GDC Bootcamp — TI-Nspire CX II Essentials

Module 2 of 46Lesson 1 of 1 · GDC Bootcamp — TI-Nspire CX II Essentials

AA SL & HL · GDC BOOTCAMP

TI-Nspire CX II — fluency is marks

Paper 1 is non-calculator — but Paper 2 is half the SL marks, and HL Papers 2 and 3 are 165 of 275 marks, so calculator fluency matters.

Paper 1: NO GDCPaper 2: GDC ✓

⚠ Non-calculator warning: Paper 1 is NON-calculator: train exact values — surds, fractions, exact trig ratios, log laws — until they are automatic.

🎯 What “Analyze Graph” earns you

Menu → 6: Analyze Graph → 4: Intersection. Read BOTH coordinates, quote them to 3 sf, and mark the point on your sketch — that is usually M1 A1 in one move.

🧰 The skill set (drill until 30 seconds each)

1. nSolve — Numerical Solve
menu → 3: Algebra → 1: Numerical Solve

P2 equations that resist algebra. Quote the equation solved for the M mark.

2. Graph & Analyze
Graphs page: menu → 6: Analyze Graph

Zeros, turning points, intersections for P2 modelling and area questions.

3. Numeric integrals & derivatives
menu → 4: Calculus

Definite integrals and derivative-at-a-point numerically — check every hand calculation from P1 practice.

4. Distributions
menu → 5: Probability → 5: Distributions

Normal and binomial cdf/inverse — draw the shaded region for the R mark.

5. Statistics & regression
Lists & Spreadsheet

1-var stats and linear regression with r.

6. Exact-value discipline
no GDC!

For P1: practise WITHOUT the calculator. Keep π and surds exact — a decimal where an exact value is demanded loses the A mark.

🔒 Press-to-Test — do this the night before

Charge to 100% and pack a spare-battery plan.
Back up any documents you care about — exam mode clears them.
Hold esc + home while powering on → choose your exam restrictions → confirm the flashing LED.
Verify the clock/angle settings: degrees for the geometry you expect, radians for calculus — know where the setting lives.

Habit: after every mock, list any GDC step that cost you more than 60 seconds — drill exactly those before the next set.

📸 TI-Nspire Step-by-Step: Worked Examples

In AA (SL and HL), Paper 1 is non-calculator — every GDC skill below is a Paper 2 skill. That is exactly why students underprepare it: they practise algebra for P1 and walk into P2 slow on the machine. Examples 1–10 fix that for everyone; Examples 11–20 add the Higher Level Paper 2 and Paper 3 skills. Every screen below is drawn exactly as it appears on the TI-Nspire CX II. Follow the key presses, copy the screens, then practise until your fingers know the menus without looking.

💻 Student Software & exam mode. Every screen below is drawn exactly as the TI-Nspire CX Student Software shows it, and every step works on the non-CAS calculator in IB exam mode (Press-to-Test). On a laptop: click menu on the on-screen keypad (same numbers as here); Enter = enter, Tab = next box; after ^ press → to leave the power; new page Ctrl+I; change page Ctrl+←/→; var Ctrl+L. Exam mode has no dot-product, cross-product or eigenvalue keys and no Diff Eq graphs — these examples show the allowed way.

EXAMPLE 1SOLVING GRAPHICALLYPaper 2

📝 EXAM-STYLE QUESTION

Solve the equation ln x = 3 − x. [3 marks]

STEP 1 — One curve each side

f1(x) = ln(x), f2(x) = 3 − x on a Graphs page. One crossing is visible.

STEP 2 — Intersection

menu6: Analyze Graph4: Intersection
Lower bound left of the crossing, upper bound right of it, enter

Both curves entered

Analyze Graph menu

Coordinates appear at the point

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

Sketch of y = ln x and y = 3 − x with the intersection marked M1
x = 2.21 (3 sf) A2

⚠️ EXAMINER TRAP

An equation you cannot solve algebraically is the GDC’s cue — ln x = 3 − x has no algebraic solution. If you spend three minutes trying algebra on P2, the paper has already beaten you. Graph it.

