GDC Bootcamp — TI-Nspire CX II Essentials

Module 2 of 47Lesson 1 of 1 · GDC Bootcamp — TI-Nspire CX II Essentials

AI SL & HL · GDC BOOTCAMP

TI-Nspire CX II — fluency is marks

Every AI paper is a calculator paper (SL: Papers 1 and 2; HL: Papers 1, 2 and 3) — GDC fluency is worth real marks in every question.

Paper 1: GDC ✓Paper 2: GDC ✓

🎯 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

Numeric root of any equation — trig on a domain, exponentials, awkward polynomials. State the equation you solved to secure the M mark.

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

Zeros, max/min, intersections. Sketch what you see and label the point — the sketch itself often earns marks.

3. Finance Solver (TVM)
menu → 8: Finance → 1: Finance Solver

Loans, investments, depreciation. Money out = negative. Write N, I%, PV, PMT, FV in your working.

4. Statistics
Lists & Spreadsheet

1-var stats, regression (linear, exponential…), r and r². Always plot before you trust a model.

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

Normal cdf/inverse, binomial, Poisson. Draw the shaded curve in your answer for the R mark.

6. χ² & t-tests
menu → 6: Statistics → 7: Stat Tests

GOF and independence tests, 2-sample t. Write hypotheses, p-value, and the comparison to α.

7. Trapezoidal check
by hand + GDC

The trapezoidal rule is asked ON PAPER — but verify your answer with a definite integral on the GDC.

🔒 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 AI SL topics in degrees, radians for AHL sinusoidal work — 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 AI (SL and HL) the GDC is allowed on every paper — the exam is written assuming you use it constantly. Examples 1–10 cover the GDC skills every student needs; Examples 11–20 add the Higher Level 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 1EXPONENTIAL MODELSPaper 1 & 2

📝 EXAM-STYLE QUESTION

The population of a town is modelled by P = 12500e^0.032t, where t is in years. Find how long it takes the population to reach 20 000. [3 marks]

STEP 1 — Open Numerical Solve

menu3: Algebra1: Numerical Solve
On a Calculator page, this gives you nSolve( ) — your single most-used exam tool.

The Algebra menu — choose 1

Type the equation, then the variable

The answer appears instantly

STEP 2 — Read & round

The GDC gives 14.6876. The question wants 3 significant figures → 14.7 years.

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

12500e^0.032t = 20000 M1
t = 14.6876… A1
t ≈ 14.7 years (3 sf) A1

⚠️ EXAMINER TRAP

Never write only “14.7”. Write the equation you solved first — if you mistype on the GDC, the M1 method mark survives. And keep the unrounded value on screen for part (b).

EXAMPLE 2LINEAR REGRESSIONPaper 2

📝 EXAM-STYLE QUESTION

Hours studied (x) and test score (y) were recorded for 8 students: (2, 34), (3, 41), (5, 50), (6, 58), (8, 63), (9, 71), (11, 80), (12, 84). Find the equation of the regression line y on x, and the value of r. [4 marks]

STEP 1 — Enter the data in Lists & Spreadsheet

ctrldoc4: Add Lists & Spreadsheet
Type a name at the top of each column (e.g. hours, score), then fill the values.

STEP 2 — Run the regression

menu4: Statistics1: Stat Calculations3: Linear Regression (mx+b)
Set X List: hours, Y List: score, then OK.

Named columns with the data

Choose Linear Regression (mx+b)

Read m, b and r from the output

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

y = 4.92x + 25.7 A1A1
r = 0.996 A2
(Interpret: strong positive linear correlation — say “strong”, “positive” AND “linear” if asked.)

⚠️ EXAMINER TRAP

Use the variables of the question — write y = 4.92x + 25.7, not “m = 4.92, b = 25.7”. Copying the raw GDC output without forming the equation loses a mark every year.

