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Mathematics: explore STEM content (page 8 of 23) · openstem

All fields Software Mathematics Physics Chemistry Biology Engineering Astronomy Environmental Other Mathematics Mathematics groups

Explore STEM Content

Search the community's STEM library — free to study, yours to make your own.

Mathematics

Algebra, calculus, proofs and statistics on openstem — flashcards, notes, quizzes and plots shared by the community. Study free, or clone anything into your library.

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Note~233 words · 1 min

Adding up what you have Add every coin and bill one at a time. The order doesn't matter; the total comes out the same. Getting change Pay more than something costs and the shopkeeper gives back the difference. That's your change, and there

Mathematics

Mathematics · L1 · Money & Making Change

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Mathematics · L1 · Money & Making Change

Quiz10 questions

Which of the following is NOT one of Kolmogorov's axioms of probability?

AP(A) ≥ 0 for every event ABP(Ω) = 1CP(A ∪ B) = P(A) + P(B) for mutually exclusive A, BDP(A) = 1 − P(Aᶜ) for every event A

Mathematics

Mathematics · L4 · Probability fundamentals — 10 Q

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Mathematics · L4 · Probability fundamentals — 10 Q

Flowchart5 objects

Mathematics

Mathematics · L1 · Telling Time & Calendars · flowchart

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Mathematics · L1 · Telling Time & Calendars · flowchart

Flashcards10 cards

State the axioms of probability (Kolmogorov).1 / 10

1. P(A) ≥ 0 for every event A. 2. P(Ω) = 1. 3. For mutually exclusive events A₁, A₂, …: P(A₁ ∪ A₂ ∪ …) = P(A₁) + P(A₂) + …

Mathematics

Mathematics · L4 · Probability — Fundamentals

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Mathematics · L4 · Probability — Fundamentals

Plot1 plot · 2 params

Mathematics

Mathematics · L3 · Slope & Intercept: y = m·x + b

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Mathematics · L3 · Slope & Intercept: y = m·x + b

Flowchart11 objects

Mathematics

Mathematics · L3 · Independent, Dependent & Conditional Probability · flowchart

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Mathematics · L3 · Independent, Dependent & Conditional Probability · flowchart

Quiz6 questions

Tom has 9 marbles. Priya has 4 marbles. How many more marbles does Tom have than Priya?

A13B5C4D9

Mathematics

Mathematics · L1 · Comparison Word Problems: More & Fewer

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Mathematics · L1 · Comparison Word Problems: More & Fewer

Flashcards5 cards

Define a normal subgroup N ⊴ G.1 / 5

N is a subgroup of G such that gNg⁻¹ = N for every g ∈ G (equivalently, every left coset equals the corresponding right coset). Normal subgroups are precisely the kernels of group homomorphisms, and they allow the construction of the quotient group G/N.

Mathematics

Mathematics · L5 · Group & Ring Theory

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Mathematics · L5 · Group & Ring Theory

Note~315 words · 2 min

Belief updating, written as arithmetic Bayes' theorem tells you how to revise a probability once evidence arrives. It's one equation. The denominator is just the law of total probability, summing both branches of the tree: The medical test,

Mathematics

Mathematics · L4 · Bayesian reasoning and Bayes' theorem

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Mathematics · L4 · Bayesian reasoning and Bayes' theorem

Note~229 words · 1 min

Similar: same shape, different size Two figures are similar when every pair of corresponding angles is equal AND every pair of corresponding sides is in the same ratio. That shared ratio is the scale factor. What the scale factor does Above

Mathematics

Mathematics · L2 · Scale Drawings & Similar Figures

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Mathematics · L2 · Scale Drawings & Similar Figures

Note~201 words · 1 min

Four relationships worth knowing on sight Spot the relationship and you can find a missing angle without measuring anything. Complementary and supplementary Vertical angles Two straight lines crossing make four angles in two matching pairs.

Mathematics

Mathematics · L2 · Angle Relationships

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Mathematics · L2 · Angle Relationships

Flowchart15 objects

Mathematics

Mathematics · L2 · Two-Way Tables & Venn Diagrams · flowchart

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Mathematics · L2 · Two-Way Tables & Venn Diagrams · flowchart

Flowchart7 objects

Mathematics

Mathematics · L1 · Left or Right? A Quick Check

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Mathematics · L1 · Left or Right? A Quick Check

Quiz5 questions

Which of these best describes a rational function?

AOne polynomial divided by another polynomialBAny function containing a square rootCA function that only has whole-number outputsDA straight line

Mathematics

Mathematics · L3 · Rational Functions & Asymptotes

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Mathematics · L3 · Rational Functions & Asymptotes

Quiz6 questions

What is 17 mod 5?

A2B3C5D12

Mathematics

Mathematics · L3 · Modular Arithmetic

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Mathematics · L3 · Modular Arithmetic

Flowchart9 objects

Mathematics

Mathematics · L1 · Fact Families & Related Facts · flowchart

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Mathematics · L1 · Fact Families & Related Facts · flowchart

Flowchart15 objects

Mathematics

Mathematics · L1 · 2D Shapes & Their Attributes

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Mathematics · L1 · 2D Shapes & Their Attributes

Flowchart11 objects

Mathematics

Mathematics · L3 · Rational Functions & Asymptotes · flowchart

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Mathematics · L3 · Rational Functions & Asymptotes · flowchart

Flowchart11 objects

Mathematics

Mathematics · L3 · Algorithms & Big-O Basics · flowchart

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Mathematics · L3 · Algorithms & Big-O Basics · flowchart

Note~196 words · 1 min

Three symbols, three answers Compare two numbers and only three things can be true: one is bigger, one is smaller, or they're the same. Comparing two-digit numbers Compare 52 and 58: both have 5 tens, so that's a tie. 58 has 8 ones and 52 o

Mathematics

Mathematics · L1 · Comparing & Ordering Numbers

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Mathematics · L1 · Comparing & Ordering Numbers

Quiz6 questions

What does it mean for an algorithm to run in O(n) time?

AIt always takes exactly n secondsBIts running time grows in direct proportion to the input size nCIt never depends on the input size at allDIt doubles the input size every step

Mathematics

Mathematics · L3 · Algorithms & Big-O Basics

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Mathematics · L3 · Algorithms & Big-O Basics

Note~305 words · 2 min

Two kinds of series, two formulas Arithmetic series The trick behind it: pair the first term with the last, the second with the second-last, and so on. Every pair adds to the same total, and there are n/2 pairs. Worked, a concert hall. Fron

Mathematics

Mathematics · L3 · Arithmetic & Geometric Series

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Mathematics · L3 · Arithmetic & Geometric Series

Note~387 words · 2 min

Distance and angle instead of across and up Cartesian coordinates locate a point by how far across and how far up. Polar coordinates use how far out and which way round. Read (r, θ) as: turn through θ, then go out a distance r. It's the nat

Mathematics

Mathematics · L3 · Polar Coordinates & Graphing

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Mathematics · L3 · Polar Coordinates & Graphing

Note~178 words · 1 min

Four coins to know Penny, nickel, dime and quarter. Before you can add coins or make change, you need to look at one and know instantly which it is and what it's worth. Colour first, then size The penny is the only copper-coloured one, so i

Mathematics