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Mathematics: explore STEM content (page 5 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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Flashcards9 cards

What is an ordinary differential equation (ODE), and what does its order mean?1 / 9

An ODE relates an unknown function y(x) to its derivatives, e.g. dy/dx = 3x − y. The order is the highest derivative that appears — dy/dx = f(x,y) is first order, d²y/dx² = f(x,y,y′) is second order.

Mathematics

Mathematics · L4 · Differential Equations — First-Order ODEs

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Mathematics · L4 · Differential Equations — First-Order ODEs

Note~212 words · 1 min

Three numbers, four facts A fact family is three numbers linked by adding and subtracting. From those three you can write four true number sentences: two additions and two subtractions. Take 4, 5 and 9. Since 4 + 5 = 9, three more facts com

Mathematics

Mathematics · L1 · Fact Families & Related Facts

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Mathematics · L1 · Fact Families & Related Facts

Flashcards9 cards

What is a translation?1 / 9

A translation slides every point of a figure the same distance in the same direction. The shape doesn't turn or flip — it just moves, keeping its size and orientation exactly the same.

Mathematics

Mathematics · L2 · Transformations: Translations, Reflections & Rotations

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Mathematics · L2 · Transformations: Translations, Reflections & Rotations

Quiz5 questions

Skip count by 2s: 2, 4, 6, __. What number is missing?

A7B8C9D10

Mathematics

Mathematics · L1 · Skip Counting & Patterns

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Mathematics · L1 · Skip Counting & Patterns

Flowchart5 objects

Mathematics

Mathematics · L1 · Simple Multiplication · flowchart

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Mathematics · L1 · Simple Multiplication · flowchart

Flowchart14 objects

Mathematics

Mathematics · L2 · Graphing Inequalities on a Number Line · flowchart

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Mathematics · L2 · Graphing Inequalities on a Number Line · flowchart

Flowchart9 objects

Mathematics

Mathematics · L1 · Symmetry & Reflection · flowchart

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Mathematics · L1 · Symmetry & Reflection · flowchart

Note~201 words · 1 min

From tally to bar Once you've counted a group, that count IS the bar height. Nothing more complicated than that. Most and least You don't even need the numbers. Your eyes can find the tallest and shortest bars straight away, which is exactl

Mathematics

Mathematics · L1 · Making & Reading Bar Graphs

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Mathematics · L1 · Making & Reading Bar Graphs

Flashcards9 cards

Define a holomorphic (complex-differentiable) function.1 / 9

f: U → ℂ (U open in ℂ) is holomorphic at z₀ if lim_{h→0} [f(z₀+h) − f(z₀)]/h exists, where h → 0 through complex values from every direction — a far stronger requirement than real differentiability.

Mathematics

Mathematics · L5 · Complex Analysis

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Mathematics · L5 · Complex Analysis

Quiz5 questions

A kite flies above a tree. What does 'above' tell you?

AThe kite is lower than the treeBThe kite is higher up than the treeCThe kite is behind the treeDThe kite and the tree are the same height

Mathematics

Mathematics · L1 · Position & Direction Words

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Mathematics · L1 · Position & Direction Words

Flashcards8 cards

What is a two-way table used for?1 / 8

A two-way table organizes counts for two categories at once. For example, a survey could record each student's grade level (the rows) crossed with their favorite subject (the columns) — every cell shows how many students fit both categories.

Mathematics

Mathematics · L2 · Two-Way Tables & Venn Diagrams

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Mathematics · L2 · Two-Way Tables & Venn Diagrams

Flashcards10 cards

What is a line of symmetry?1 / 10

A line of symmetry is an imaginary line that cuts a shape into two matching halves. If you fold the shape along that line, both sides land exactly on top of each other.

Mathematics

Mathematics · L1 · Symmetry & Reflection

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Mathematics · L1 · Symmetry & Reflection

Quiz5 questions

A survey of 90 students records grade level against favorite subject in the table below. What is the grand total shown in the table?

A60B90C96D88

Mathematics

Mathematics · L2 · Two-Way Tables & Venn Diagrams

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Mathematics · L2 · Two-Way Tables & Venn Diagrams

Flowchart7 objects

Mathematics

Mathematics · L1 · Patterns: Repeating & Growing · flowchart

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Mathematics · L1 · Patterns: Repeating & Growing · flowchart

Flashcards9 cards

What makes a relationship between x and y "proportional"?1 / 9

A relationship is proportional if y is always a constant multiple of x — that is, y = kx for some fixed number k. Every pair of values shares the same ratio y/x, and if x doubles, y doubles too.

Mathematics

Mathematics · L2 · Proportional Relationships

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Mathematics · L2 · Proportional Relationships

Plot1 plot · 2 params

Mathematics

Mathematics · L5 · Normal Density: shift the mean μ and scale σ

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Mathematics · L5 · Normal Density: shift the mean μ and scale σ

Note~241 words · 1 min

One rule, shown several times A function table pairs inputs with outputs. Every pair follows the same hidden rule. Hunting for the rule Using the rule Writing a rule from a real pattern If 1 pencil costs $2, 2 cost $4, and 3 cost $6, the ru

Mathematics

Mathematics · L2 · Function Tables & Input-Output Rules

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Mathematics · L2 · Function Tables & Input-Output Rules

Plot1 plot · 2 params

Mathematics

Mathematics · L3 · The Cosine Wave: y = a·cos(b·x)

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Mathematics · L3 · The Cosine Wave: y = a·cos(b·x)

Flowchart16 objects

Mathematics

Mathematics · L4 · Derivative rules overview

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Mathematics · L4 · Derivative rules overview

Flowchart11 objects

Mathematics

Mathematics · L3 · How Many Solutions Does a System Have?

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Mathematics · L3 · How Many Solutions Does a System Have?

Note~447 words · 2 min

One extra requirement, enormous consequences Complex differentiability demands the limit be the same no matter which direction h approaches 0 from. In ℝ there are only two directions. In ℂ there are infinitely many, and forcing them all to

Mathematics

Mathematics · L5 · Complex Analysis: Holomorphic Functions and Cauchy's Theorem

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Mathematics · L5 · Complex Analysis: Holomorphic Functions and Cauchy's Theorem

Flashcards5 cards

What does x mean in algebra?1 / 5

x is a placeholder for an unknown number. The goal is to find what number x must be to make the equation true.

Mathematics

Mathematics · L2 · Introduction to Algebra

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Mathematics · L2 · Introduction to Algebra

Quiz5 questions

What is 3/4 written as a percent?

A34%B43%C75%D25%

Mathematics

Mathematics · L2 · Decimals & Percents

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Mathematics · L2 · Decimals & Percents

Flowchart8 objects

Mathematics

Mathematics · L1 · Number Bonds to 10 and 20 · flowchart

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Mathematics · L1 · Number Bonds to 10 and 20 · flowchart

Flowchart5 objects

Mathematics

Mathematics · L3 · Logic & Truth Tables · flowchart

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Mathematics · L3 · Logic & Truth Tables · flowchart

Flashcards11 cards

What does it mean when an equation has 'variables on both sides'?1 / 11

The letter x (or another variable) appears in terms on the left side AND the right side, like 5x + 3 = 2x + 12. Before you can do the usual two-step moves, you first gather all the x-terms onto one side by adding or subtracting one of them from both sides.

Mathematics