STARMAST full index
summary
This is a complete index of links to all available written materials on the STARMAST site, sorted by topics.
The study guide for each topic is marked with:
- (✕) when its QuickCheck problem remains incomplete
- (✓) when all questions have been answered correctly
Study guides, questions, answers
Key skills in algebra
| Topic | guide | questions | answers |
|---|---|---|---|
| Introduction to rearranging equations | guide | questions | answers |
| Rationalizing the denominator | guide | questions | answers |
| Introduction to solving simultaneous equations | guide | questions | answers |
| Factorization | guide | questions | answers |
Solving equations
| Topic | guide | questions | answers |
|---|---|---|---|
| Introduction to quadratic equations | guide | questions | answers |
| Completing the square | guide | questions | answers |
| The quadratic formula | guide | questions | answers |
Topics in arithmetic
| Topic | guide | questions | answers |
|---|---|---|---|
| Introduction to sigma notation | guide | questions | answers |
Exponentials and logarithms
| Topic | guide | questions | answers |
|---|---|---|---|
| Laws of indices | guide | questions | answers |
| Solving exponential equations | guide | questions | answers |
| Introduction to logarithms | guide | questions | answers |
| Solving equations involving logarithms | guide | questions | answers |
Angles and trigonometry
| Topic | guide | questions | answers |
|---|---|---|---|
| Radians | guide | questions | answers |
| Introduction to trigonometry (degrees) | guide | questions | answers |
| Introduction to trigonometry (radians) | guide | questions | answers |
| Trigonometric identities (degrees) | guide | questions | answers |
| Trigonometric identities (radians) | guide | questions | answers |
Topics in complex numbers
| Topic | guide | questions | answers |
|---|---|---|---|
| Introduction to complex numbers | guide | questions | answers |
| Arithmetic on complex numbers | guide | questions | answers |
Topics in vectors
| Topic | guide | questions | answers |
|---|---|---|---|
| Introduction to vectors | guide | questions | answers |
| Vector addition and scalar multiplication | guide | questions | answers |
| The scalar product | guide | questions | answers |
Topics in calculus
| Topic | guide | questions | answers |
|---|---|---|---|
| Introduction to differentiation and the derivative | guide | questions | answers |
| The product rule | guide | questions | answers |
| The quotient rule | guide | questions | answers |
| The chain rule | guide | questions | answers |
| Introduction to integration | guide | questions | answers |
| Introduction to partial differentiation | guide | questions | answers |
| Multivariate chain rule | guide | questions | answers |
Probability and statistics
| Topic | guide | questions | answers |
|---|---|---|---|
| Introduction to probability | guide | questions | answers |
| PMFs, PDFs, CDFs | guide | questions | answers |
| Expected value, variance, standard deviation | guide | questions | answers |
| Conditional probability | guide | questions | answers |
| Law of total probability and Bayes’ theorem | guide | questions | answers |
| Introduction to hypothesis testing | guide | questions | answers |
Overviews
| Topic | overview |
|---|---|
| Probability distributions | overview |
Factsheets
Mathematics
| Topic | factsheet |
|---|---|
| Laws of logarithms | factsheet |
| Laws of indices | factsheet |
| Trigonometric identities (degrees) | factsheet |
| Trigonometric identities (radians) | factsheet |
| Hyperbolic identities | factsheet |
| Rules of calculus | factsheet |
| List of derivatives | factsheet |
| List of integrals | factsheet |
| Greek letters | factsheet |
Statistics
| Topic | factsheet |
|---|---|
| Beta distribution | factsheet |
| Binomial distribution | factsheet |
| Chi-squared distribution | factsheet |
| Continuous uniform distribution | factsheet |
| Discrete uniform distribution | factsheet |
| Exponential distribution | factsheet |
| \(F\)-distribution | factsheet |
| Gamma distribution | factsheet |
| Geometric distribution | factsheet |
| Lognormal distribution | factsheet |
| Negative binomial distribution | factsheet |
| Normal distribution | factsheet |
| Poisson distribution | factsheet |
| \(t\)-distribution | factsheet |
Proof sheets
| Topic | proof sheet |
|---|---|
| Quadratic formula | proof sheet |
| Scalar product | proof sheet |
| Derivatives of functions from first principles | proof sheet |
| Rules of differentiation | proof sheet |
| PMFs, PDFs, CDFs | proof sheet |
| Law of total probability and Bayes’ theorem | proof sheet |
Calculators
Mathematics
| Topic | calculator |
|---|---|
| Blank 2D graphical | calculator |
| Blank 3D graphical | calculator |
| Solving quadratic equations | calculator |
Statistics
| Topic | calculator |
|---|---|
| \(t\)-testing | calculator |
| \(Z\)-testing | calculator |
| \(Z\)-scores | calculator |
Other interactive apps
| Topic | calculator |
|---|---|
| Coin flip | interactive |
| Coin flip with tracking | interactive |
| \(6\)-sided die roll | interactive |
| \(n\)-sided die roll | interactive |
| Hypothesis testing flowchart | interactive |
| Mean and variance of normal distribution | interactive |
| Mean and variance of exponential distribution | interactive |
| Mean and variance of beta distribution | interactive |