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Calculus

The ten rungs of the Calculus ladder as a year: the average rate and the limit; the derivative by the power rule and the chain rule; motion, the marginal unit, optimisation and related rates in the shop; the integral as accumulation — every one of them a number you can measure on the Science Floor or cost at the Fab Shop.

THE MIX · HOW MUCH OF EACH CORE SUBJECT THIS COURSE CARRIES · IN ORDER
MATHSCIENCEREADING & WRITINGTECHNOLOGY & TRADES
The squares are a picture of a course — how much of each core subject its own rooms carry, read from the rooms’ text — never a score of a student. Every course in a lab is graded to the core across the board; the squares say which columns it feeds most.
OFFERED ASThe Year · 36 wkSemester 1 · 18 wkSemester 2 · 18 wkQuarter 1 · 9 wkQuarter 2 · 9 wkQuarter 3 · 9 wkQuarter 4 · 9 wk
WHAT YOU WILL BE ABLE TO DO
  • Evaluate limits and interpret the derivative as an instantaneous rate
  • Differentiate with the power and chain rules and apply derivatives to motion
  • Solve optimisation, marginal-cost and related-rates problems from the labs
  • Interpret the definite integral as accumulated change and compute it
AT A GLANCE · 36 WEEKS
Q1 The rate and the limit — Two Minutes
Q2 The derivative — The Ramp That Proves the Squared Second
Q3 Calculus in the shop — The break-even and the marginal unit
Q4 The integral · accumulation — The Second Hill Can Never Be Taller

Semester 1

WEEKS 1–18 · QUARTERS 1 AND 2
The rate and the limit
WEEKS 1–9
THE WEEKS · THE ROOMS EACH ONE OPENS
WK 1–4
Average rate of change
The slope between two points on something you measured.
WK 5–7
The limit
What the rate heads toward as the interval shrinks.
WK 8–9
THE PROJECT · WHAT THE QUARTER IS FOR
Two Minutes
The question. Two minutes: how fast does your output fall — the average rate over the first minute, the second, the last ten seconds, and what it is heading toward?
The make. Two Minutes — the build on the Science Floor, in the Movement Floor: the number, the count, the sheet.
The evidence. The fatigue sheet with the shrinking average rates and the limit argued, handed in through the Science Floor
HS-LS1-3HS-LS1-7HS-FHS-A
The derivative
WEEKS 10–18
THE WEEKS · THE ROOMS EACH ONE OPENS
WK 10–12
The power rule
The slope of x to the n, in one move.
WK 13–16
The chain rule and motion
A function inside a function; position, velocity, acceleration.
WK 17–18
THE PROJECT · WHAT THE QUARTER IS FOR
The Ramp That Proves the Squared Second
The question. The ramp that proves the squared second: from the position readings, what are the velocity and the acceleration — as derivatives, then as a fit?
The make. The Ramp That Proves the Squared Second — the build on the Science Floor, in the Fab Shop: the number, the count, the sheet.
The evidence. The ramp sheet with position differentiated twice against the measured acceleration, handed in through the Science Floor
MS-PS2-2HS-PS2-1HS-F

Semester 2

WEEKS 19–36 · QUARTERS 3 AND 4
Calculus in the shop
WEEKS 19–27 · IN THIS OFFERING
THE WEEKS · THE ROOMS EACH ONE OPENS
WK 19–21
The marginal unit
The cost of the next one, as a derivative.
WK 22–25
Optimise; related rates
The least material, the most volume; two rates tied by one equation.
WK 26–27
THE PROJECT · WHAT THE QUARTER IS FOR
The break-even and the marginal unit
The question. At the Fab Shop: what does the next part cost, where is the break-even, and what dimensions use the least material for the volume the order needs?
The make. A costed production run at the Fab Shop with the marginal cost, the break-even and the optimised part dimensions worked as derivatives
The evidence. The run sheet with the derivatives shown, handed in through the Fab Shop’s business lane and kept in My Work
HS-FHS-A
The integral · accumulation
WEEKS 28–36
THE WEEKS · THE ROOMS EACH ONE OPENS
WK 28–31
The integral
Area under the curve as a sum of thin pieces.
WK 32–34
Accumulation
The total from the rate: distance from speed, energy from power.
WK 35–36
THE PROJECT · WHAT THE QUARTER IS FOR
The Second Hill Can Never Be Taller
The question. The second hill can never be taller: integrate the force over the track to get the energy — and show the area under the curve is the height you measured.
The make. The Second Hill Can Never Be Taller — the build on the Science Floor, in the Fab Shop: the number, the count, the sheet.
The evidence. The energy sheet with the integral computed and matched to the measured height, handed in through the Science Floor
MS-PS3-5HS-PS3-1HS-PS3-2HS-AHS-F

A course is a quarter, a semester or a year — nine, eighteen or thirty-six weeks — a project a quarter. Offered as the year, a semester or a quarter, it is the same course seen through a window. A lab is a family: its year, each of its tracks as a course, and its rooms. The evidence is what a student hands in through the room; the Report reads it from there. Nothing in the catalog is a grade.

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THE PASS · THIS COURSE AND EVERY OTHER ONE
One pass includes Calculus and every course in the catalog. Pick a pass, or enter a school code; checkout stays on this page.
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