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Mathematics: explore STEM content (page 4 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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Quiz6 questions

Why do the bars in a histogram touch each other with no gaps, unlike in a bar chart?

ABecause a histogram groups continuous numeric data into ranges (bins) that flow directly into one anotherBBecause histograms only show categories, just like bar chartsCTo make the histogram look neaterDBars in a histogram never actually touch

Mathematics

Mathematics · L2 · Histograms & Box Plots

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Mathematics · L2 · Histograms & Box Plots

Quiz6 questions

If A = {2, 3, 5, 7} and B = {1, 3, 5, 7, 9}, what is A ∩ B?

A{2, 3, 5, 7, 9}B{3, 5, 7}C{2}D{1, 9}

Mathematics

Mathematics · L3 · Sets & Set Operations

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Mathematics · L3 · Sets & Set Operations

Note~206 words · 1 min

Counting in jumps Skip counting means counting forward in equal jumps instead of one at a time. It's a fast way to count things that come in groups, like pairs of shoes or fingers on hands. Odd and even Skip counting by 2s from 2 lists only

Mathematics

Mathematics · L1 · Skip Counting & Patterns

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Mathematics · L1 · Skip Counting & Patterns

Flowchart7 objects

Mathematics

Mathematics · L2 · Scale Drawings & Similar Figures

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Mathematics · L2 · Scale Drawings & Similar Figures

Collection8 items

01Mathematics · L5 · Real Analysis Foundations

02Mathematics · L5 · Group & Ring Theory

03Mathematics · L5 · Groups: Axioms and First Examples

+5 more

Mathematics

Mathematics · L5 · Analysis, Algebra & Topology

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Mathematics · L5 · Analysis, Algebra & Topology

Flashcards7 cards

You sort a box of toy blocks by one rule: colour. What do you do with all the red blocks?1 / 7

Put all the red blocks together in one group. Every block in that group must be red — that is the one rule.

Mathematics

Mathematics · L1 · Sorting with Venn Diagrams

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Mathematics · L1 · Sorting with Venn Diagrams

Note~283 words · 1 min

Turning a solved inequality into a picture Once you have something like x > 3 or x ≤ −2, the graph has two parts: a circle at the boundary number, and shading showing which other numbers are solutions. Open circle or closed? The circle answ

Mathematics

Mathematics · L2 · Graphing Inequalities on a Number Line

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Mathematics · L2 · Graphing Inequalities on a Number Line

Quiz10 questions

In simple linear regression, what does the slope β₁ represent?

AThe predicted value of Y when X = 0BThe expected change in Y for a one-unit increase in XCThe correlation coefficient between X and YDThe proportion of variance in Y explained by X

Mathematics

Mathematics · L4 · Regression & Bayesian Methods — 10 Q

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Mathematics · L4 · Regression & Bayesian Methods — 10 Q

Note~190 words · 1 min

A matrix is a labelled grid Rows and columns of numbers, each number an entry. Dimensions are always rows first, then columns. Two rows, three columns, so that's a 2 × 3 matrix. Adding and subtracting Both matrices must have identical dimen

Mathematics

Mathematics · L3 · Introduction to Matrices

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Mathematics · L3 · Introduction to Matrices

Quiz5 questions

A fair six-sided die is about to be rolled once. What is the theoretical probability of rolling a 4?

A1/6B1/4C4/6D1/2

Mathematics

Mathematics · L2 · Probability: Experimental vs Theoretical

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Mathematics · L2 · Probability: Experimental vs Theoretical

Note~479 words · 2 min

Pick the shape before you start writing Most stuck proofs are stuck because the wrong technique was chosen in the first thirty seconds. The statement's form usually tells you which one to reach for. Direct proof Assume the hypothesis, walk

Mathematics

Mathematics · L4 · Mathematical proof techniques

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Mathematics · L4 · Mathematical proof techniques

Flashcards8 cards

What is a function table?1 / 8

A function table lists pairs of input and output values that all follow the same rule. Each input goes in, the rule is applied, and an output comes out.

