High School Algebra 2

Decimals with no pattern, no repeat, no end — like √2 and π.

Negative + positive, and how to think about each.

Find primes with the Sieve of Eratosthenes — interactive.

GCD, LCM and divisibility rules — the hidden structure of numbers.

5! = 5×4×3×2×1 = 120. Click and watch the tree fan out.

Every number on the number line — the big family.

Distance from zero, ignoring sign — |−7| = 7.

6.02 × 10²³ — a tidy way to write very big or very small numbers.

Round to the nearest 10, 100, or decimal place — and the tie-breaker rules.

Two numbers whose only common factor is 1 — they share no factors.

Counting → naturals → integers → rationals → reals → complex. The story.

a + bi where i² = −1. The numbers that live off the real line.

Real on x, imaginary on y — every complex number is a 2D point.

What you can measure: length, mass, capacity, time, temperature.

A standard chunk you compare other things against — and why standards matter.

Convert any length, mass, volume, area, speed, or temperature — with the cancel-the-units trick.

Inch, foot, pound, gallon, acre, Fahrenheit — the system that runs the US, with a visual size chart.

kilo, mega, giga, milli, micro, nano — 14 prefixes that scale every metric unit.

mm, cm, m, km — and inches and feet.

mm, cm, m, km — base 10, easy to convert.

Inch, foot, yard, mile — and the conversions you really need.

Read clocks, count minutes, work with durations.

How many days in this month? When does the leap year fall?

Twelve months, names and origins — and how many days each one has.

Seven days, where the names come from, and how the modern week was set.

Sunrise to sunrise — and the 24 hours in between.

One trip around the sun — and why it's not exactly 365 days.

Spring, summer, autumn, winter — and the tilt of the Earth that drives them.

Seconds, minutes, hours, days — convert between any two.

Measuring elapsed time — for races, recipes and physics experiments.

Two ways to display the same time — read either at a glance.

Swap a letter for a number. The simplest move in algebra.

Combine like terms — simplify with a tap.

3x and 5x add to 8x. 3x and 5y don't combine. Why like terms matter.

Multiply out the brackets — distribute, FOIL, then simplify.

Balance both sides of a scale and solve for the unknown.

ax + b = c. The cleanest equation — one variable, one solution.

Slope-intercept, point-slope, two-point — every form for y = mx + b.

If P(a) = 0, then (x − a) is a factor. The fastest factor check there is.

Polynomials in fractions. Add, subtract, multiply, divide — same rules as fractions.

Break x² + 5x + 6 into (x+2)(x+3) — split the middle.

Find two numbers that multiply to c and add to b — the quadratic factor trick.

x = (−b ± √(b² − 4ac)) / 2a — solves every quadratic.

Two equations, two unknowns — substitute, eliminate, or matrix-solve.

Letters stand in for unknown numbers. The first idea — and why it works.

Parentheses, square brackets, braces — when each one is used and why.

Cancel, combine and rewrite — make the expression as small as possible.

Less-than, greater-than, and number-line shading.

Same moves as equations — except multiplying by a negative flips the sign.

What number times itself is 16? See roots as the inverse of powers.

6.02 × 10²³ — a tidy way to write very big or very small numbers.

What number, multiplied by itself three times, gives this?

Square, cube, fourth, fifth — the general inverse of powers.

Less-than, greater-than, and number-line shading.

Same moves as equations — except multiplying by a negative flips the sign.

Shade the half-plane below or above — and the boundary line tells you which.

ax + b = c. The cleanest equation — one variable, one solution.

Maximise (or minimise) a linear thing under linear constraints.

Find two numbers that multiply to c and add to b — the quadratic factor trick.

Rewrite ax² + bx + c into a(x − h)² + k — and solve any quadratic.

Parabola playground — change a, b, c and see the curve respond.

x = (−b ± √(b² − 4ac)) / 2a — solves every quadratic.

Add, subtract and multiply expressions with x², x³ and beyond.

Long division — but the divisor and dividend are polynomials.

Expand (a + b)ⁿ without multiplying — Pascal's triangle does the work.

Union, intersection, difference, complement — the visual grammar of sets.

Twice the input, twice (or half) the output — two flavours of proportion.

Slide m and b on y = mx + b and watch the line move.

f(3) means: drop 3 in for x, simplify, read the answer.

Mirror across the y-axis (even) or rotate around the origin (odd).

The matrix that undoes another — like 1/x but for matrices.

1, 4, 9, 16… spot the pattern, predict the next.

Sum of a sequence with constant difference — and the n(n+1)/2 trick.

Sum of a sequence with constant ratio — and when it converges.

∑ — the compact way to write a long sum.

Sums that go on forever — and the surprising ones that still settle on a number.

Arrows with size and direction — add and subtract them visually.

Vectors with length 1 — the direction without the magnitude.

Multiply two vectors to get a number — and read off the angle between them.

Multiply two 3D vectors to get a third one perpendicular to both.

A single number that tells you if a matrix is invertible — and how it scales area.

Numbers in a rectangle — the language of transformations and systems.

Row times column — a rule that's everywhere from graphics to neural nets.

The matrix that undoes another — like 1/x but for matrices.

Shade the half-plane below or above — and the boundary line tells you which.

Slide m and b on y = mx + b and watch the line move.

The waves trigonometry draws when you sweep an angle.