IB Math Applications and Interpretation — Core flashcards

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All five topics of IB Mathematics: Applications and Interpretation: error, finance, modelling, Voronoi diagrams, chi-square and t-tests, calculus, with HL matrices, graph theory, Poisson tests, Markov chains and differential equations.

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Learn deck · part of IB Mathematics: Applications and Interpretation · written against: IB Diploma Programme IB Mathematics: Applications and Interpretation subject guide for first assessment 2021; SL and HL in one deck, HL-only cards under subtopic tags starting HL. Updated 2026-10-10.

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A length is recorded as 7.4 cm, correct to 1 decimal place. What are its lower and upper bounds?

7.35 cm and 7.45 cm — the true value lies within half a unit of the last recorded digit, so $7.35 \le L < 7.45$ ⁠.
Number and Algebra › Approximation and Financial Mathematics
A rectangle measures 5 m by 8 m, each to the nearest metre. What is the upper bound of its area?

46.75 m² — multiply the two upper bounds: $5.5 \times 8.5$ ⁠.

Watch out: for a difference or a quotient, the upper bound pairs an upper bound with a lower bound.
Number and Algebra › Approximation and Financial Mathematics
A ball's height is $h(t) = -4.9t^2 + 14.7t + 2$ metres after $t$ seconds. When does it reach its greatest height, and how high is that?

At $t = 1.5$ s, at about 13.0 m — the vertex of a quadratic model is at $t = -\frac{b}{2a} = \frac{14.7}{9.8}$ ⁠; substituting gives $h(1.5) = 13.025$ ⁠.
Functions › Modelling with Functions
A cooling model is $T(t) = 20 + 70(0.9)^t$ ⁠, with $t$ in minutes. What do the 20, the 70 and the 0.9 mean?

20°C is the room temperature (the horizontal asymptote), 70°C is the initial excess over it, and 0.9 means that excess falls by 10% each minute. The starting temperature is $T(0) = 90$ °C.
Functions › Modelling with Functions
In a Voronoi diagram, what are the sites, cells, edges and vertices?

Sites are the given points; a site's cell is the region closer to it than to any other site; edges are pieces of perpendicular bisectors, equidistant from two sites; vertices are where edges meet, equidistant from three or more sites.
Geometry and Trigonometry › Triangles Solids and Voronoi Diagrams
What is the equation of the Voronoi edge between the sites $(1, 2)$ and $(5, 4)$ ⁠?

$y = -2x + 9$ — the edge lies on the perpendicular bisector: it passes through the midpoint $(3, 3)$ and has gradient $-2$ ⁠, the negative reciprocal of the segment's gradient $\frac{1}{2}$ ⁠.
Geometry and Trigonometry › Triangles Solids and Voronoi Diagrams
How many degrees of freedom does a χ² test for independence on a 3 × 4 contingency table have?

6 — degrees of freedom are $(r - 1)(c - 1) = 2 \times 3$ ⁠. The null hypothesis is that the two variables are independent.
Statistics and Probability › Statistics and Hypothesis Tests
What condition must the expected frequencies meet in a χ² test, and what do you do if it fails?

Every expected frequency should be greater than 5; if one is not, combine adjacent rows, columns or categories, which also reduces the degrees of freedom.

Watch out: the condition is on expected counts, never on observed counts. The IB counts an expected frequency of exactly 5 as too small, though many textbooks accept it.
Statistics and Probability › Statistics and Hypothesis Tests
How do you use the trapezoidal rule with 4 strips to estimate $\int_0^2 2^x dx$ ⁠, and is the estimate too big or too small?

About 4.37, an overestimate — with $h = 0.5$ ⁠, $\frac{h}{2}\left(y_0 + y_4 + 2\left(y_1 + y_2 + y_3\right)\right) = 0.25\left(1 + 4 + 2(1.414 + 2 + 2.828)\right)$ ⁠. The curve is concave up, so the chords lie above it (exact value 4.33).
Calculus › Differentiation and Integration
What is the derivative of $f(x) = 3x^4 - \frac{6}{x}$ ⁠?

$f'(x) = 12x^3 + \frac{6}{x^2}$ — rewrite $-\frac{6}{x}$ as $-6x^{-1}$ ⁠, then use $\frac{d}{dx}\left(ax^n\right) = anx^{n-1}$ ⁠.

Watch out: $-6 \times (-1) = +6$ ⁠, so the second term becomes positive.
Calculus › Differentiation and Integration

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Review status: Second-reader reviewed, with corrections applied.

Checked against:

IB Diploma Programme subject guide (topic outline only; no text copied): Mathematics: applications and interpretation guide for first assessment 2021, topics 1–5 (SL and AHL).
OpenStax Calculus Volumes 1–3, OpenStax Precalculus 2e and OpenStax Introductory Statistics, consulted as references; no text copied.

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