Mathematics

Mathematics · L2 · Function Tables & Input-Output Rules

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Mathematics · L2 · Function Tables & Input-Output Rules

Flowchart15 objects

Mathematics

Mathematics · L2 · Circles: Circumference & Area

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Mathematics · L2 · Circles: Circumference & Area

Note~215 words · 1 min

Comparing without numbers Line up one end of each object and put them side by side. Whichever sticks out further is longer. No numbers needed at all. Measuring with everyday objects Before rulers, people measured with whatever they had: pap

Mathematics

Mathematics · L1 · Measuring Length & Weight

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Mathematics · L1 · Measuring Length & Weight

Flowchart15 objects

Mathematics

Mathematics · L3 · Sum, Difference & Double-Angle Identities

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Mathematics · L3 · Sum, Difference & Double-Angle Identities

Note~178 words · 1 min

Pair things up Every whole number is either odd or even, and pairing is the way to find out which. 6 blocks make exactly 3 pairs, so 6 is even. 5 blocks make 2 pairs and one lonely block, so 5 is odd. The last-digit shortcut Pairing up 138

Mathematics

Mathematics · L1 · Odd & Even Numbers

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Mathematics · L1 · Odd & Even Numbers

Flowchart5 objects

Mathematics

Mathematics · L2 · Area vs Perimeter

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Mathematics · L2 · Area vs Perimeter

Flowchart5 objects

Mathematics

Mathematics · L1 · Addition & Subtraction Stories · flowchart

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Mathematics · L1 · Addition & Subtraction Stories · flowchart

Note~116 words · 1 min

Sharing equally A fraction shows a part of a whole thing. Whenever you share something so everyone gets the same amount, you're using fractions. Cut a pizza into 2 equal pieces and eat one, and you ate half the pizza. The pieces have to be

Mathematics

Mathematics · L1 · Half and Quarter: Your First Fractions

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Mathematics · L1 · Half and Quarter: Your First Fractions

Note~314 words · 2 min

When SOH-CAH-TOA runs out Those ratios need a right angle. Most triangles don't have one. Oblique triangles need two new tools. Law of Sines Every side divided by the sine of its opposite angle gives the same value. Use it when you know two

Mathematics

Mathematics · L3 · Law of Sines & Cosines

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Mathematics · L3 · Law of Sines & Cosines

Flowchart9 objects

Mathematics

Mathematics · L1 · Fact Families & Related Facts

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Mathematics · L1 · Fact Families & Related Facts

Flowchart5 objects

Mathematics

Mathematics · L2 · Factors, Multiples & Primes · flowchart

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Mathematics · L2 · Factors, Multiples & Primes · flowchart

Flashcards8 cards

What does each letter in PEMDAS stand for?1 / 8

PEMDAS is a memory trick for the order to solve a math expression with more than one operation.

Mathematics

Mathematics · L2 · Order of Operations

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Mathematics · L2 · Order of Operations

Flashcards9 cards

In graph theory, what are the two basic building blocks of a graph?1 / 9

Vertices (also called nodes) — the points — and edges — the connections between pairs of vertices. A graph is just a set of vertices plus a set of edges joining some of them.

Mathematics

Mathematics · L3 · Graph Theory Basics

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Mathematics · L3 · Graph Theory Basics

Quiz6 questions

Which expression correctly gives sin(A + B)?

Asin A cos B + cos A sin BBsin A + sin BCcos A cos B − sin A sin BDsin A cos B − cos A sin B

Mathematics

Mathematics · L3 · Sum, Difference & Double-Angle Identities

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Mathematics · L3 · Sum, Difference & Double-Angle Identities

Flowchart14 objects

Mathematics

Mathematics · L2 · Subtracting Mixed Numbers with Borrowing

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Mathematics · L2 · Subtracting Mixed Numbers with Borrowing

Flowchart9 objects

Mathematics

Mathematics · L1 · Ordering Numbers from Smallest to Largest

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Mathematics · L1 · Ordering Numbers from Smallest to Largest

Note~216 words · 1 min

Two hands, two jobs At half past, the short hand sits BETWEEN two numbers, not on one. That's a good clue you've read it right. Days of the week Seven days, always in the same order, and after Sunday it starts again at Monday. Months of the

Mathematics

Mathematics · L1 · Telling Time & Calendars

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Mathematics · L1 · Telling Time & Calendars

Flowchart8 objects

Mathematics

Mathematics · L3 · Modular Arithmetic

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Mathematics · L3 · Modular Arithmetic

Note~149 words · 1 min

Multiply the numbers, then decide the sign Two separate jobs. The size comes from ordinary multiplication; the sign comes from the two signs you started with. Division uses the identical rule Three or more numbers? Count the negatives (−2)

Mathematics

Mathematics · L2 · Multiplying & Dividing Integers

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Mathematics · L2 · Multiplying & Dividing Integers

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