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IB Maths: Applications & Interpretation revision notes Group 5 · Maths · SL / HL
AI Topic 1 is about numbers in the real world: rounding, errors, and money that grows or shrinks over time. Your GDC does a lot of the work, so learn what to type.
Course topics Number and algebra · Standard form, error, sequences, compound interest, loans · 15 subtopics Functions · Linear, exponential and sinusoidal models, fitting data · 10 subtopics Geometry and trigonometry · Voronoi diagrams, bearings, 3D measurement, matrices (HL) · 16 subtopics Statistics and probability · Sampling, hypothesis tests, correlation, distributions · 19 subtopics Calculus · Rates of change, optimisation, integration, differential equations (HL) · 18 subtopics Free lesson: Number and algebra Standard form Write any number as a × 10ᵏ with 1 ≤ a < 10 Percentage error How far your estimate is from the true value, as a % Compound interest Interest is added to the balance, so next time you earn interest on interest \[\varepsilon=\left|\frac{v_A-v_E}{v_E}\right|\times100\%\]
\(v_A\) is the approximate value and \(v_E\) the exact value.
\[FV=PV\times\left(1+\frac{r}{100k}\right)^{kn}\qquad V=V_0\left(1-\frac{r}{100}\right)^{n}\]
\(r\) = annual rate (%), \(k\) = compounding periods per year, \(n\) = years.
On the GDC, use the TVM / finance solver : N = n·k, I% = r, PV is negative (money you pay in), P/Y = C/Y = k.
Give money answers to 2 decimal places and other answers to 3 significant figures unless told otherwise. Worked example Léa invests €2,000 at 3% per year, compounded monthly. How much does she have after 5 years?
Identify: PV = 2000, r = 3, k = 12, n = 5. \(FV=2000\left(1+\frac{3}{1200}\right)^{60}=2000\times1.0025^{60}\) \(1.0025^{60}\approx1.16162\) FV ≈ €2,323.23 . On the TVM solver: N = 60, I% = 3, PV = −2000, PMT = 0, P/Y = C/Y = 12, solve FV. Common mistakes Entering PV as positive in the TVM solver and getting a negative answer. Using N = 5 instead of N = 60 for monthly compounding. Rounding in the middle of a calculation. Keep full values until the end. Dividing by the approximate value in percentage error instead of the exact one. Quick check Write 0.000452 in standard form. 4.52 × 10⁻⁴ . Move the decimal point 4 places right to get 4.52, so the power is −4.
The exact value is 50 and the estimate is 48. What is the percentage error? 4% . |48 − 50| / 50 × 100 = 2/50 × 100 = 4%. Divide by the exact value.
€1,000 is invested at 5% per year, compounded annually. What is it worth after 2 years? €1,102.50 . 1000 · 1.05² = 1000 · 1.1025 = €1,102.50.
A €15,000 car loses 20% of its value each year. What is it worth after 2 years? €9,600 . 15000 · 0.8² = 15000 · 0.64 = €9,600. Each year you keep 80%.
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FAQ What topics are in IB Maths: Applications & Interpretation? IB Maths: Applications & Interpretation (SL / HL) is organised into: Number and algebra; Functions; Geometry and trigonometry; Statistics and probability; Calculus.
Are these IB Maths: Applications & Interpretation notes free? Yes. The topic pages, key terms and the first lesson are free. The full lessons, interactive diagrams and exam-style practice papers with mark schemes are in the FortyFive app, which you can start for free.
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