IB Math Analysis and Approaches — 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 sequences, logs, functions, trigonometry, probability and calculus, with HL counting, complex numbers, vectors and further calculus.

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Practice deck · part of IB Mathematics: Analysis and Approaches · written against: IB Diploma Programme IB Mathematics: Analysis and Approaches 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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In an arithmetic sequence $u_3 = 11$ and $u_8 = 31$ ⁠. What is $u_{20}$ ⁠?

A) $79$
B) $83$
C) $87$
D) $75$

A) $79$

Five steps take the sequence from 11 to 31, so $d = 4$ and $u_1 = 11 - 2 \times 4 = 3$ ⁠; then $u_{20} = u_1 + 19d = 3 + 76 = 79$ ⁠. Using $20d$ instead of $(n - 1)d$ gives 83.
Number and Algebra › Sequences Series and Finance
What is the sum of the first 8 terms of the geometric sequence 3, 6, 12, …?

A) $768$
B) $384$
C) $765$
D) $1533$

C) $765$

With $u_1 = 3$ and $r = 2$ ⁠, $S_8 = \frac{3\left(2^8 - 1\right)}{2 - 1} = 3 \times 255 = 765$ ⁠. The value 384 is only the 8th term, $3 \times 2^7$ ⁠, not the sum.
Number and Algebra › Sequences Series and Finance
$f(x) = 3x - 1$ and $g(x) = x^2 + 2$ ⁠. What is $(g \circ f)(2)$ ⁠?

A) $27$
B) $17$
C) $11$
D) $30$

A) $27$

$g \circ f$ applies $f$ first: $f(2) = 5$ ⁠, then $g(5) = 25 + 2 = 27$ ⁠. Applying $g$ first gives $f(6) = 17$ ⁠, which is $(f \circ g)(2)$ ⁠.
Functions › Functions and Graphs
In triangle ABC, $A = 30^\circ$ ⁠, $B = 45^\circ$ and $a = 5$ ⁠. What is $b$ ⁠?

A) $\frac{5\sqrt{2}}{2}$
B) $5\sqrt{2}$
C) $\frac{5\sqrt{6}}{3}$
D) $10$

B) $5\sqrt{2}$

The sine rule gives $b = \frac{a\sin B}{\sin A} = \frac{5 \times \frac{\sqrt{2}}{2}}{\frac{1}{2}} = 5\sqrt{2}$ ⁠. Inverting the ratio of sines gives $\frac{5\sqrt{2}}{2}$ ⁠.
Geometry and Trigonometry › Triangles Circles and Trigonometry
A data set has mean 10 and standard deviation 3. Every value $x$ is replaced by $2x - 5$ ⁠. What are the mean and standard deviation of the new values?

A) Mean 15, standard deviation 1
B) Mean 15, standard deviation 12
C) Mean 15, standard deviation 6
D) Mean 20, standard deviation 6

C) Mean 15, standard deviation 6

The mean undergoes the full transformation, $2 \times 10 - 5 = 15$ ⁠, but subtracting 5 does not change the spread, so the standard deviation is $2 \times 3 = 6$ ⁠. Applying the $-5$ to the standard deviation as well gives 1.
Statistics and Probability › Statistics and Probability
$f(x) = (3x - 1)^4$ ⁠. What is $f'(1)$ ⁠?

A) $24$
B) $16$
C) $96$
D) $32$

C) $96$

By the chain rule $f'(x) = 4(3x - 1)^3 \times 3 = 12(3x - 1)^3$ ⁠, so $f'(1) = 12 \times 8 = 96$ ⁠. Leaving out the inner derivative 3 gives 32.
Calculus › Differentiation

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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: analysis and approaches guide for first assessment 2021, topics 1–5 (SL and AHL).
OpenStax Calculus Volumes 1–3, OpenStax Precalculus 2e, OpenStax Algebra and Trigonometry 2e and OpenStax Introductory Statistics, consulted as references; no text copied.

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