High School 2 mathematics
Step 8 covers High School 2. All 25 planned activities for this grade are now translated into English, with the same quizzes and best-score tracking as the Korean site.
🧮 Calculus
Derivative Lab
Watch a secant become a tangent as you squeeze the gap between two points toward zero.
Open English lesson → 📈Applications of the Derivative
Use the sign of f'(x) and f''(x) to find extrema and concavity, then solve a real optimization problem.
Open English lesson → 🟩Integral Lab
See how Riemann sums pin down the exact area under a curve, and how area below the x-axis counts as negative.
Open English lesson → 🎯Intermediate Value Theorem Lab
Use bisection to repeatedly halve an interval and see for yourself why a continuous function must pass through every intermediate value.
Open English lesson → 📉Secant to Tangent Lab
Explore how the slope of the secant line through two points converges to the tangent slope, or derivative, as the distance h between the points approaches 0.
Open English lesson → 🔄Rotating Sector Solid Lab
Change the radius and central angle to explore the solid formed by rotating a sector about one radius. Find the surface area of the spherical sector using a net, and find its volume by splitting it into a cone and part of a sphere.
Open English lesson →📈 Functions & graphs
Exponential & Logarithmic Functions
Change the base with a slider and see the exponential and logarithmic graphs reflect across y=x like a mirror.
Open English lesson → 📊Properties of Logarithms
Verify with real numbers how multiplication turns into addition, and a power turns into multiplication.
Open English lesson → 🎯Limits & Continuity of Functions
See how a function's value can be undefined while its limit still exists, and compare three types of discontinuity.
Open English lesson → 📦Box Volume Optimization Lab
Use derivatives to find the point where the volume of a box made by cutting and folding the four corners of a square sheet of paper is maximized.
Open English lesson →🔢 Sequences & series
Arithmetic & Geometric Sequences
See Gauss's pairing trick and compound-interest growth to understand the sum formulas from the ground up.
Open English lesson → 🎯Limits of Sequences
Grow n very large and see whether a sequence converges to a value or diverges without settling down.
Open English lesson → ΣSeries Lab
Watch arithmetic and geometric series sum formulas with a bar chart and sigma notation, side by side.
Open English lesson → 🌀Grouped Sequences Lab
Pick a position in the whole sequence and see which group it lands in and where it sits inside that group.
Open English lesson → ♟️Mathematical Induction Lab
Use falling dominoes to explore the base case and inductive step of mathematical induction.
Open English lesson → 🔁Recursive Definition of Sequences Lab
Explore recursive definitions of sequences by changing the first term and the rule that generates each next term.
Open English lesson → ΣSequence Sum Lab
Explore the sum formulas for arithmetic and geometric sequences with sigma notation and bar graphs.
Open English lesson →📐 Trigonometry
Unit Circle & Trig Ratios
Rotate a point on the unit circle and watch its coordinates trace out the sin and cos waves.
Open English lesson → 📈Graphs of Trig Functions
Adjust amplitude, period, phase shift, and vertical shift to see how sin, cos, and tan graphs transform.
Open English lesson →📊 Probability & statistics
Basic Probability & Complementary Events
See why "at least one" problems get much easier once you flip them into a complementary event.
Open English lesson → 🌳Conditional Probability & Independent Trials
See with a tree diagram how drawing without replacement changes the next probability.
Open English lesson → ⚖️Random Variables & Expected Value
See the expected value as the balance point of probability as weight, with a dice prize game.
Open English lesson → 📊Binomial Distribution
See as a histogram the probability of exactly k successes when a trial repeats n times.
Open English lesson → 🔔Normal Distribution
Change the mean and standard deviation and check the 68-95-99.7 rule and standard scores.
Open English lesson → 🎯Normal Distribution & Estimation
See how a confidence interval narrows as sample size grows, estimating a population from a sample.
Open English lesson → 📏Standard Deviation & Variance
See how two groups can share a mean yet differ in spread, using deviation and variance.
Open English lesson → 📈Correlation Coefficient & Regression Line
See what the correlation coefficient means from a scatter plot, and fit a regression line yourself.
Open English lesson → 🔺Binomial Theorem Lab
Expand (a+b)ⁿ and see how the coefficients of each term connect to Pascal’s triangle.
Open English lesson → 🎱Lottery Odds Calculator
See just how low the odds of winning the lottery are when choosing 6 numbers from 45, calculate the number of combinations, and compare it with other rare events.
Open English lesson →🌀 Fun patterns
Fibonacci Sequence & Spiral
Watch squares grow into a spiral, and see the ratio of neighboring terms approach the golden ratio.
Open English lesson → ▲Pascal's Triangle
Set the number of rows and watch the triangle grow, then color odd and even numbers to reveal a fractal.
Open English lesson → 🌻Fibonacci Sequence and the Golden Ratio Lab
Explore how the ratio of two consecutive Fibonacci numbers gradually approaches the golden ratio φ.
Open English lesson →