EXAMPLE 3NORMAL DISTRIBUTIONPaper 1 & 2

📝 EXAM-STYLE QUESTION

The heights of students are normally distributed with mean 171 cm and standard deviation 8.2 cm. (a) Find the probability a student is taller than 180 cm. (b) Find the minimum height of the tallest 5% of students. [5 marks]

STEP 1 — (a) Normal Cdf for a probability

menu5: Probability5: Distributions2: Normal Cdf
Lower: 180 Upper: 9E999 (i.e. ∞) μ: 171 σ: 8.2

STEP 2 — (b) Inverse Normal for a boundary value

menu5: Probability5: Distributions3: Inverse Normal
Area is to the LEFT: tallest 5% → Area = 0.95, μ = 171, σ = 8.2

(a) Normal Cdf dialog

(a) result

(b) Inverse Normal — area 0.95

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

(a) P(X > 180) = 0.136 (3 sf) M1A1 — sketch a bell curve and shade the right tail A1
(b) P(X < h) = 0.95 M1 → h = 184.488… ≈ 184 cm A1

⚠️ EXAMINER TRAP

Inverse Normal always takes the area to the left. For the tallest 5% you must enter 0.95, not 0.05 — entering 0.05 gives 157.5 cm, which is obviously the shortest students. Sanity-check against the mean!

EXAMPLE 4FINANCE SOLVER (TVM)Paper 1 & 2

📝 EXAM-STYLE QUESTION

P5000 is invested at 4.5% per annum, compounded monthly. Find the value of the investment after 6 years. [3 marks]

STEP 1 — Open the Finance Solver

menu8: Finance1: Finance Solver
Fill every field, then put the cursor on FV and press enter

STEP 2 — The sign convention

Money you pay in is negative (PV = −5000), money you receive comes out positive. N is in payment periods: 6 years × 12 = 72.

Finance Solver filled in

Cursor on FV, press enter

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

N = 72, I = 4.5%, PV = −5000, PpY = CpY = 12 M1A1
FV = P6546.52 A1
Money answers: always 2 decimal places, not 3 sf.

⚠️ EXAMINER TRAP

The most common zero-mark error in the whole course: CpY left at 1. Compounded monthly means CpY = 12. And write the TVM values you used on paper — that IS your method mark.

EXAMPLE 5GRAPHING & INTERSECTIONPaper 2

📝 EXAM-STYLE QUESTION

A company’s weekly cost is C(x) = 120 + 18x + 0.5x² and revenue is R(x) = 40x, for x items. Find the break-even values of x. [4 marks]

STEP 1 — Graph both functions

ctrldoc2: Add Graphs
f1(x) = 120+18x+0.5x², f2(x) = 40x. Set the window with menu4: Window (x: 0 to 45, y: 0 to 1600).

STEP 2 — Find the intersections

menu6: Analyze Graph4: Intersection
Click a lower bound left of the crossing and an upper bound right of it. Repeat for the second crossing.

Analyze Graph menu

First crossing marked on screen

Second crossing

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

Break-even when C(x) = R(x) M1
Sketch of both curves with intersections labelled A1
x = 6.38 and x = 37.6 (3 sf) A1A1

⚠️ EXAMINER TRAP

A “sketch” question means: copy the GDC screen onto paper with axes labelled, intersection coordinates marked, and the window values on the axes. An empty pair of axes gets zero.

🎯 More Worked Examples — Full Variety Pack

Five more examples covering the rest of the AI SL GDC toolbox: statistics from frequency tables, the two hypothesis tests, loans, and series. Master all ten and there is no GDC task left on the paper that can surprise you.

EXAMPLE 6STATISTICS FROM A TABLEPaper 1 & 2

📝 EXAM-STYLE QUESTION

The table shows quiz scores of 40 students: score 5 (freq 3), 6 (7), 7 (12), 8 (9), 9 (6), 10 (3). Find the mean, standard deviation, median and interquartile range. [5 marks]

STEP 1 — Two named columns

Lists & Spreadsheet page: column A = score (5–10), column B = freq (3, 7, 12, 9, 6, 3). Never type 40 separate numbers — the frequency column does it.

STEP 2 — One-Variable Statistics

menu4: Statistics1: Stat Calculations1: One-Variable Statistics
X1 List: score Frequency List: freq — this field is the one everyone misses!

