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Mathematics: explore STEM content (page 23 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~221 words · 1 min

Splitting into equal parts You have 12 cookies and 4 friends. Hand them out one at a time going round the group until they're gone, and everyone ends up with 3. That's 12 ÷ 4 = 3. The ÷ symbol means divide, or share equally. Two questions,

Mathematics

Mathematics · L1 · Simple Division

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Mathematics · L1 · Simple Division

Flowchart7 objects

Mathematics

Mathematics · L2 · Adding & Subtracting Fractions · flowchart

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Mathematics · L2 · Adding & Subtracting Fractions · flowchart

Flowchart11 objects

Mathematics

Mathematics · L3 · Coordinate Geometry · flowchart

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Mathematics · L3 · Coordinate Geometry · flowchart

Plot3 segments

Mathematics

Mathematics · L3 · A Right Triangle on the Grid

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Mathematics · L3 · A Right Triangle on the Grid

Note~244 words · 1 min

Three ways to write one ratio A ratio compares two quantities. Two cups of flour for every three of sugar can be written: Same relationship, three notations. Pick whichever suits the question. Simplifying Divide both sides by their greatest

Mathematics

Mathematics · L2 · Ratios & Unit Rates

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Mathematics · L2 · Ratios & Unit Rates

Collection8 items

01Mathematics · L3 · Permutations, Combinations & Probability

02Mathematics · L3 · Independent, Dependent & Conditional Probability

03Mathematics · L3 · Permutations, Combinations & Probability

+5 more

Mathematics

Mathematics · L3 · Probability

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Mathematics · L3 · Probability

Flowchart18 objects

Mathematics

Mathematics · L4 · Linear algebra concept map

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Mathematics · L4 · Linear algebra concept map

Flashcards5 cards

What is a negative number?1 / 5

A negative number is less than zero. On a number line, negative numbers sit to the left of zero. Temperature below freezing is a good real-life example: −5°C is 5 degrees below zero.

Mathematics

Mathematics · L2 · Integers and Negative Numbers

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Mathematics · L2 · Integers and Negative Numbers

Flowchart7 objects

Mathematics

Mathematics · L2 · Ratios and Proportions

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Mathematics · L2 · Ratios and Proportions

Flashcards11 cards

State the ε–δ definition of lim(x→a) f(x) = L.1 / 11

For every ε > 0 there exists δ > 0 such that 0 < |x − a| < δ implies |f(x) − L| < ε. In words: f(x) can be made arbitrarily close to L by taking x sufficiently close (but not equal) to a.

Mathematics

Mathematics · L4 · Calculus I — Limits & Derivatives

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Mathematics · L4 · Calculus I — Limits & Derivatives

Flowchart11 objects

Mathematics

Mathematics · L3 · Mathematical Induction

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Mathematics · L3 · Mathematical Induction

Note~226 words · 1 min

Putting groups together Some stories ask how many there are altogether. Watch for the words altogether, in total, or now. Maya has 4 apples and picks 3 more. To find how many she has now, add: 4 + 3 = 7. Taking some away Other stories ask h

Mathematics

Mathematics · L1 · Addition & Subtraction Stories

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Mathematics · L1 · Addition & Subtraction Stories

Flowchart19 objects

Mathematics

Mathematics · L3 · Sets & Set Operations

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Mathematics · L3 · Sets & Set Operations

Flashcards9 cards

What does it mean to write A = {2, 4, 6, 8}?1 / 9

A is the set containing exactly the elements 2, 4, 6, and 8. Order and repetition do not matter — {2, 4, 6, 8} and {8, 6, 4, 2} are the same set.

Mathematics

Mathematics · L3 · Sets & Set Operations

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Mathematics · L3 · Sets & Set Operations

Flashcards8 cards

What two pieces of information define a vector?1 / 8

A vector is defined by its magnitude (length) and its direction. It's often drawn as an arrow — the length of the arrow shows the magnitude, and the way it points shows the direction.

Mathematics

Mathematics · L3 · Introduction to Vectors

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Mathematics · L3 · Introduction to Vectors

Quiz6 questions

This parabola is drawn with a = 1, b = 0 and c = −4, so its equation is y = x² − 4. Where does it cross the x-axis?

AAt x = −4 and x = 4BAt x = −2 and x = 2CAt x = 0 onlyDIt never crosses the x-axis

Mathematics

Mathematics · L3 · Reading Graphs — 6 Q

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Mathematics · L3 · Reading Graphs — 6 Q

Flowchart9 objects

Mathematics

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

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

Note~243 words · 1 min

Comparing without measuring Long before a ruler, you can tell which of two things is longer just by lining them up carefully. That's called direct comparison. Place them side by side with one end lined up EXACTLY together, like two pencils

Mathematics

Mathematics · L1 · Comparing Length: Longer, Shorter, Taller

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Mathematics · L1 · Comparing Length: Longer, Shorter, Taller

Flowchart14 objects

Mathematics

Mathematics · L4 · Choosing an ODE solution method

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Mathematics · L4 · Choosing an ODE solution method

Flashcards10 cards

What is a 'table of values' used for?1 / 10

It's a way to find points on a line before you draw it. Pick a few x-values, plug each into the equation, solve for y, and you get (x, y) pairs you can plot.

Mathematics

Mathematics · L2 · Graphing Linear Equations

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Mathematics · L2 · Graphing Linear Equations

Quiz3 questions

Which property of ℝ guarantees that every Cauchy sequence converges?

ACompletenessBCompactnessCConnectednessDDensity of ℚ

Mathematics

Mathematics · L5 · Real Analysis

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Mathematics · L5 · Real Analysis

Note~218 words · 1 min

Slope is a rate, not just a steepness It answers: when x goes up by one, what happens to y? Reading slope from a table No graph needed. Watch what the output does each time the input steps up by one. What the sign tells you Drag m below and

Mathematics

Mathematics · L2 · Slope & Rate of Change

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Mathematics · L2 · Slope & Rate of Change

Flowchart7 objects

Mathematics

Mathematics · L3 · Sets & Set Operations · flowchart

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Mathematics · L3 · Sets & Set Operations · flowchart

Quiz3 questions

Lagrange's theorem states that if H is a subgroup of a finite group G, then:

A|H| divides |G|B|G| divides |H|C|H| = |G| − 1D|H|² = |G|

Mathematics

Mathematics · L5 · Group & Ring Theory

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Mathematics · L5 · Group & Ring Theory

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