在同一個地方查看目前所有測驗包、主題測驗與概念測驗。

物理

Physics Connections Pack

Connect motion, oscillation, wave behavior, and orbital reasoning across one compact physics assessment.

Mechanics • Oscillations • Waves • Gravity and Orbits

數學

Math Linked Representations Pack

Move between transformed graphs, local rates, vectors, and complex-plane motion without treating each representation as a separate island.

Functions • Calculus • Vectors • Complex Numbers and Parametric Motion

化學

Chemistry Connected Systems Pack

Connect reaction progress, recipe limits, and solution balance across the current chemistry topics.

Rates and Equilibrium • Stoichiometry and Yield • Solutions and pH

物理

力學

用向量、軌跡、圓周運動、轉動效應、動量與碰撞，在同一條精簡的模擬分支裡理解運動與交互作用。

物理

重力與軌道

從單一質量源的重力場出發，再把位能井、圓軌道、軌道週期與逃逸速度留在同一條線索上。

物理

振盪

把位移、回復力、能量交換、阻尼與受迫共振都留在同一個振子分支裡。

物理

波動

從一條行進波走到都卜勒位移、干涉與駐波，讓波長、相位與允許模態保持連在一起。

物理

聲音

把聲音牢牢綁在真實介質上，讓縱波運動、音高與響度、拍頻與空氣柱共振都留在同一條聲學分支裡。

物理

流體

從壓力出發，連到靜水壓、連續方程、伯努利原理、浮力與終端速度。

物理

熱力學

把溫度、內能、理想氣體、熱傳與相變化放在同一條熱學路線中理解。

物理

電學

把電荷、電場與電位整理清楚，讓來源、方向與電壓意義在進入電路之前先站穩。

物理

電路

用同一套電池與負載語言，把電流、電壓、功率、支路行為與等效電阻串成一條清楚的電路分支。

物理

磁學

先看電流產生的磁場，再用同一個磁場去理解移動電荷與載流導線所受的磁力。

物理

電磁學

用磁通改變、麥士威四條定律的整合視角與電磁波，把隨時間變化的場如何耦合與傳播講清楚。

物理

光學

沿著光的波動身分走過偏振、繞射、雙縫干涉、折射、色散與全反射，再把成像系統留給獨立分支。

物理

鏡面與透鏡

把鏡面與透鏡當成成像系統比較，再用解析度極限說明真實儀器為甚麼不能無限分辨細節。

物理

現代物理

把光電效應、原子光譜、德布羅意物質波、波耳模型與放射性／半衰期留在同一條受限但誠實的現代物理分支上。

數學

函數

用父函數變換、平移後的倒數函數家族，以及同一個指數變化工作台，把圖像位移、漸近線、定義域斷裂、增長與衰減、以及目標時間問題維持在同一條可視化支線上，之後再延伸到局部變化與累積變化。

數學

微積分

從圖像上的斜率本身開始，用受限矩形工作台讓真正的極大值變得可見，再把極限與連續性的行為留在同一個目標點上，最後延伸到有號面積與累積量，讓變化率與總變化保持連在同一條視覺支線上。

數學

向量

用同一個二維平面，把向量讀成箭頭、有序對、矩陣作用、對齊量與投影，之後再讓同一套語言自然橋接回運動。

數學

複數與參數運動

用一條受限的數學支線，把複數平面、單位圓旋轉、極座標、三角恆等式、反三角角度判讀，以及由方程描出的運動軌跡都綁在同一套座標語言上。

化學

反應速率與平衡

用一條緊湊的化學支線，先讓碰撞成功率解釋反應速率，再用同一套粒子語言延伸到可逆變化與新的平衡混合。

化學

化學計量與產率

用一條緊湊的化學支線，讓可視化配方工作台把化學計量比、限制試劑與百分產率連在同一套粒子與配方語言裡。

化學

溶液與 pH

用一條緊湊的化學支線，讓濃度、溶解度、酸鹼平衡、緩衝與 pH 都維持在同一個有邊界的溶液故事中。

電腦科學

演算法與搜尋

用一條受限的電腦科學支線，讓可視化的列表操作一路長成同一個連貫的圖遍歷工作台，於是排序、二分搜尋、鄰接、廣度優先搜尋、深度優先搜尋與已訪狀態都能留在緊湊的即時互動介面上。

物理

Simple Harmonic Motion

SHM

See one repeating system from displacement to acceleration and back again, with the math tied directly to the motion on screen.

物理

Oscillation Energy

Energy in SHM

Watch kinetic and potential energy trade places in simple harmonic motion while the total stays fixed by amplitude and spring stiffness.

物理

Wave Speed and Wavelength

Wave speed

Follow one traveling wave across the same medium and connect crest spacing, travel delay, source timing, and the relation v = f lambda on one honest live stage.

物理

Sound Waves and Longitudinal Motion

Sound waves

See sound as a longitudinal wave by keeping parcel motion, compression and rarefaction, probe timing, and energy transfer tied to one compact medium-first bench.

