# Units 08–09 Cumulative Benchmark Study Guide

## Structure

- 60 objective questions
- 30 questions from Unit 08
- 30 questions from Unit 09
- Four constructed responses
- Objective mastery: 48/60
- Recommended final mastery: 80/100
- Calculator, blank paper, and supplied constants permitted
- Corrections and retakes permitted

## Unit 08 — Motion, Forces & Energy

Review SI units; scalar and vector quantities; distance, displacement, speed, velocity and acceleration; position–time and velocity–time graphs; graph slope and area; free fall near Earth; contact and field forces; free-body diagrams; net force; Newton’s three laws; inertia; mass and weight; friction and drag; momentum; impulse; one-dimensional momentum conservation; collision safety; work; kinetic energy; gravitational potential-energy change; conservation and dissipation; power; efficiency; system boundaries; reference frames; model assumptions; uncertainty; and safe engineering analysis.

## Unit 09 — Electricity, Waves & Information

Review charge, current, potential difference, resistance, Ohm’s law under stated conditions, series and parallel circuits, junction current, electrical power and energy, I–V evidence, magnetic fields, electromagnets, motor effect, induction, generators, ideal transformers, wave speed, frequency, wavelength, period, amplitude, reflection, refraction, diffraction, superposition, sound, hearing safety, light, electromagnetic spectrum, wave and photon models, analog and digital signals, binary encoding, sampling, aliasing, parity, noise, error checking, storage, privacy, security, energy use and accessibility.

## Core Equations

- Average speed = total distance ÷ total time
- Average velocity = displacement ÷ elapsed time
- Acceleration = change in velocity ÷ elapsed time
- Net force = mass × acceleration
- Momentum = mass × velocity
- Impulse = change in momentum = average force × time
- Work = force × displacement in the force direction
- Kinetic energy = ½mv²
- Gravitational potential-energy change = mgΔh
- Power = energy transferred ÷ time
- Efficiency = useful output ÷ total input × 100%
- Charge = current × time
- Potential difference = energy transferred ÷ charge
- Resistance = potential difference ÷ current
- Electrical power = potential difference × current
- Electrical energy = power × time
- Wave speed = frequency × wavelength
- Period = 1 ÷ frequency

## Earth-Science Transition

The final response applies existing physics to Earth observation. Be ready to identify the measured variable, sensor, energy source, electrical pathway, signal carrier, encoding method, channel, receiver, error check, storage system, model, uncertainty and inference.

A direct measurement is not the same as a calculation. A calculation is not the same as a model. A model is not the same as an Earth-system inference.

## Evidence and System Reasoning

Define the system boundary before applying conservation, energy, circuit, wave, or information models. Identify what enters, what leaves, what is measured, and what is inferred.