IB Math Applications and Interpretation — Practice Questions flashcards

6 of 55 questions free to study here · 5 topics · the whole deck is built into Willys

Multiple-choice practice on the syllabus, one best answer each, on bounds and financial maths, modelling, trigonometry and Voronoi diagrams, statistics and tests, calculus and HL extensions.

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Practice 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 cyclist rides 240 m, measured to the nearest 10 m, in a time of 30 s, measured to the nearest second. What is the upper bound of her average speed, to 3 significant figures?

A) 7.97 m/s
B) 8.03 m/s
C) 8.31 m/s
D) 8.00 m/s

C) 8.31 m/s

Speed is distance divided by time, so its upper bound pairs the upper bound of the distance with the lower bound of the time: $\frac{245}{29.5} \approx 8.31$ ⁠. Using both upper bounds, $\frac{245}{30.5}$ ⁠, makes the denominator too big and gives a smaller speed.
Number and Algebra › Approximation and Financial Mathematics
A student estimates the length of a school corridor as 24 m. Its measured length is 25.6 m. What is the percentage error of the estimate?

A) 93.8%
B) 6.25%
C) 6.67%
D) 1.60%

B) 6.25%

Percentage error is $\frac{|v_A - v_E|}{|v_E|} \times 100 = \frac{1.6}{25.6} \times 100 = 6.25$ ⁠%, dividing by the exact value. Dividing by the estimate (24) instead gives 6.67%.
Number and Algebra › Approximation and Financial Mathematics
A candle burns down at a constant rate. It is 22 cm tall 2 hours after it is lit and 13 cm tall after 5 hours. How tall was it when it was lit?

A) 25 cm
B) 19 cm
C) 28 cm
D) 16 cm

C) 28 cm

The gradient is $\frac{13 - 22}{5 - 2} = -3$ cm per hour, so the initial height is $22 + 3 \times 2 = 28$ cm, the intercept of $h = 28 - 3t$ ⁠. Working out $22 - 3 \times 2 = 16$ gets the sign of the gradient wrong.
Functions › Modelling with Functions
In triangle ABC, angle A = 40°, angle B = 65° and BC = 12 cm. What is the length of AC, to 3 significant figures?

A) 16.9 cm
B) 8.51 cm
C) 19.5 cm
D) 18.0 cm

A) 16.9 cm

By the sine rule, $\frac{AC}{\sin 65^\circ} = \frac{12}{\sin 40^\circ}$ ⁠, so $AC = \frac{12\sin 65^\circ}{\sin 40^\circ} \approx 16.9$ cm. 18.0 cm is AB, the side opposite the third angle of 75°.
Geometry and Trigonometry › Triangles Solids and Voronoi Diagrams
A χ² test for independence uses a contingency table of 5 age groups by 3 preferred news sources. How many degrees of freedom does the test have?

A) 14
B) 6
C) 8
D) 15

C) 8

Degrees of freedom are $(r - 1)(c - 1) = 4 \times 2 = 8$ ⁠. 14, the number of cells minus one, is the count for a goodness-of-fit test with 15 categories, not for a contingency table.
Statistics and Probability › Statistics and Hypothesis Tests
What is the gradient of the curve $y = 2x^3 - 5x^2 + 4$ at the point where $x = 2$ ⁠?

A) 4
B) 0
C) 14
D) 8

A) 4

$\frac{dy}{dx} = 6x^2 - 10x$ ⁠, which at $x = 2$ is $24 - 20 = 4$ ⁠. 0 is the y-coordinate at $x = 2$ ⁠, not the gradient, and 8 wrongly keeps the constant 4 after differentiating.
Calculus › Differentiation and Integration

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About these cards

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.
Every numerical answer and main distractor was recomputed by script.

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