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Mathematics: explore STEM content (page 6 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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Flashcards8 cards

How do you add two fractions that already have the same denominator, like 2/9 + 4/9?1 / 8

Add the numerators (the top numbers) and keep the denominator the same. Then check if the answer can be simplified — here 6/9 reduces to 2/3.

Mathematics

Mathematics · L2 · Adding & Subtracting Fractions

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Mathematics · L2 · Adding & Subtracting Fractions

Quiz6 questions

Two angles are complementary. What do their measures add up to?

A45°B90°C180°D360°

Mathematics

Mathematics · L2 · Angle Relationships

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Mathematics · L2 · Angle Relationships

Collection4 items

01Mathematics · L4 · Statistical Inference — Estimation & Tests

02Mathematics · L4 · p-values and statistical significance: what they really mean

03Mathematics · L4 · Hypothesis testing decision flowchart

+1 more

Mathematics

Mathematics · L4 · Hypothesis Testing

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Mathematics · L4 · Hypothesis Testing

Flowchart5 objects

Mathematics

Mathematics · L1 · Number Lines & Rounding to Ten · flowchart

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Mathematics · L1 · Number Lines & Rounding to Ten · flowchart

Flashcards7 cards

You buy a $60 pair of shoes with a 15% discount. How do you find the sale price?1 / 7

Find 15% of $60: 0.15 × 60 = $9. Subtract that discount from the original price: $60 − $9 = $51. The sale price is $51.

Mathematics

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

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

Flowchart13 objects

Mathematics

Mathematics · L3 · The Quadratic Formula

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Mathematics · L3 · The Quadratic Formula

Flashcards7 cards

Factor: x² + 5x + 6.1 / 7

Find two numbers that multiply to 6 and add to 5: they are 2 and 3. So x² + 5x + 6 = (x + 2)(x + 3).

Mathematics

Mathematics · L3 · Quadratics

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Mathematics · L3 · Quadratics

Flowchart5 objects

Mathematics

Mathematics · L1 · Doubling & Halving · flowchart

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Mathematics · L1 · Doubling & Halving · flowchart

Flashcards10 cards

What does it mean for a number to be EVEN?1 / 10

A number is even if you can split it into two equal groups, or pair everything up with nothing left over.

Mathematics

Mathematics · L1 · Odd & Even Numbers

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Mathematics · L1 · Odd & Even Numbers

Note~395 words · 2 min

One formula, and what each piece is called The denominator comes from the law of total probability: P(E) = ΣP(E|Hᵢ)P(Hᵢ). It's the normalising sum over every hypothesis you're considering. The medical test that catches everyone out Updating

Mathematics

Mathematics · L4 · Bayes' theorem: updating beliefs with evidence

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Mathematics · L4 · Bayes' theorem: updating beliefs with evidence

Quiz6 questions

In the Euclidean algorithm, once you divide a by b and get remainder r = 0, what is GCD(a, b)?

AaBbCrDa + b

Mathematics

Mathematics · L3 · Number Theory: GCD, LCM & the Euclidean Algorithm

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Mathematics · L3 · Number Theory: GCD, LCM & the Euclidean Algorithm

Flashcards8 cards

How many sides does a triangle have?1 / 8

3 sides and 3 corners. "Tri" means three, just like a tricycle has 3 wheels.

Mathematics

Mathematics · L1 · 2D Shapes & Their Attributes

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Mathematics · L1 · 2D Shapes & Their Attributes

Note~239 words · 1 min

Magnitude AND direction A vector carries both a size and a direction. A scalar carries only size. Speed is a scalar: 60 km/h. Velocity is a vector: 60 km/h north. Draw them as arrows. The length is the magnitude, the way it points is the di

Mathematics

Mathematics · L3 · Introduction to Vectors

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Mathematics · L3 · Introduction to Vectors

Quiz5 questions

What are the two tens on either side of 62 on a number line?