EXAMPLE 2TRIG EQUATIONS & MODEPaper 2

📝 EXAM-STYLE QUESTION

Solve sin 2x = 0.4 for 0 ≤ x ≤ π. [4 marks]

STEP 1 — CHECK THE MODE FIRST

Top-right of the screen must say RAD. The domain [0, π] tells you the question is in radians. Change it: doc7: Settings2: Document Settings

STEP 2 — Graph, don’t just nSolve

f1(x) = sin(2x), f2(x) = 0.4, window 0 to π. TWO crossings — nSolve alone would find only one.

RAD showing top-right — safe

First intersection

Second intersection

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

Sketch showing both solutions in the domain M1
x = 0.206 A1 and x = 1.37 A1 (3 sf) A1

⚠️ EXAMINER TRAP

DEG mode on a radians question wrecks the whole paper quietly — every trig answer wrong, no error message. Make checking the RAD indicator the first thing you do when the invigilator says begin.

EXAMPLE 3DERIVATIVE AT A POINTPaper 2

📝 EXAM-STYLE QUESTION

Let f(x) = x³ ln x. Find the gradient of the curve at x = 2. [2 marks]

STEP 1 — Use the derivative template

menu4: Calculus1: Numerical Derivative at a Point
Variable: x Value: 2 Derivative: 1st — then type the function into the template.

Dialog before the template

Result

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

f ′(2) = 12.3 (3 sf) M1A1
Write the notation f ′(2) = … — the method mark is for the calculus statement, not the keystrokes.

⚠️ EXAMINER TRAP

If the same question appeared on Paper 1 you would need the product rule: f ′(x) = 3x²ln x + x². Use the GDC value 12.3178 to CHECK your P1-style algebra when you revise — that is the smartest revision habit in this course.

EXAMPLE 4DEFINITE INTEGRALS & AREAPaper 2

📝 EXAM-STYLE QUESTION

The diagram shows the curve y = x e^−x. Find the area of the region enclosed by the curve, the x-axis and the line x = 2. [3 marks]

STEP 1 — Integral template

menu4: Calculus3: Numerical Integral
Fill in: lower 0, upper 2, function x·e^(−x), dx.

STEP 2 — Or straight from the graph

On a Graphs page: menu6: Analyze Graph6: Integral — it shades the region and prints the value, ideal when the question says “shade and find”.

Calculator page template

Graphs page: region shaded

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

Area = ∫₀² x e^−x dx M1A1
= 0.594 (3 sf) A1

⚠️ EXAMINER TRAP

The M1 is for writing the integral with correct limits and dx. Students who write only “0.594” hand back two of the three marks. Notation first, number second — every single time.

EXAMPLE 5BINOMIAL DISTRIBUTIONPaper 2

📝 EXAM-STYLE QUESTION

A biased coin gives heads with probability 0.35. It is tossed 12 times. Find (a) P(exactly 4 heads), (b) P(at most 4 heads). [4 marks]

STEP 1 — Pdf for “exactly”, Cdf for ranges

menu5: Probability5: Distributions
A: Binomial Pdf for exactly 4; B: Binomial Cdf for at most 4 (lower 0, upper 4).

Binomial Pdf dialog

(a) exactly 4

(b) at most 4: lower 0, upper 4

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

X ~ B(12, 0.35) A1
(a) P(X = 4) = 0.237 A1
(b) P(X ≤ 4) = 0.583 M1A1

⚠️ EXAMINER TRAP

Translate the words before touching the GDC: “at most 4” = X ≤ 4, “fewer than 4” = X ≤ 3, “at least 4” = 1 − P(X ≤ 3). Write the inequality on paper — it is usually worth a mark on its own.

🎯 More Worked Examples — Full Variety Pack

Five more Paper 2 skills: finding zeros, full normal-distribution fluency, series sums, turning points, and tangent lines. Together with Examples 1–5 this is the complete AA SL calculator toolkit.

