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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~215 words · 1 min

One skill, a whole shopping trip Discounts, tax, tips and markup all start identically: find the percent of the price. Then you either add it or subtract it. Discount and tax, side by side Tips without a calculator Find 10% by moving the de

Mathematics

Mathematics · L2 · Percent Applications: Discount, Tax & Tip

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Flashcards10 cards

What does Big-O notation describe about an algorithm?1 / 10

It describes how the running time (or number of steps) grows as the input size n grows — not the exact number of seconds, just the shape of the growth as n gets larger. Constant factors and small details are ignored.

Mathematics

Mathematics · L3 · Algorithms & Big-O Basics

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Flashcards8 cards

What is a frequency table?1 / 8

A frequency table lists every value (or category) that appears in a data set alongside a count of how many times it occurs. Tallying the raw data into a table is usually the first step in making sense of it.

Mathematics

Mathematics · L2 · Data Displays: Dot Plots & Frequency Tables

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Note~316 words · 2 min

Two categories at once A two-way table records counts for two things together: here, grade level down the rows and favourite subject across the columns. Each cell counts students who are in BOTH. Relative frequency A count compared to a tot

Mathematics

Mathematics · L2 · Two-Way Tables & Venn Diagrams

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Flowchart9 objects

Mathematics

Mathematics · L3 · Circles: Arcs, Sectors & Equations · flowchart

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Collection8 items

01Mathematics · L2 · Integers and Negative Numbers

02Mathematics · L2 · Introduction to Algebra

03Mathematics · L2 · Fractions, Decimals, and Percents

+5 more

Mathematics

Mathematics · L2 · Pre-Algebra & Ratios

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Flowchart11 objects

Mathematics

Mathematics · L3 · Proof Techniques: Direct, Contrapositive & Contradiction · flowchart

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Quiz6 questions

What two properties fully define a vector?

AMagnitude and directionBLength and areaCOnly its magnitudeDIts x-component only

Mathematics

Mathematics · L3 · Introduction to Vectors

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Flowchart11 objects

Mathematics

Mathematics · L3 · Graphing Trig Functions · flowchart

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Flashcards8 cards

What is a rational function?1 / 8

A function that can be written as one polynomial divided by another, f(x) = p(x) / q(x), where q(x) is not the zero polynomial. Since division by zero is undefined, the domain excludes every x that makes q(x) = 0.

Mathematics

Mathematics · L3 · Rational Functions & Asymptotes

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Flowchart9 objects

Mathematics

Mathematics · L4 · Function composition flowchart

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Quiz5 questions

A fish tank is 40 cm long, 20 cm wide, and 25 cm tall. What is its volume?

A20,000 cm³B8,500 cm³C2,000 cm³D85 cm³

Mathematics

Mathematics · L2 · Volume & Surface Area of Prisms

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Flashcards9 cards

What is the radius of a circle?1 / 9

The radius (r) is the distance from the center of the circle to any point on its edge. Every radius of the same circle has the same length.

Mathematics

Mathematics · L2 · Circles: Circumference & Area

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Flowchart9 objects

Mathematics

Mathematics · L1 · Fractions of a Group

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Flowchart9 objects

Mathematics

Mathematics · L2 · Algebraic Expressions · flowchart

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Flashcards8 cards

What are complementary angles?1 / 8

Two angles whose measures add up to 90°. They don't need to be next to each other — they just need to sum to a right angle.

Mathematics

Mathematics · L2 · Angle Relationships

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Quiz5 questions

You flip a coin and roll a 6-sided die. Using the counting principle, how many total outcomes are possible?

A6B8C12D36

Mathematics

Mathematics · L2 · Compound Events & Probability

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Flowchart11 objects

Mathematics

Mathematics · L2 · Function Tables & Input-Output Rules · flowchart

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Flashcards10 cards

In y = A·sin(B(x − C)) + D, what does A control, and how do you find its value from the equation?1 / 10

A controls the amplitude — how far the graph rises and falls above and below its midline. Amplitude = |A|. For example, y = 3·sin(x) oscillates between −3 and 3.

Mathematics

Mathematics · L3 · Graphing Trig Functions

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Flowchart7 objects

Mathematics

Mathematics · L2 · Same Sign or Different Sign?

