This is the only arithmetic in Big Idea 4 on the AP exam. It’s worth doing correctly — and it’s one division.
No reading — this page is the reading. You’ll need 6.9’s idea: the sequential portion doesn’t shrink.
Internet region, systems side. 6.9 showed the ceiling by watching. Today you calculate it.
Every speedup question on the exam is these two lines.
Speedup is how many times faster the parallel version is: time to run sequentially ÷ time to run in parallel. A speedup of 2 means twice as fast.
Shape 1 — one task, split evenly. A job takes 60 seconds on one processor: 20 seconds must run in order, and 40 seconds can be split evenly.
| Processors | Parallel time | Speedup |
|---|---|---|
| 1 | 20 + 40 = 60 s | 60 ÷ 60 = 1 |
| 2 | 20 + 20 = 40 s | 60 ÷ 40 = 1.5 |
| 4 | 20 + 10 = 30 s | 60 ÷ 30 = 2 |
| 8 | 20 + 5 = 25 s | 60 ÷ 25 = 2.4 |
Doubling from 4 to 8 processors only took the time from 30 to 25. The 20-second sequential portion is the floor, so the speedup can never reach 3 (60 ÷ 20), no matter how many processors.
Shape 2 — separate processes, assigned to processors. This is the exam’s favorite. Three independent processes take 40, 30, and 50 seconds. On two processors, the best split puts 50 on one and 40 + 30 = 70 on the other. They run at the same time, so the parallel time is the longer one: 70 seconds. Sequential time is 40 + 30 + 50 = 120. Speedup = 120 ÷ 70 ≈ 1.71.
Distributed computing is the same idea across many separate computers connected by a network, instead of many cores in one computer. It makes problems possible that no single machine could handle — too much data to store in one place, or too much work to finish in a lifetime — like searching the whole web or analyzing data from millions of devices.
Shape 1. Change the portions and the processor count. Watch the curve flatten under its ceiling.
Shape 2. Enter process times (seconds, separated by commas) and a processor count. The calculator tries every assignment and finds the fastest.
Five questions. Write both formulas at the top of your paper first.
Volunteer projects have let ordinary people donate their computers’ idle time to research — simulating how proteins fold, searching radio-telescope data. Each home computer does a small independent piece. That’s distributed computing powered by the public.