EXAMPLE 6ZEROS OF A FUNCTIONPaper 2

📝 EXAM-STYLE QUESTION

Find all solutions of x³ − 4x + 1 = 0. [4 marks]

STEP 1 — Graph, count, then find

f1(x) = x³−4x+1. A cubic can have 1, 2 or 3 real roots — the graph shows THREE crossings here.

STEP 2 — Zero tool, three times

menu6: Analyze Graph1: Zero — bracket each crossing in turn with lower/upper bounds.

Three crossings visible

Zero tool on each

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

Sketch showing three x-intercepts M1
x = −2.11, x = 0.254, x = 1.86 (3 sf) A1A1A1

⚠️ EXAMINER TRAP

The number of answer lines in the answer box hints at how many roots the examiner expects. Three lines, one root written = two marks gone. Always graph first and COUNT before you solve.

EXAMPLE 7NORMAL DISTRIBUTIONPaper 2

📝 EXAM-STYLE QUESTION

IQ scores are modelled by X ~ N(100, 15²). (a) Find P(85 < X < 120). (b) Find the score exceeded by only 10% of people. [5 marks]

STEP 1 — (a) Normal Cdf with two real bounds

menu5: Probability5: Distributions2: Normal Cdf
Lower 85, Upper 120, μ = 100, σ = 15. No infinity needed — both ends are given.

STEP 2 — (b) Top 10% → area to the LEFT is 0.9

3: Inverse Normal with Area 0.9.

(a) both bounds finite

(b) area 0.9 to the left

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

(a) P(85 < X < 120) = 0.750 M1A1 with a shaded sketch A1
(b) P(X < k) = 0.9 M1 → k = 119 (3 sf) A1

⚠️ EXAMINER TRAP

“Exceeded by only 10%” means 90% lie BELOW — area 0.9, not 0.1. Draw the bell, shade it, and the right number becomes obvious. The sketch is not decoration; it is your error-detector and often a mark.

EXAMPLE 8SERIES WITH THE Σ TEMPLATEPaper 2

📝 EXAM-STYLE QUESTION

Evaluate Σₖ₋₁²⁰ (3k + 2). [3 marks]

STEP 1 — The template key

templates opens the maths template palette — choose the Σ symbol. Fill: k = 1 below, 20 above, expression 3k+2.

STEP 2 — Check with the arithmetic formula

This is arithmetic: u₁ = 5, d = 3, n = 20 → S₂₀ = 202 × (2×5 + 19×3) = 670. GDC and formula must agree.

Sum template filled

Formula agrees

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

Arithmetic series, u₁ = 5, d = 3, n = 20 A1
S₂₀ = 202 (2(5) + 19(3)) M1 = 670 A1

⚠️ EXAMINER TRAP

On Paper 2 the Σ template alone gets the answer — but show the series formula anyway. If the question moves to Paper 1 territory (find n given the sum), only the formula method survives, so practise both together.

EXAMPLE 9TURNING POINTSPaper 2

📝 EXAM-STYLE QUESTION

Find the coordinates of the local maximum and local minimum of f(x) = x³ − 4x² + 2. [4 marks]

STEP 1 — Analyze Graph twice

Graph f1(x) = x³−4x²+2. Then menu6: Analyze Graph3: Maximum near x = 0, and 2: Minimum near x = 2.7 — bracket each one separately.

Local maximum

Local minimum

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

Local maximum (0, 2) A1A1
Local minimum (2.67, −7.48) (3 sf) A1A1
Check by calculus: f ′(x) = 3x² − 8x = x(3x − 8) = 0 at x = 0 and x = 83 ✓

⚠️ EXAMINER TRAP

The GDC shows 2.67 but the exact x-value is 83. If the question says “exact”, the graph tool is only your starting point — finish with f ′(x) = 0 algebra. “Exact” and “3 sf” are instructions, not suggestions.

EXAMPLE 10TANGENT LINESPaper 2

📝 EXAM-STYLE QUESTION

Find the equation of the tangent to y = ln x at x = 2. [4 marks]

STEP 1 — Gradient from the GDC

Calculator page: d/dx template → d/dx(ln(x)) | x=2 gives 0.5. Or on the graph: menu8: Geometry1: Points & Lines7: Tangent — click the curve at x = 2 and the equation appears on screen.