Frequency List set to freq

Scroll the output for everything

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

mean = 7.43 (3 sf) A1 σ = 1.34 A1
median = 7 A1 IQR = Q3 − Q1 = 8 − 6 = 2 M1A1

⚠️ EXAMINER TRAP

The output shows TWO standard deviations: sx (sample, 1.357) and σx (population, 1.340). IB questions want σx unless they explicitly say “unbiased estimate”. Picking the wrong row costs the mark.

EXAMPLE 7χ² TEST FOR INDEPENDENCEPaper 2

📝 EXAM-STYLE QUESTION

120 students were asked their favourite subject: Maths (Boys 18, Girls 12), Science (22, 28), Art (10, 30). Test at the 5% level whether subject choice is independent of gender. [6 marks]

STEP 1 — Put the table in a matrix

Calculator page: menu7: Matrix & Vector1: Create1: Matrix — 2 rows × 3 columns, fill in the observed values. Store it: ctrlvar as obs.

STEP 2 — Run the test

menu6: Statistics7: Stat Tests8: χ² 2-way Test — Observed Matrix: obs.

Observed matrix stored as obs

Test output

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

H₀: choice independent of gender; H₁: not independent A1
χ² = 8.83, df = 2 A2
p = 0.0121 < 0.05 R1
Reject H₀ — subject choice is NOT independent of gender A1A1

⚠️ EXAMINER TRAP

The conclusion sentence must compare p with the significance level and be in context. “Reject H₀” alone loses the final mark — say what it means for boys, girls and subjects. And df = (rows−1)(cols−1) = 2: quote it, it is often a mark.

EXAMPLE 8TWO-SAMPLE t-TESTPaper 2

📝 EXAM-STYLE QUESTION

Plant heights (cm) with fertiliser A: 23.1, 24.5, 22.8, 25.0, 23.9, 24.2 and fertiliser B: 21.9, 22.5, 23.0, 21.4, 22.8, 22.1, 22.6. Test at the 5% level whether the mean heights differ. [6 marks]

STEP 1 — Data into two lists

Lists & Spreadsheet: columns fa and fb.

STEP 2 — 2-Sample t Test, Pooled: Yes

menu4: Statistics4: Stat Tests4: 2-Sample t Test
List 1: fa, List 2: fb, Alternate Hyp: μ1 ≠ μ2, Pooled: Yes (IB always pools).

Dialog — note Pooled: Yes

Test output

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

H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂ A1
p = 0.00182 (3 sf) A2
0.00182 < 0.05, reject H₀ R1 — the mean heights with the two fertilisers differ A1A1

⚠️ EXAMINER TRAP

“Do the means differ?” = two-tailed (≠). “Is A better than B?” = one-tailed (>). Choosing the wrong Alternate Hyp changes p and usually the conclusion. Underline the question’s wording before opening the dialog.

EXAMPLE 9FINANCE — LOAN REPAYMENTSPaper 1 & 2

📝 EXAM-STYLE QUESTION

Thabo borrows P85 000 to buy a car, at 11% per annum compounded monthly, repaid over 4 years with equal monthly payments. Find the monthly repayment and the total interest paid. [4 marks]

STEP 1 — Loans flip the signs

menu8: Finance1: Finance Solver
The bank gives Thabo money now: PV = +85000. He pays it back: Pmt will come out negative. FV = 0 — the loan ends fully paid.

Solve for Pmt

Cursor on Pmt, press enter

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

N = 48, I = 11%, PV = 85000, FV = 0, PpY = CpY = 12 M1
Monthly repayment = P2196.87 A1
Total paid = 48 × 2196.87 = P105 449.73 M1
Interest = 105 449.73 − 85 000 = P20 449.73 A1

⚠️ EXAMINER TRAP

Total interest = (number of payments × payment) − amount borrowed. Students who try to compute interest with a percentage formula here always get it wrong — amortised loans do not work that way.

EXAMPLE 10SEQUENCES & SERIESPaper 1 & 2

📝 EXAM-STYLE QUESTION

Naledi deposits P200 at the start of each year into an account. Each deposit’s value grows by 5% per year. Show the total after the 15th deposit is a geometric series and find its sum. [4 marks]

STEP 1 — Use the sum template

Calculator page: templates then pick the Σ template — or menu4: Calculus3: Sum. Fill: k from 0 to 14, expression 200·1.05^k.

