Quick check · Percentages
Level I · Optional · Open anytime
Mathematical Foundations & Linear Algebra
Begin with a short mathematical refresher, then explore pure linear algebra through vectors, spaces, transformations, and eigenvalues. Follow small worked calculations and quick checks at your own pace. The portfolio-risk example connects the ideas to research, and four closing sections train the mental math behind fast sanity checks.
Study any section in any order. These checks do not affect your core course or assessments. Choice answers and elective progress are tracked in this browser.
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Section 1 of 2
Start with quantities, percentages, and units
A number becomes useful when you know what it measures. A return of 0.05 is a proportion; written as a percentage it is 5%. A price of 50 is a currency amount. You cannot add a currency amount directly to a return and expect a meaningful result. Write down the unit before calculating.
A percentage change compares a difference with the original value: (new − old) / old. A percentage-point change subtracts two percentages. When a rate rises from 4% to 6%, it increases by 2 percentage points, or 50% relative to its starting rate. These statements answer different questions.
Parentheses make the intended calculation explicit. In 100 × (1 + 0.05), the growth factor is 1.05, so ending wealth is 105. Keep precision during intermediate steps and round the final presentation. Small rounding differences do not fix an incorrect denominator.
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Keep in mind: Keep the quantity, unit, and reference value attached to each number.
Pause and try two quick checks.
You can move on at any time. Each answer explains the reasoning.
Quick check · Units
Which decimal represents a return of 2.5%?
Further reading and documentation
- OpenStax: Algebra and Trigonometry ↗
- MIT OpenCourseWare: Linear Algebra ↗
- Georgia Tech: Interactive Linear Algebra ↗
- Krista King: Become a Linear Algebra Master (external paid course) ↗
- Arthur Benjamin: A performance of mathemagic (TED talk); the techniques are developed in Benjamin & Shermer, Secrets of Mental Math ↗
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The full elective is included with Level I enrollment, together with the core course and the official examination.
Go further · Optional resources
Build your mathematics, statistics, and Python toolkit.
Open these resources at any time. They are separate from the core modules and do not count toward examination eligibility, practice scores, or certification. Programming remains optional.
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Mathematical Foundations & Linear Algebra
Build mathematical confidence, then study pure linear algebra with step-by-step examples, geometric interpretation, and quick checks, closing with mental math techniques.
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Introduction to Descriptive Statistics
A compact companion to the core course: calculate medians and modes, compare ranges and quartiles, read empirical percentiles, and build honest frequency summaries.
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Introductory Python for Research
Learn to read basic Python and follow simple pandas workflows, with code examples and instant-feedback checks.
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