STEP 2 — Build the line

Point (2, ln 2) = (2, 0.693). Line: y − 0.693 = 0.5(x − 2).

Gradient at the point

Geometry tool draws it too

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

f ′(2) = 0.5 A1 point (2, ln 2) A1
y − 0.693 = 0.5(x − 2) M1
y = 0.5x − 0.307 (3 sf) A1

⚠️ EXAMINER TRAP

Exact vs decimal again: ln 2 − 1 is the exact intercept, −0.307 the 3 sf version. Match whatever the question demands — and never mix (“y = 0.5x + ln 2 − 1” or “y = 0.5x − 0.307”, not half of each).

HIGHER LEVEL ONLY

Examples 11–20: the HL calculator skills

Sitting Standard Level? You can stop at Example 10. HL students: these ten examples cover the extra Paper 2 and Paper 3 calculator work — all done the exam-mode way on the non-CAS TI-Nspire.

EXAMPLE 11INTERSECTION OF CURVESPaper 2

📝 EXAM-STYLE QUESTION

Find the coordinates of the point of intersection of y = e^−x and y = x². [3 marks]

STEP 1 — Graph both, think first

f1(x) = e^(−x), f2(x) = x². For x < 0, e^−x grows faster than x² — so there is exactly one intersection, for x > 0.

STEP 2 — Intersection tool

menu6: Analyze Graph4: Intersection

One crossing only

Coordinates shown at the point

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

e^−x = x² M1
x = 0.703, y = 0.495 (3 sf) A1A1
Give BOTH coordinates — the question said “coordinates”.

⚠️ EXAMINER TRAP

Before accepting the GDC’s answer, argue how many intersections exist (growth rates, signs, turning points). HL examiners set curves with sneaky second crossings far outside the default window.

EXAMPLE 12POLYNOMIAL EQUATIONSPaper 2 & 3

📝 EXAM-STYLE QUESTION

Solve 2x³ − 5x² − 4x + 3 = 0. [4 marks]

STEP 1 — Polynomial Tools

menu3: Algebra3: Polynomial Tools1: Find Roots of Polynomial
Degree: 3, Roots: Real, then type the coefficients 2, −5, −4, 3.

Polynomial Tools menu

Coefficient entry

All three roots at once

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

x = −1, x = ½, x = 3 A2A1A1
On Paper 1 the same question means: factor theorem → try x = −1 → factorise (x + 1)(2x − 1)(x − 3). Use the GDC roots to check your P1 factorisation when revising.

⚠️ EXAMINER TRAP

If the question says “solve over ℂ”, use option 3: Complex Roots — a cubic with one real root has two complex conjugate roots the Real mode silently hides.

EXAMPLE 13NORMAL — UNKNOWN σPaper 2 & 3

📝 EXAM-STYLE QUESTION

X ~ N(54, σ²). Given that P(X < 50) = 0.12, find σ. [4 marks]

STEP 1 — You cannot invNorm your way out directly

Inverse Normal needs σ — which is the unknown. So standardise: find the z-value with the standard normal, then unpack it.

STEP 2 — invNorm on N(0,1), then solve

z = invNorm(0.12, 0, 1) = −1.17499. Then (50 − 54)/σ = −1.17499 — solve with nSolve or by hand.

Step 1: the z-value

Step 2: unpack sigma

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

P(X < 50) = 0.12 ⇒ z = −1.17499… M1A1
(50 − 54)/σ = −1.175 M1
σ = 3.40 (3 sf) A1

⚠️ EXAMINER TRAP

Keep ALL the decimals of z in your working (use the GDC’s ans key). Rounding z to −1.17 before solving gives σ = 3.42 — outside the accepted answer range. Premature rounding is the #1 accuracy-mark killer at HL.