STEP 2 — Check against the formula

This is geometric: u₁ = 200, r = 1.05, n = 15. S₁₅ = 200(1.05¹⁵ − 1)0.05. The template and the formula must agree — instant self-check.

Sum template

Formula gives the same

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

Geometric with u₁ = 200, r = 1.05 A1
S₁₅ = 200(1.05¹⁵ − 1)1.05 − 1 M1A1
= P4315.71 A1

⚠️ EXAMINER TRAP

15 deposits growing from k = 0 to k = 14 — not 1 to 15. Off-by-one in the counter is the classic series error; the GDC sum makes it visible because you can recount the terms on screen.

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 11SYSTEMS OF EQUATIONSPaper 1, 2 & 3

📝 EXAM-STYLE QUESTION

Solve the system: x + y + z = 6, 2x − y + z = 3, x + 2y − z = 2. [4 marks]

STEP 1 — Open the linear-system solver

menu3: Algebra2: Solve System of Linear Equations
Set Number of equations: 3, Variables: x,y,z

STEP 2 — Fill in the template

A 3-row template appears — type one equation per row exactly as written in the question.

Choose the linear-system solver

One equation per row

The solution triple

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

Solving the system (GDC) M1
x = 1, y = 2, z = 3 A3
In context questions, finish with a sentence: “so the prices are P1, P2 and P3.”

⚠️ EXAMINER TRAP

The output {1,2,3} is in the ORDER of your variable list {x,y,z}. If you typed {z,y,x} you will assign every value to the wrong unknown and lose all the accuracy marks.

EXAMPLE 12EQUATIONS WITH TWO ROOTSPaper 2 & 3

📝 EXAM-STYLE QUESTION

The concentration of a drug is modelled by C(t) = t e^−0.4t. Find both times at which C(t) = 0.5. [4 marks]

STEP 1 — Graph it first — ALWAYS

f1(x) = x·e^(−0.4x) and f2(x) = 0.5. The graph shows the line crosses the curve twice — so one nSolve is not enough.

STEP 2 — nSolve twice, with a guess each time

nSolve returns only the root nearest your guess. Add a starting guess as the third argument: one near 1, one near 6.

The graph reveals TWO crossings

Guess 1 finds the first root

Guess 6 finds the second

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

t e^−0.4t = 0.5 M1
Sketch showing both intersections A1
t = 0.648 and t = 6.36 (3 sf) A1A1

⚠️ EXAMINER TRAP

Writing only t = 0.648 loses half the marks. Any model that rises then falls (drug doses, projectiles, logistic-ish curves) hits most values TWICE. The graph is your insurance — draw it before you solve.

EXAMPLE 13POISSON DISTRIBUTIONPaper 1 & 2

📝 EXAM-STYLE QUESTION

Calls arrive at a rate of 4.2 per hour. Find the probability of receiving at least 6 calls in an hour. [3 marks]

STEP 1 — Translate “at least 6”

P(X ≥ 6) = 1 − P(X ≤ 5). The GDC only gives ≤ directly, so the complement does the work.

STEP 2 — Poisson Cdf

menu5: Probability5: DistributionsK: Poisson Cdf
λ: 4.2 Lower: 6 Upper: 9E999 — or compute 1 − poissCdf(4.2, 0, 5).

Distributions menu (scroll down)

Lower 6, upper infinity

The probability

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

X ~ Po(4.2) A1
P(X ≥ 6) = 1 − P(X ≤ 5) M1
= 0.247 (3 sf) A1

⚠️ EXAMINER TRAP

State the distribution and its parameter (“X ~ Po(4.2)”) before any number. If your GDC entry is wrong, that line still earns the first mark. “More than 6” would be P(X ≥ 7) — read inequality words twice.

