts/intersections — TRACE only hits pixel centres and will be wrong to 3 s.f. Always use CALC.

Zeros & Intersections (Step by Step)

Finding a zero of $f(x)$:

Enter $f(x)$ in Y1, graph it.
2nd CALC → 2:Zero.
Move cursor left of zero → ENTER (Left Bound).
Move cursor right → ENTER (Right Bound).
Press ENTER once more (Guess).

Intersection of two curves:

Enter $f$ in Y1, $g$ in Y2. Use ZOOM 7 (ZTrig) for trig.
2nd CALC → 5:Intersect.
Press ENTER, ENTER, ENTER.

Multiple intersections? Repeat from step 2 with cursor near each one.

Derivatives & Tangent Lines

Tangent line at a point:

Enter function in Y=. Graph it.

2nd DRAW → 5:Tangent( → type $x$-value → ENTER.

TI displays the tangent equation.

Example at $x=2$ for $y=x^2$: gives $y=4x-4$.

Numerical derivative $f'(a)$:

ALPHA F2 → 3:nDeriv(expr, x, value)

Or graph → 2nd CALC → 6:dy/dx → type $x$.

Example: $\dfrac{d}{dx}(x^2)\Big|_{x=2}$ → $4$.

TI-84 gives numerical derivatives only. It cannot give $f'(x)$ as an expression.

Definite Integrals

Method 1 — Graphical (recommended):

Graph function in Y1.
2nd CALC → 7:∫f(x)dx.
Type lower bound → ENTER.
Type upper bound → ENTER.

Example: $\displaystyle\int_1^3 x^2\,dx$ → $8.67$.

Method 2 — Home screen:

MATH → 9:fnInt(expr, x, a, b)

Or ALPHA F2 → 4:fnInt(.

Area Between Two Curves

Integrate $|f(x)-g(x)|$ between intersection points.

Use abs(Y1-Y2) in a new Y, then integrate, or split at crossings and add.

Graphing the Inverse Function

Enter $f(x)$ in Y1. Quit to home screen.

ZOOM 5:ZSquare first (equal axis scaling).

2nd DRAW → 8:DrawInv( Y1.

TI graphs the inverse whether or not $f$ passes the HLT.

To clear: 2nd DRAW → 1:ClrDraw.

Composite Functions

Graph $f(g(x))$: set Y3 = Y1(Y2(X)).

Access $Y_n$: VARS → Y-VARS → 1:Function.

Or press ALPHA F4 for Y1 shortcut (OS 2.55MP).

Logarithms & Exponentials

Change of base: $\log_a x = \dfrac{\ln x}{\ln a} = \dfrac{\log x}{\log a}$.

Direct log base: ALPHA F2 → 5:logBASE(x, a).

Example: $\log_2 3$: logBASE(3,2) $\approx 1.585$.

Or: log(3)/log(2).

Solve $3=2^x$: graph $Y_1=2^x,\ Y_2=3$; intersect → $x\approx1.585$.

V.A. of Logs Not Visible

The vertical asymptote of $y=\log(x-1)$ is not drawn by the TI — it is still there. Do not report it as absent.

TABLE (2nd GRAPH)

Setup: 2nd TBLSET → set TblStart, ΔTbl.

View: 2nd TABLE.

Investment problem: \$5000 at 6.3\% exceeds \$10{,}000 after $n$ full years?

Y3 = 5000(1.063)^x; TblStart=0, ΔTbl=1.

Scroll until $Y_3 > 10000$ → $n=12$.

Piecewise Functions

Multiply each piece by its boolean condition and sum:

$Y_1=(x{+}1)(x{\le}0)+x^2(x{>}0)$

Logical operators: 2nd TEST; AND/OR: 2nd TEST LOGIC.

TABLE works cleanly since there is only one equation.

▶ Algebra, Equations & Matrices

Solving Equations Graphically

One equation $f(x)=0$: Graph and use CALC 2:Zero.

Two-sided equation $f(x)=g(x)$: Enter both sides as $Y_1$ and $Y_2$; use CALC 5:Intersect.

Multiple solutions: Repeat for each intersection — change guess position each time.

PlySmlt2: Polynomial Roots

APPS → PlySmlt2 → 1:Poly Root Finder

Finds all roots (real) of any polynomial up to degree 10.

Example: $3x^3-2x+1=0$ → only real root: $x=-1$.

PlySmlt2: Simultaneous Equations

APPS → PlySmlt2 → 2:Simult. Eq. Solver

Up to 10 equations × 10 unknowns.

Example: $2x+3y=5,\ 3x+5y=7 \Rightarrow x=4,\ y=-1$.

Matrix Operations

Create: 2nd MATRIX → EDIT → [A] → enter dimensions → type values.

Recall: 2nd MATRIX → NAMES → [A].

Determinant: MATRIX → MATH → 1:det([A]) → ENTER.

Inverse: [A]^{-1} on home screen.

Solve $AX=B$: [A]^{-1}[B] → gives solution vector.

Example: $A^{-1}B$

Solve: $x-3y=1,\ 2x+z=2,\ 4x+y+3z=-1$.

