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Mathematics: explore STEM content (page 13 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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Quiz5 questions

Which of these is a recursive definition of a sequence?

Aa_n = 3n + 1Ba_1 = 4, a_n = a_(n-1) + 3Ca_n = 2^nDa_n = n²

Mathematics

Mathematics · L3 · Recursive Sequences & Fibonacci

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Mathematics · L3 · Recursive Sequences & Fibonacci

Quiz3 questions

Solve: x + 6 = 10.

Ax = 16Bx = 4Cx = 6Dx = 60

Mathematics

Mathematics · L2 · Solving for x

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Mathematics · L2 · Solving for x

Note~192 words · 1 min

Doubling Doubling makes a number twice as big. The easy way is to add it to itself: double 4 is 4 + 4 = 8. A doubles fact is just an addition where both numbers match, like 6 + 6. Learn 6 + 6 = 12 and you've learned double 6 as well; they'r

Mathematics

Mathematics · L1 · Doubling & Halving

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Mathematics · L1 · Doubling & Halving

Flowchart11 objects

Mathematics

Mathematics · L5 · Algebraic Structures

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Mathematics · L5 · Algebraic Structures

Quiz6 questions

The numbers 4, 5, and 9 form a fact family. Which of these is NOT one of the four facts?

A4 + 5 = 9B9 - 5 = 4C9 + 4 = 5D5 + 4 = 9

Mathematics

Mathematics · L1 · Fact Families & Related Facts

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Mathematics · L1 · Fact Families & Related Facts

Quiz8 questions

Which of the following is NOT one of the topology axioms for τ on X?

A∅ and X are both in τBτ is closed under arbitrary unionsCτ is closed under finite intersectionsDτ is closed under arbitrary intersections

Mathematics

Mathematics · L5 · Point-Set Topology

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Mathematics · L5 · Point-Set Topology

Collection1 items

01Mathematics · L4 · Probability Foundations

Mathematics

Mathematics · L4 · Probability Distributions

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Mathematics · L4 · Probability Distributions

Flashcards7 cards

You know two angles and a side of a triangle (AAS or ASA). Which law finds the missing sides, and why does it work?1 / 7

The Law of Sines. In any triangle, the ratio of a side to the sine of its opposite angle is the same for all three sides:

Mathematics

Mathematics · L3 · Law of Sines & Cosines

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Mathematics · L3 · Law of Sines & Cosines

Collection7 items

01Mathematics · L1 · Counting and Numbers

02Mathematics · L1 · Place Value: Tens and Ones

03Mathematics · L1 · Basic 2D Shapes

+4 more

Mathematics

Mathematics · L1 · Counting, Shapes & Fractions

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Mathematics · L1 · Counting, Shapes & Fractions

Flowchart7 objects

Mathematics

Mathematics · L1 · Skip Counting & Patterns · flowchart

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Mathematics · L1 · Skip Counting & Patterns · flowchart

Flowchart9 objects

Mathematics

Mathematics · L2 · Range, Outliers & Data Spread · flowchart

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Mathematics · L2 · Range, Outliers & Data Spread · flowchart

Quiz5 questions

What do we call the flat pattern a 3D solid makes when you unfold it along its edges?

AA netBA cross-sectionCA projectionDA prism

Mathematics

Mathematics · L2 · Surface Area of Prisms & Pyramids

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Mathematics · L2 · Surface Area of Prisms & Pyramids

Collection20 items

01Mathematics · L1 · Fact Families & Related Facts

02Mathematics · L1 · Estimating & Benchmark Numbers

03Mathematics · L1 · Comparison Word Problems: More & Fewer

+17 more

Mathematics

Mathematics · L1 · Number Facts & Problem Solving

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Mathematics · L1 · Number Facts & Problem Solving

Note~272 words · 1 min

Pairs that make a target A number bond is two numbers that add to make a target. Learning the bonds to 10 and 20 by heart makes everything else faster, because you stop counting and start remembering. Each bond works both ways round: 7 + 3

Mathematics

Mathematics · L1 · Number Bonds to 10 and 20

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Mathematics · L1 · Number Bonds to 10 and 20

Flowchart7 objects

Mathematics

Mathematics · L3 · Graphing Trig Functions · flowchart

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Mathematics · L3 · Graphing Trig Functions · flowchart

