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Integration78%

Differentiation92%

Vectors65%

Probability

MediumIB Math AA HL

Complex Numbers

HardIB Math AA HL

Paper 11:30:00

18Questions

85%Score

Paper 11:30:00

18Questions

85%Score

Adaptive Diagnostic

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Our diagnostic tracks 528 individual skills, not just topics, but the specific steps and contexts where you struggle. Questions adapt in real time to find your true level fast.

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Knowledge Gaps Found

Deep analysis complete

Skills tracked

528

97 Topics+42 Features+389 Micro-skills

Your Weak Areas — Pinpointed

Topic

Integration by parts

—

Skill

Apply chain rule in trig contexts

—

Feature

3D geometry problems

—

Topic

Areas between curves

—

Skill

Isolate subject with fractions

—

Not just "weak at calculus" — we identify exactly which step or context trips you up.

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Every question moves you forward

Our algorithm tracks your skill on 97 topics, 42 question types, and 389 micro-skills, then recommends the exact questions that will improve you fastest. Not random practice, surgical practice.

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Recommended For You

Targeting 528 skills across your weak areas

Highest Impact Questions

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Integration by parts

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Chain rule in 3D

apply chain rule3dGap detected

82

Areas between curves

area between curves setupDue for review

65

Quadratic equations

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Impact Score

How much this question improves your weakest micro-skills — not just topics.

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Paper 1 Mock Exam

IB Math AA HL • No calculator

110 marks

Reading Time

5 minutes

Writing Time

2 hours

Reading Time

5:00

You may read the questions but cannot write yet

Exam conditions:

No calculator allowed
Formula booklet available
Show all working

Question Bank

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4,800+ IB exam-style questions with powerful filters. Topic, difficulty, calculator, paper type. Find what you need in seconds.

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mediumExam6pts

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mediumExam

7pts

The line L passes through A(2, 5, 3) and B(4, −1, 2). Find the vector equation...

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hardExam8pts

A bag contains 5 red and 3 blue balls. Two balls are drawn without replacement...

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hardExam10pts

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hardExam9pts

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4pts

The function f is defined by f(x) = 2x³ − 3x² + 1. Find f'(x).

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In triangle ABC, AB = 8 cm, BC = 6 cm and angle ABC = 120°. Find the area...

hardExam10pts

A particle moves along a straight line. Its velocity v ms⁻¹ at time t seconds...

hardExam9pts

The function f(x) = ax³ + bx² + cx + d has a local maximum at (−1, 5) and...

Detailed Solution & Markscheme

Step-by-step with IB mark allocation

Marks: 4/4(100%)

Rearrange so all y terms (with dy) are on one side and all x terms (with dx) are on the other.

1√1 − y² dy = 4x1 + 2x² dx

Integrate both sides with respect to their variables.

∫ 1√1 − y² dy = arcsin y

Let u = 1 + 2x² so that du = 4x dx.

∫ 4x1 + 2x² dx = ln(1 + 2x²) + C

arcsin y = ln(1 + 2x²) + C

Use y = 0 when x = 0 to find C.

0 = ln(1 + 2 · 0²) + C = ln 1 + C ⟹ C = 0

Take the sine of both sides to get the explicit solution.

y = sin(ln(1 + 2x²))

MMethodAAccuracyRReasoning

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IB Markscheme

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Marks: 4/4(100%)

1√1 − y² dy = 4x1 + 2x² dx

∫ 4x1 + 2x² dx = ln(1 + 2x²) + C

0 = ln 1 + C ⟹ C = 0

y = sin(ln(1 + 2x²))

MMethodAAccuracyRReasoning

Mark Your Mistakes

Click ✕ where you went wrong

Marks: 0/4(0%)

Rearrange so all y terms (with dy) are on one side and all x terms (with dx) are on the other.

1√1 − y² dy = 4x1 + 2x² dx

Integrate both sides with respect to their variables.

∫ 1√1 − y² dy = arcsin y

Let u = 1 + 2x² so that du = 4x dx.

∫ 4x1 + 2x² dx = ln(1 + 2x²) + C

arcsin y = ln(1 + 2x²) + C

Use y = 0 when x = 0 to find C.

0 = ln(1 + 2 · 0²) + C = ln 1 + C ⟹ C = 0

Take the sine of both sides to get the explicit solution.

y = sin(ln(1 + 2x²))

Formula References

Linked to your IB formula booklet

y = ln(1 + 2x²)

y = sin(ln(1 + 2x²))

Integrate both sides of the separated equation:

∫ 1√1 − y² dy = arcsin y

Formula Booklet • IB 5.15g

∫ 1√a² − x² dx = arcsinxa + C

For the RHS, let u = 1 + 2x² so du = 4x dx:

∫ 4x1 + 2x² dx = ln(1 + 2x²) + C

Combined: arcsin y = ln(1 + 2x²) + C

Using y = 0 when x = 0 gives C = 0. Taking sine of both sides:

y = sin(ln(1 + 2x²))

Hover the book icon to see formula booklet references

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6/10

Curriculum coverage60%

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