Enter $A$ (coefficients) and $B$ (RHS). Compute [A]^{-1}[B].

→ $x=4,\ y=1,\ z=-6$.

Binomial Expansion & Combinatorics

Binomial coefficient $\dbinom{n}{r}$:

n MATH PRB 3:nCr r

Example: $\dbinom{5}{3} = $ 5 nCr 3 $= 10$.

Permutations $P(n,r)$: n MATH PRB 2:nPr r.

Factorial: n MATH PRB 4:!

Expand $(a+b)^n$: Use nCr to find coefficients term by term. Verify using PlySmlt2 if expanded form is a polynomial.

Identifying Exact Answers

If result looks irrational:

Square it → integer? → it’s $\sqrt{n}$.
Divide by $\pi$ → rational? → involves $\pi$.

Example: $1.7320\ldots \xrightarrow{x^2} 3 \Rightarrow \sqrt{3}$.

Factoring Polynomials

TI-84 cannot factor symbolically. Instead: graph and find zeros with CALC 2:Zero.

Example: $x^2-3x-4$.

Zeros at $x=4$ and $x=-1$ → $(x-4)(x+1)$.

Quadratic: also use PlySmlt2 (Poly Root Finder) with degree 2 — faster for SL quadratics.

Or use MATH → 0:Solver for a single equation root.

Polynomial Division Check

After factoring, verify: substitute a root into original → should give 0. Use Y1(value) on home screen.

▶ Statistics & Probability

Lists & STAT Editor

Enter data: STAT → EDIT → 1:Edit → type into L1.

If frequencies exist, type them into L2.

Clear list contents: cursor to list name (e.g. L1) → CLEAR ENTER.

Do NOT press DEL — this deletes the list name itself, not just contents.

Recreating a Deleted List

If L1 disappears from the editor: STAT → 5:SetUpEditor → ENTER. Restores L1–L6.

Sorting a List

STAT → 2:SortA(L1) — ascending.

STAT → 3:SortD(L1) — descending.

Useful for reading off median, quartiles manually from ordered data.

Descriptive Statistics (1-Var Stats)

STAT → CALC → 1:1-Var Stats L1

With frequencies: 1-Var Stats L1, L2

Outputs:

$\bar{x}$ — mean
$\Sigma x$ — sum, $\Sigma x^2$ — sum of squares
$S_x$ — sample SD, $\sigma_x$ — population SD
$n$ — count
Scroll ↓: minX, Q1, Med, Q3, maxX

Do NOT use 1-Var Stats for Median, Q1, Q3 directly — scroll down in the output to read these. IB sometimes uses a different Q1/Q3 convention — always check.

Linear Regression & Correlation

Enter $x$-values in L1, $y$-values in L2.

STAT → CALC → 4:LinReg(ax+b) L1, L2, Y1

Storing to Y1 plots the line automatically.

Output: $a$ (gradient), $b$ (intercept), $r$ (correlation coeff), $r^2$.

Enable Diagnostics (r and r²)

Must do this once after any reset:

2nd CATALOG → DiagnosticOn → ENTER ENTER.

Without this, $r$ and $r^2$ are hidden from regression output.

Scatter Plot

2nd STATPLOT → 1:Plot1 → On → Type: scatter → set Xlist:L1, Ylist:L2.

Then ZOOM 9:ZoomStat to auto-fit the window.

Normal Distribution

normalcdf(lower, upper, μ, σ)

For $P(X<a)$: lower = -1E99 (type (-) 1 EE 99).

For $P(X>a)$: upper = 1E99.

Example: $\mu=20,\sigma=3$:

normalcdf(19, 23, 20, 3) $\approx 0.4719$.

normalPDF( is never needed in IB SL.

invNorm — Finding a Cutoff

invNorm(area to LEFT, μ, σ)

Example: $P(X<d)=0.05,\ \mu=20,\sigma=3$:

invNorm(0.05, 20, 3) $\approx 15.1$.

For $P(X>d)=0.1$: use invNorm(0.90, μ, σ).

Find Unknown μ or σ

Use $\dfrac{x-\mu}{\sigma}=\texttt{invNorm}(p,0,1)$.

Rearrange → set as equation in $Y=$, solve graphically.

Example: $P(X<84)=0.15,\ \sigma=3$:

invNorm(0.15,0,1) = (84-X)/3 → solve for $X$ → $\mu\approx87.1$.

Discrete Distributions

Binomial $X\sim B(n,p)$:

2nd DISTR → A:binomPDF(n, p, k) → $P(X=k)$.

2nd DISTR → B:binomCDF(n, p, k) → $P(X\le k)$.

For $P(X\ge k)$: $1-\texttt{binomCDF}(n,p,k-1)$.

For $P(a\le X\le b)$: $\texttt{binomCDF}(n,p,b)-\texttt{binomCDF}(n,p,a-1)$.

Example: $n=6,\ p=0.75$, find $P(X=6)$:

binomPDF(6, 0.75, 6) $\approx 0.178$.

Poisson $X\sim\text{Po}(\lambda)$:

poissonPDF(λ, k) → $P(X=k)$.

poissonCDF(λ, k) → $P(X\le k)$.