EXAMPLE 14NUMERICAL CALCULUSPaper 2 & 3

📝 EXAM-STYLE QUESTION

For f(x) = x e^0.5x, find (a) f ′(3) and (b) ∫₀³ f(x) dx. [4 marks]

STEP 1 — Derivative at a point

menu4: Calculus1: Numerical Derivative at a Point
Or press the template key templates and pick the d/dx template. Variable x, value 3.

STEP 2 — Definite integral

menu4: Calculus2: Numerical Integral
Fill the template: lower 0, upper 3, function, dx.

Calculus menu

(a) derivative at x = 3

(b) integral from 0 to 3

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

(a) f ′(3) = 11.2 (3 sf) M1A1
(b) ∫₀³ x e^0.5x dx = 13.0 (3 sf) M1A1
Method mark = writing the derivative / integral notation, not the GDC keystrokes.

⚠️ EXAMINER TRAP

On paper, 12.9634 rounds to 13.0 — write “13.0”, not “13”: three significant figures means showing the third figure even when it is a zero.

EXAMPLE 15FINANCE — ANNUITYPaper 1 & 2

📝 EXAM-STYLE QUESTION

Naledi saves P500 at the end of every month into an account paying 6% per annum, compounded monthly. Find the value after 5 years. [3 marks]

STEP 1 — Finance Solver with a payment

menu8: Finance1: Finance Solver
This time Pmt is not zero: regular deposits go in as Pmt = −500 (money leaving her pocket).

N = 60 months, Pmt negative

Cursor on FV, press enter

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

N = 60, I = 6%, PV = 0, Pmt = −500, PpY = CpY = 12 M1A1
FV = P34 885.02 A1

⚠️ EXAMINER TRAP

Annuity questions have TWO money slots: PV (lump sum now) and Pmt (regular payment). Putting 500 into PV instead of Pmt gives a wildly wrong answer that still looks plausible — check which one the story describes.

🎯 More Worked Examples — Full Variety Pack

Five more examples covering the rest of the AI HL toolbox: matrix powers for Markov chains, eigenvalues, goodness of fit, optimisation from a graph, and fitting exponential models to data. These are the Paper 3 workhorses.

EXAMPLE 16MARKOV CHAINS & MATRIX POWERSPaper 2 & 3

📝 EXAM-STYLE QUESTION

Each year 20% of customers switch from network A to B, and 30% switch from B to A. Initially the market is split 50–50. Find the market shares after 10 years. [4 marks]

STEP 1 — Build the transition matrix

Columns = where you ARE, rows = where you GO. Stay at A: 0.8, B→A: 0.3, A→B: 0.2, stay at B: 0.7. Store: ctrlvar as t, and the initial state as v.

STEP 2 — Raise to the power, multiply

Type t^10·v — the GDC does the whole 10-step evolution in one line.

Store T and v

Ten years in one line

Check the long-run steady state

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

T = [[0.8, 0.3],[0.2, 0.7]], v₀ = [0.5, 0.5]ᵀ A1A1
v₁₀ = T¹⁰v₀ = [0.600, 0.400]ᵀ M1
A has 60.0%, B has 40.0% A1

⚠️ EXAMINER TRAP

Check your matrix columns sum to 1 BEFORE computing — 0.8+0.2 = 1 ✓, 0.3+0.7 = 1 ✓. A transition matrix whose columns don’t sum to 1 is wrong with certainty, and the GDC will happily give you a wrong answer from it.

EXAMPLE 17EIGENVALUES & EIGENVECTORSPaper 2 & 3

📝 EXAM-STYLE QUESTION

Find the eigenvalues and corresponding eigenvectors of M = [[4, 1],[2, 3]]. [5 marks]

STEP 1 — Eigenvalues from the characteristic equation

In IB exam mode the eigenvalue keys are blocked, so use λ² − (a+d)λ + det M = 0. Store M as m, then type det(m) → 10 and polyRoots({1,−7,10}) → {2,5}.

STEP 2 — Eigenvectors by hand, checked on the GDC

Solve (M − λI)v = 0 for each λ: λ = 5 gives (1, 1) and λ = 2 gives (1, −2). Check on the GDC: m·[1;1] → [5;5] = 5·(1, 1) and m·[1;−2] → [2;−4] = 2·(1, −2).