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Flowchart5 objects

Mathematics

Mathematics · L1 · Addition & Subtraction Stories · flowchart

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Note~455 words · 2 min

A differential equation ties a function to its own rate of change. Separable equations An ODE is separable if it can be written . Move all the y-terms to one side and all the x-terms to the other, then integrate both sides independently: W

Mathematics

Mathematics · L4 · Solving first-order differential equations

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Flashcards8 cards

What does an exponent tell you to do?1 / 8

An exponent tells you how many times to multiply a number (the base) by itself. In 5³, the base is 5 and the exponent is 3, so you multiply 5 × 5 × 5.

Mathematics

Mathematics · L2 · Exponents & Square Roots

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Note~378 words · 2 min

The property that makes optimisation tractable Convexity is the line between problems you can solve and problems that are, in general, hopeless. In a convex problem the local view IS the global view, which is exactly what lets a gradient me

Mathematics

Mathematics · L5 · Convex Optimization: Convexity, Duality, and KKT Conditions

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Flashcards7 cards

Sam has 8 stickers. Ana has 5 stickers. How many more stickers does Sam have?1 / 7

3 more. Subtract the smaller amount from the bigger amount: 8 - 5 = 3.

Mathematics

Mathematics · L1 · Comparison Word Problems: More & Fewer

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Note~195 words · 1 min

The theorem Right triangle, legs a and b, hypotenuse c: Triples that come out whole are worth knowing on sight: The triangle below is drawn on the grid. Read the legs off the axes, then confirm the hypotenuse yourself. Distance is Pythagora

Mathematics

Mathematics · L3 · The Pythagorean Theorem & Coordinate Geometry

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Note~246 words · 1 min

An exponent is a counter It counts how many copies of the base get multiplied together. Squares and cubes Square roots undo squaring A root asks squaring's question backwards: what times itself gives this? Estimating a root that isn't exact

Mathematics

Mathematics · L2 · Exponents & Square Roots

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Flowchart9 objects

Mathematics

Mathematics · L3 · Polar Coordinates & Graphing · flowchart

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Note~203 words · 1 min

x on both sides Two-step equations keep x on one side. Multi-step ones often don't. Distribute, then combine, then solve A number outside brackets multiplies EVERY term inside. The reliable order for any multi-step equation: distribute, com

Mathematics

Mathematics · L2 · Multi-Step Equations & Inequalities

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Quiz6 questions

Simplify: (x² − 16) / (x − 4).

Ax + 4Bx − 4Cx² − 4D16 / x

Mathematics

Mathematics · L3 · Rational Expressions & Equations

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Mathematics

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Mathematics

Mathematics · L2 · Percent Applications: Discount, Tax & Tip

Mathematics · L3 · Algorithms & Big-O Basics

Mathematics · L2 · Data Displays: Dot Plots & Frequency Tables

Mathematics · L2 · Two-Way Tables & Venn Diagrams

Mathematics · L3 · Circles: Arcs, Sectors & Equations · flowchart

Mathematics · L2 · Pre-Algebra & Ratios

Mathematics · L3 · Proof Techniques: Direct, Contrapositive & Contradiction · flowchart

Mathematics · L3 · Introduction to Vectors

Mathematics · L3 · Graphing Trig Functions · flowchart

Mathematics · L3 · Rational Functions & Asymptotes

Mathematics · L4 · Function composition flowchart

Mathematics · L2 · Volume & Surface Area of Prisms

Mathematics · L2 · Circles: Circumference & Area

Mathematics · L1 · Fractions of a Group

Mathematics · L2 · Algebraic Expressions · flowchart

Mathematics · L2 · Angle Relationships

Mathematics · L2 · Compound Events & Probability

Mathematics · L2 · Function Tables & Input-Output Rules · flowchart

Mathematics · L3 · Graphing Trig Functions

Mathematics · L2 · Same Sign or Different Sign?

Mathematics · L1 · Addition & Subtraction Stories · flowchart

Mathematics · L4 · Solving first-order differential equations

Mathematics · L2 · Exponents & Square Roots

Mathematics · L5 · Convex Optimization: Convexity, Duality, and KKT Conditions

Mathematics · L1 · Comparison Word Problems: More & Fewer

Mathematics · L3 · The Pythagorean Theorem & Coordinate Geometry

Mathematics · L2 · Exponents & Square Roots

Mathematics · L3 · Polar Coordinates & Graphing · flowchart

Mathematics · L2 · Multi-Step Equations & Inequalities

Mathematics · L3 · Rational Expressions & Equations