EXAMPLE 14CHECKING PAPER 1 WORKRevision superpower

📝 EXAM-STYLE QUESTION

(A Paper 1 question, done by hand:) Show that ∫₀^π/3 tan x dx = ln 2. — and how to CHECK it with the GDC when you revise. [5 marks on P1]

STEP 1 — Do the algebra on paper

∫ tan x dx = ln|sec x| + c, so the integral is ln(sec π3) − ln(sec 0) = ln 2 − 0 = ln 2.

STEP 2 — Now make the GDC vote

Evaluate both the integral and ln 2 numerically. If the two decimals agree, your algebra is right. This habit catches sign errors before the mark scheme does.

Numerical integral

Compare with ln 2

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

(On Paper 1 you must show the algebra — the GDC check earns nothing in the exam room but saves you from handing in wrong algebra during revision.)
∫ tan x dx = ln|sec x| M1A1 → ln(sec π3) − ln(sec 0) M1 = ln 2 A1AG

⚠️ EXAMINER TRAP

“Show that” questions end at the printed answer (AG = answer given). The GDC can never be quoted as the reason on Paper 1 — but every AA HL 7-scorer uses it exactly like this at home.

EXAMPLE 15COMPLEX NUMBERSPaper 2 & 3

📝 EXAM-STYLE QUESTION

Write z = 1 + i√3 in the form r e^iθ. [3 marks]

STEP 1 — Modulus and argument directly

On a Calculator page (RAD mode): abs( ) gives the modulus, angle( ) gives the argument. Get i from π key or the symbol palette.

STEP 2 — Or convert in one move

Check the answer: type 2·e^(i·π/3) and the calculator gives back 1.+1.73205·i.

Modulus and argument

Check: 2e^iπ/3 gives back 1 + 1.73205i

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

r = |z| = 2 A1 θ = arg z = π3 A1
z = 2e^iπ/3 A1

⚠️ EXAMINER TRAP

In RAD mode the GDC returns 1.0472 (= π3 — the non-CAS calculator gives decimals) — in DEG mode it returns 60 and students then write e⁶⁰ⁱ, which is nonsense. Euler form is ALWAYS radians. Check the mode indicator.

🎯 More Worked Examples — Full Variety Pack

Five more HL skills: infinite series behaviour, 3D vectors, solving for unknown n in probability, volumes of revolution, and points of inflection. With Examples 1–5 this covers every GDC move the AA HL mocks demand.

EXAMPLE 16SERIES & CONVERGENCEPaper 2 & 3

📝 EXAM-STYLE QUESTION

Let Sₙ = Σᵣ₋₁ⁿ 1r². Find S₅₀, and comment on the behaviour of Sₙ as n → ∞. [4 marks]

STEP 1 — Σ template

templates → Σ symbol. r from 1 to 50, expression 1r².

STEP 2 — Probe the limit numerically

Re-run with n = 500 and n = 5000. The sums creep towards 1.6449… = π²6 — numerical evidence of convergence.

Fifty terms

Pushing n up

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

S₅₀ = 1.63 (3 sf) A1
As n increases the sums approach a limit ≈ 1.645; the series converges M1A1 (in fact to π²6) A1

⚠️ EXAMINER TRAP

“The terms go to zero so it converges” is FALSE reasoning (Σ1r has terms → 0 and diverges — try it on the GDC and watch it climb!). Argue from the partial sums levelling off, not from the terms shrinking.

EXAMPLE 173D VECTORSPaper 2 & 3

📝 EXAM-STYLE QUESTION

Given a = (2, 1, −2) and b = (3, −4, 0), find (a) the angle between a and b, (b) the area of the parallelogram they span. [6 marks]

STEP 1 — Type the components (exam mode)

In IB exam mode the dot-product and cross-product keys are blocked, so type the components: a·b = 2·3 + 1·(−4) + (−2)·0, and a × b = [a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁]. norm( ) still works for magnitude. Enter vectors as [2,1,−2].

STEP 2 — Angle from the dot product

cos θ = a·b|a||b| — type it in one line: cos⁻¹((2·3+1·(−4)+(−2)·0)/(norm(a)·norm(b))).