A50 and 60B60 and 70C70 and 80D60 and 80

Mathematics

Mathematics · L1 · Number Lines & Rounding to Ten

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Mathematics · L1 · Number Lines & Rounding to Ten

Note~170 words · 1 min

Two kinds of sequence Arithmetic sequences Note the (n − 1): the first term hasn't had d added to it yet. Sum of the first n terms: Geometric sequences Why geometric growth feels different Arithmetic sequences trace a straight line. Geometr

Mathematics

Mathematics · L3 · Sequences & Series

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Mathematics · L3 · Sequences & Series

Quiz6 questions

Which of these is an ordinal number?

A6 pencilsB6th in lineC6 applesD6 dogs

Mathematics

Mathematics · L1 · Ordinal Numbers & Ordering

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Mathematics · L1 · Ordinal Numbers & Ordering

Flowchart7 objects

Mathematics

Mathematics · L3 · Modular Arithmetic · flowchart

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Mathematics · L3 · Modular Arithmetic · flowchart

Flowchart9 objects

Mathematics

Mathematics · L1 · Comparison Word Problems: More & Fewer

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Mathematics · L1 · Comparison Word Problems: More & Fewer

Quiz5 questions

A tally shows 4 marks for apples and 7 marks for bananas. How should the banana bar compare to the apple bar?

AThe banana bar should be the same height as the apple barBThe banana bar should be taller than the apple barCThe banana bar should be shorter than the apple barDNo bar is needed for bananas

Mathematics

Mathematics · L1 · Making & Reading Bar Graphs

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Mathematics · L1 · Making & Reading Bar Graphs

Quiz5 questions

What is (−6) × (−7)?

A42B−42C13D−13

Mathematics

Mathematics · L2 · Multiplying & Dividing Integers

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Mathematics · L2 · Multiplying & Dividing Integers

Flashcards7 cards

What is the polar coordinate system, and what do r and θ represent?1 / 7

Instead of locating a point by horizontal and vertical distances (x, y), polar coordinates locate it by a distance and an angle: r is the distance from the pole (the origin), and θ is the angle measured counterclockwise from the polar axis (the positive x-axis).

Mathematics

Mathematics · L3 · Polar Coordinates & Graphing

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Mathematics · L3 · Polar Coordinates & Graphing

Flowchart7 objects

Mathematics

Mathematics · L2 · Slope & Rate of Change · flowchart

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Mathematics · L2 · Slope & Rate of Change · flowchart

Flowchart7 objects

Mathematics

Mathematics · L1 · Patterns: Repeating & Growing

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Mathematics · L1 · Patterns: Repeating & Growing

Flowchart9 objects

Mathematics

Mathematics · L1 · Patterns: Repeating & Growing · flowchart

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Mathematics · L1 · Patterns: Repeating & Growing · flowchart

Flowchart13 objects

Mathematics

Mathematics · L1 · Comparing & Ordering Numbers · flowchart

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Mathematics · L1 · Comparing & Ordering Numbers · flowchart

Flowchart7 objects

Mathematics

Mathematics · L2 · The Coordinate Plane · flowchart

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Mathematics · L2 · The Coordinate Plane · flowchart

Flashcards5 cards

What is the mean of a set of numbers?1 / 5

The mean is the average. Add all the numbers together, then divide by how many numbers there are. For 2, 4, 6: add to get 12, divide by 3 = mean of 4.

Mathematics

Mathematics · L2 · Mean, Median, and Mode

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Mathematics · L2 · Mean, Median, and Mode

Flowchart9 objects

Mathematics

Mathematics · L4 · Bayesian reasoning and Bayes' theorem · flowchart

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Mathematics · L4 · Bayesian reasoning and Bayes' theorem · flowchart

Quiz6 questions

Which of these best describes a direct proof of 'If P then Q'?

AAssume P is true and derive Q through a chain of stepsBAssume Q is false and derive that P must also be falseCAssume the conclusion is false and search for a logical impossibilityDCheck every possible value of the variables one at a time

Mathematics

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

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

Flowchart10 objects

Mathematics

Mathematics · L2 · Exponents & Square Roots · flowchart

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Mathematics · L2 · Exponents & Square Roots · flowchart

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