Flowchart7 objects

Mathematics

Mathematics · L2 · Decimals & Percents · flowchart

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Mathematics · L2 · Decimals & Percents · flowchart

Note~255 words · 1 min

Rational: it can be written as a fraction That includes whole numbers (5 = 5/1), ordinary fractions (3/4), and negatives (−2/3). In decimal form a rational number always does one of exactly two things: Irrational: it can't An irrational num

Mathematics

Mathematics · L2 · Rational vs Irrational Numbers

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Mathematics · L2 · Rational vs Irrational Numbers

Collection19 items

01Mathematics · L1 · Counting and Sorting

02Mathematics · L1 · Tally Marks

03Mathematics · L1 · Sorting with Venn Diagrams

+16 more

Mathematics

Mathematics · L1 · Statistics

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Mathematics · L1 · Statistics

Note~240 words · 1 min

Two things happening together You can already find the chance of one event, like rolling a 3. A compound event asks about two or more together: flip a coin AND roll a die. To handle that you first need to count every possible combination. T

Mathematics

Mathematics · L2 · Compound Events & Probability

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Mathematics · L2 · Compound Events & Probability

Flowchart17 objects

Mathematics

Mathematics · L2 · Volume & Surface Area of Prisms · flowchart

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Mathematics · L2 · Volume & Surface Area of Prisms · flowchart

Flowchart9 objects

Mathematics

Mathematics · L1 · Bridging Through 10 to Add

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Mathematics · L1 · Bridging Through 10 to Add

Note~347 words · 2 min

Population versus sample All of statistical inference is one move: use what the sample tells you to say something responsible about the population you couldn't measure. Why not just ask everyone? Random versus biased In a random sample ever

Mathematics

Mathematics · L3 · Sampling & Statistical Inference Basics

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Mathematics · L3 · Sampling & Statistical Inference Basics

Quiz3 questions

What is 4 + 3?

A6B7C8D5

Mathematics

Mathematics · L1 · Numbers and Counting

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Mathematics · L1 · Numbers and Counting

Flashcards8 cards

You have 12 cookies and share them equally among 4 friends. How many cookies does each friend get?1 / 8

3 cookies each. Give one cookie at a time to each friend, going around the group, until all 12 are gone: 4 friends × 3 cookies = 12 cookies.

Mathematics

Mathematics · L1 · Simple Division

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Mathematics · L1 · Simple Division

Flashcards10 cards

State the Fundamental Theorem of Arithmetic.1 / 10

Every integer n > 1 is either prime or can be written as a unique product of prime numbers (up to order). Example: 360 = 2³ · 3² · 5.

Mathematics

Mathematics · L4 · Number Theory & Combinatorics

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Mathematics · L4 · Number Theory & Combinatorics

Flashcards7 cards

The sun will rise tomorrow morning. Is this certain, likely, unlikely, or impossible?1 / 7

It is certain. The sun has risen every single morning, so we know for sure it will happen again.

Mathematics

Mathematics · L1 · Likely, Unlikely, Certain

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Mathematics · L1 · Likely, Unlikely, Certain

Flashcards8 cards

12 sweets are shared equally between 3 friends. How many sweets does each friend get?1 / 8

Each friend gets 4 sweets. 12 ÷ 3 = 4. Sharing them out one at a time keeps it fair.

Mathematics

Mathematics · L1 · Fractions of a Group

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Mathematics · L1 · Fractions of a Group

Flashcards8 cards

What does i² equal, and why does that rule matter for complex numbers?1 / 8

i² = −1. Every time a product of two complex numbers produces an i² term, that rule is what lets you turn it into a real number — it is the single fact that makes all complex arithmetic work.

Mathematics

Mathematics · L3 · Complex Number Operations

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Mathematics · L3 · Complex Number Operations

Flowchart7 objects

Mathematics

Mathematics · L3 · Parametric Equations & Motion · flowchart

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Mathematics · L3 · Parametric Equations & Motion · flowchart

Flowchart5 objects

Mathematics

Mathematics · L1 · Sorting with Venn Diagrams · flowchart

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Mathematics · L1 · Sorting with Venn Diagrams · flowchart

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