(a) angle in one line

(b) cross product & area

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

(a) a·b = 2, |a| = 3, |b| = 5 A1A1
cos θ = 215 → θ = 1.44 rad (or 82.3°) M1A1
(b) a × b = (−8, −6, −11), area = |a × b| = 14.9 M1A1

⚠️ EXAMINER TRAP

Vector brackets, not matrix brackets: type [2,1,−2] with single commas. And remember which product answers which question: DOT for angles and projections, CROSS for areas and normals. Mixing them up is instant zero on the part.

EXAMPLE 18BINOMIAL — FIND nPaper 2

📝 EXAM-STYLE QUESTION

A darts player hits the bullseye with probability 0.2 per throw. Find the minimum number of throws so that P(at least one bullseye) > 0.95. [5 marks]

STEP 1 — Set up the complement

P(at least one) = 1 − P(none) = 1 − 0.8ⁿ. Need 1 − 0.8ⁿ > 0.95, i.e. 0.8ⁿ < 0.05.

STEP 2 — nSolve, then THINK integer

nSolve treats n as continuous → 13.4. n must be a whole number of throws, and the probability must EXCEED 0.95 → round up.

Continuous solution first

Verify the two candidates

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

1 − 0.8ⁿ > 0.95 M1A1
0.8ⁿ < 0.05 → n > 13.4 A1
Check: n = 13 gives 0.945 (✗), n = 14 gives 0.956 (✓) M1
n = 14 A1

⚠️ EXAMINER TRAP

The verification line is not optional showing-off — it IS the method mark. “n = 14” with no check of 13 and 14 drops two marks. Solve continuously, then test the integers either side, every time.

EXAMPLE 19VOLUME OF REVOLUTIONPaper 2

📝 EXAM-STYLE QUESTION

The region under y = e^−x from x = 0 to x = 1 is rotated 360° about the x-axis. Find the volume of the solid formed. [4 marks]

STEP 1 — Write the formula BEFORE touching the GDC

V = π ∫₀¹ y² dx = π ∫₀¹ e^−2x dx — the squaring step is where the marks (and the errors) live.

STEP 2 — Then evaluate numerically

Integral template with the SQUARED function, multiplied by π.

One line, squared integrand

Exact check (revision habit)

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

V = π ∫₀¹ (e^−x)² dx M1A1
= 1.36 (3 sf) A2

⚠️ EXAMINER TRAP

Forgetting to square y is the single most common volume error — and the GDC cannot catch it because π ∫e^−xdx also produces a plausible-looking number (1.99). Write V = π∫y²dx first, then type what you wrote.

EXAMPLE 20POINTS OF INFLECTIONPaper 2

📝 EXAM-STYLE QUESTION

Find the coordinates of the point of inflection of f(x) = x³ − 3x² + x. [4 marks]

STEP 1 — Straight from the graph

Graph f1, then look where the curve changes its bend (here x = 1). The non-CAS TI-Nspire has no Inflection tool, so confirm it with the second-derivative template in Step 2.

STEP 2 — Confirm with the second derivative

Calculator page: second-derivative template at the point — d²dx² should give 0 there, and change sign either side.

The bend changes at (1, −1)

Second-derivative check

✍️ WHAT YOU WRITE ON PAPER (the marks live here!)

f ″(x) = 6x − 6 = 0 ⇒ x = 1 M1A1
Sign change of f ″ through x = 1 (concavity changes) R1
Point of inflection (1, −1) A1

⚠️ EXAMINER TRAP

f ″ = 0 alone does NOT prove an inflection (y = x⁴ has f ″(0) = 0 but no inflection — graph it and see). You must show the sign CHANGE. The GDC’s either-side check is the fastest way to justify it.

IB DP Mathematics: Analysis and Approaches (AA) — SL and HL GDC Bootcamp — TI-Nspire CX II Essentials

IB DP Mathematics: Analysis and Approaches (AA) — SL and HL

TI-Nspire CX II — fluency is marks

🎯 What “Analyze Graph” earns you

🧰 The skill set (drill until 30 seconds each)

🔒 Press-to-Test — do this the night before