Eigenvalues: det and polyRoots

Check: m·v = λ·v

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

λ₁ = 5, λ₂ = 2 A1A1
For λ = 5: eigenvector (1, 1) A1; for λ = 2: eigenvector (1, −2) M1A1
Verify by hand: det(M − λI) = λ² − 7λ + 10 = (λ−5)(λ−2).

⚠️ EXAMINER TRAP

Pair each eigenvector with its own eigenvalue — check it with m·v on the GDC before you write it. Any non-zero multiple is correct, but examiners expect simple whole numbers such as (1, 1) and (1, −2).

EXAMPLE 18χ² GOODNESS OF FITPaper 2 & 3

📝 EXAM-STYLE QUESTION

A die is rolled 60 times: frequencies 8, 12, 9, 11, 6, 14 for faces 1–6. Test at the 5% level whether the die is fair. [6 marks]

STEP 1 — Observed and expected lists

Lists & Spreadsheet: obs = {8,12,9,11,6,14}, exp = {10,10,10,10,10,10} (fair die → 606 each).

STEP 2 — GOF test

menu4: Statistics4: Stat Tests7: χ² GOF — Observed: obs, Expected: exp, Deg of Freedom: 5 (categories − 1).

GOF dialog

Output

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

H₀: the die is fair; H₁: it is not fair A1
Expected values all 10 A1
χ² = 4.20, df = 5, p = 0.521 A2
0.521 > 0.05: insufficient evidence to reject H₀ — the die is consistent with being fair R1A1

⚠️ EXAMINER TRAP

Never write “H₀ is accepted” or “the die IS fair” — a test can only fail to find evidence against fairness. That wording distinction is worth a mark at HL, and Paper 3 loves to probe it.

EXAMPLE 19OPTIMISATION FROM A GRAPHPaper 2 & 3

📝 EXAM-STYLE QUESTION

A firm’s daily profit is P(x) = −0.4x² + 22x − 120 for x items. Find the number of items that maximises profit, and the maximum profit. [3 marks]

STEP 1 — Graph and Analyze

f1(x) = −0.4x²+22x−120, window x: 0 to 60, y: 0 to 220. Then menu6: Analyze Graph3: Maximum — bracket the peak with lower and upper bounds.

Maximum found and labelled

Calculus check (optional)

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

Maximum at x = 27.5 from the graph M1
x must be a whole number of items: P(27) = 182.4, P(28) = 182.4 → 27 or 28 items A1
Maximum profit P182.50 at x = 27.5 (if x continuous) A1

⚠️ EXAMINER TRAP

Context decides whether x = 27.5 is acceptable. Items, people, tickets → integers: evaluate both neighbours and say so. A pure “find the maximum of the function” → 27.5 stands. Read the noun in the question.

EXAMPLE 20EXPONENTIAL REGRESSIONPaper 2 & 3

📝 EXAM-STYLE QUESTION

Bacteria counts (thousands) were measured: t = 0, 1, 2, 3, 4 hours; N = 12, 17, 25, 36, 52. Fit a model N = a·bᵗ and estimate N at t = 6. [5 marks]

STEP 1 — Data in, regression out

Lists & Spreadsheet: columns time, count. Then menu4: Statistics1: Stat CalculationsA: Exponential Regression.

STEP 2 — Save the equation, then predict

In the dialog set “Save RegEqn to” f1 — then f1(6) evaluates the model instantly. No retyping, no rounding error.

Regression output

Predict with the saved model

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

N = 11.9 × 1.45ᵗ A1A1 (r = 0.9999: excellent fit A1)
N(6) = 109 (3 sf) → about 109 000 bacteria M1A1

⚠️ EXAMINER TRAP

t = 6 is OUTSIDE the data range (0–4) — that is extrapolation. State it: “this assumes exponential growth continues, which may not be reliable”. That sentence is a standing 1-mark reward in AI papers.

IB DP Mathematics: Applications and Interpretation (AI) — SL and HL GDC Bootcamp — TI-Nspire CX II Essentials

IB DP Mathematics: Applications and Interpretation (AI) — 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