For $P(X\ge k)$: $1-\texttt{poissonCDF}(\lambda,k-1)$.

Graph to find unknown parameter:

If $P(X=4)=0.12,\ X\sim B(5,p)$:

Y1 = binomPDF(5,X,4)-0.12. Window $-0.1\to1.1$. CALC Zero → $p\approx0.459$.

Same method for Poisson: Y1 = poissonPDF(X,k)-target.

All CDF gives $P(X\le k)$. IB often asks $P(X\ge k)$ or $P(X>k)$ — adjust by 1 carefully: $P(X\ge k)=1-P(X\le k-1)$.

Bivariate Data & Regression (Full Workflow)

Step 1: Enter $x$ in L1, $y$ in L2 via STAT EDIT.

Step 2: Draw scatter: STATPLOT → Plot1 On → scatter → L1, L2. Then ZOOM 9:ZoomStat.

Step 3: STAT → CALC → 4:LinReg(ax+b) L1, L2, Y1.

Step 4: Graph with GRAPH to see line on scatter plot.

Step 5: Note $a,b,r,r^2$ from output.

Predict $y$ from $x$: On home screen type Y1(x-value) → gives predicted $y$.

Pearson’s $r$: close to ±1 → strong linear correlation. Must enable DiagnosticOn first.

Other SL regression types:

ExpReg — $y=ab^x$
PwrReg — $y=ax^b$
QuadReg — $y=ax^2+bx+c$

All store to Y1 same way; $r^2$ shown for fit quality.

▶ Finance & Sequences

Finance App — TVM Solver

APPS → 1:Finance → 1:TVM Solver

Variables:

N — total number of periods
I% — annual interest rate (as %, e.g. 5 not 0.05)
PV — present value (negative = cash paid out)
PMT — regular payment per period
FV — future value
P/Y — payments per year
C/Y — compounding periods per year

Fill known values. Cursor to unknown → ALPHA ENTER to solve.

Sign convention: money paid OUT is negative; received is positive. Be consistent or answers will be wrong.

Sequences & Series

Sum of a sequence (home screen):

2nd LIST → MATH → 5:sum(seq(expr, x, start, end))

Example: $\displaystyle\sum_{k=1}^{10}k^2$:

sum(seq(X², X, 1, 10)) $= 385$.

Generate sequence as list:

seq(2X-1, X, 1, 5) → $\{1,3,5,7,9\}$.

Store to list: seq(…) STO► L3.

Compound Interest via TABLE

Y1 = 5000(1.063)^x; TblStart=0, ΔTbl=1. Scroll to find when target is exceeded. Faster than algebra when $n$ must be an integer.

Arithmetic & Geometric Sequences

AP: $u_n = u_1 + (n-1)d$.

Evaluate Y1 = A + (X-1)*D; use TABLE with step 1 to list terms.

GP: $u_n = u_1 \cdot r^{n-1}$.

Evaluate Y1 = A * R^(X-1) in TABLE.

Partial sums via sum(seq(:

AP sum to $n$: sum(seq(A+(X-1)*D, X, 1, n)).

GP sum to $n$: sum(seq(A*R^(X-1), X, 1, n)).

IB-Allowed Calculator Apps

PlySmlt2 — Polynomial Root Finder & Simultaneous Equation Solver
Finance — TVM Solver (compound interest, loans, annuities)
CtlgHelp — Catalogue Help
Language apps, CBL/CBR

Delete all other apps:

2nd MEM → 2:Mem Mgmt/Del → A:APPS → cursor → DEL.

Pre-Exam Checklist

Mode: RADIAN (unless degrees stated).
Run DiagnosticOn for $r$ values.
Clear all Y= functions.
Clear STAT lists (L1, L2).
Check battery level.

▶ Exam Technique & Precision

IB SL Paper 2 — GDC Exam Strategy

Showing GDC work (IB requirement):

Write the equation/expression entered.
State the result at full precision first.
Then round to 3 s.f. for final answer.
Write “by GDC” or “from GDC” where applicable.
Sketch the graph if intersection/zero method used.

Precision rules (IB SL):

Default: 3 significant figures.
Exact answers (integers, fractions, $\pi$): write exactly.
Money: 2 decimal places.
Probabilities: 4 d.p. or 3 s.f.
Never round intermediate values — use Ans.
Degrees: 1 d.p.; Radians: 3 s.f.

Common SL GDC question types:

Solve equations → intersect / zero.
Min/max of function → CALC min/max.
Area under curve → definite integral.
Normal probabilities → normalcdf / invNorm.
Binomial probabilities → binomPDF/CDF.
Regression → LinReg + scatter plot.
Compound interest → Finance TVM.
Matrix equations → $A^{-1}B$.

Quick fix flowchart:

Blank graph? → Check Y= not empty; check WINDOW.
DIM MISMATCH? → Turn off STATPLOT in Y=.
CALC gives wrong answer? → Zoom in, re-check bounds.
No $r$ in regression? → Run DiagnosticOn.
Strange $E{-}12$ output? → It means 0.
Everything broken? → Hard reset (MEM → Reset).

TI-84 Skills for the IB Maths SL - New Syllabus

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