物理

Pitch, Frequency, and Loudness / Intensity

Pitch and loudness

Keep one compact sound bench while separating pitch from frequency, loudness from amplitude and an amplitude-squared intensity cue, and probe delay from the source sound itself.

物理

Beats

Superpose two nearby sound frequencies, watch the fast carrier sit inside a slower envelope, and connect beat rate to the frequency difference on one compact bench.

物理

Doppler Effect

Doppler effect

Watch a moving sound source compress wavefronts ahead and stretch them behind, then see how source motion and observer motion combine to change the heard pitch on one bounded classical bench.

物理

Wave Interference

Interference

Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.

物理

Standing Waves

Standing waves

Track fixed nodes, moving antinodes, and harmonic mode shapes on one live string while the same probe trace shows the underlying oscillation in time.

物理

Resonance in Air Columns / Open and Closed Pipes

Air-column resonance

Compare open and closed pipe boundary conditions on one compact air column so standing-wave shapes, missing even harmonics, probe motion, and pressure cues stay tied to the same resonance state.

物理

Uniform Circular Motion

UCM

Track a particle moving at constant speed around a circle and connect radius, angular speed, tangential speed, centripetal acceleration, and the inward-force requirement to the same live state.

物理

Damping / Resonance

Damping

Explore how damping removes energy, how driving frequency changes amplitude, and why resonance becomes dramatic near the natural frequency.

物理

Vectors and Components

Vectors

Rotate and scale a live vector, decompose it into horizontal and vertical parts, and watch those components drive the same straight-line motion and geometry.

物理

Torque

Push on one pivoted bar and see how lever arm distance, force direction, and turning effect stay tied to the same compact rotational bench.

物理

Static Equilibrium / Centre of Mass

Static equilibrium

Shift one support region under one loaded plank and see how centre of mass, support reactions, and torque balance decide whether the object stays stable or tips.

物理

Rotational Inertia / Moment of Inertia

Rotational inertia

Keep the same total mass and torque, then slide equal masses inward or outward to see why moment of inertia makes some rotors much harder to spin up than others.

物理

Rolling Motion

Rolling motion

Roll a sphere, cylinder, hoop, or custom mass distribution down one incline and see how rolling without slipping ties translation, rotation, and rotational inertia to the same honest run.

物理

Angular Momentum

Angular momentum

Treat angular momentum as rotational momentum on one compact rotor where mass radius and spin rate stay tied to the same readouts, response maps, and same-L conservation story.

物理

Momentum and Impulse

Momentum / Impulse

Push one cart with a timed force pulse and watch momentum, impulse, and force-time area stay tied to the same motion, readouts, and graphs.

物理

Conservation of Momentum

Momentum conservation

Watch two carts trade momentum through one bounded internal interaction and see the total stay fixed while the individual momenta, velocities, and center-of-mass motion update together.

物理

Collisions

Collide two carts on one honest track, keep total momentum in view, and see how elasticity, mass, and incoming speed shape the rebound or stick-together outcome.

物理

Projectile Motion

Projectile

Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.

物理

Gravitational Fields

Gravity fields

See how one source mass creates an inward gravitational field, how source mass and distance set the field strength, and how a probe mass turns that field into force without changing the field itself.

物理

Gravitational Potential and Potential Energy

Gravity potential

See one source mass create a negative potential well, compare how potential and potential energy change with distance, and connect the downhill slope of phi to the gravitational field on the same live model.

物理

Pressure and Hydrostatic Pressure

Pressure in fluids

Use one piston-and-tank bench to connect force per area, pressure acting in all directions, and the way density, gravity, and depth build hydrostatic pressure.

物理

Continuity Equation

Continuity

Keep one steady stream tube on screen and use Q = Av to connect cross-sectional area, flow speed, and the same volume flow rate through narrow and wide sections.

物理

Bernoulli's Principle

Bernoulli

Follow one steady ideal-flow pipe and see how pressure, speed, and height trade within the same Bernoulli budget while continuity keeps the flow-rate story honest.

物理

Buoyancy and Archimedes' Principle

Buoyancy

Use one immersed-block bench to connect pressure difference, displaced fluid, and the density balance behind floating, sinking, and neutral buoyancy.

物理

Drag and Terminal Velocity

Terminal speed

Drop one body through a fluid and use mass, area, and drag strength to see drag grow with speed until force balance settles into terminal velocity.

物理

Temperature and Internal Energy

Temperature vs U

Compare average particle motion with whole-sample energy, vary amount and heating, and see why a phase-change shelf breaks naive temperature-only reasoning on one compact thermal bench.

物理

Ideal Gas Law and Kinetic Theory

Ideal gas law

Connect pressure, volume, temperature, and particle number on one bounded particle box, then read the same pressure changes back as changes in particle speed and wall-collision rate.

物理

Heat Transfer

Heat transfer

See heat as energy transfer driven by temperature difference while conduction, convection, and radiation compete on one compact bench with honest pathway rates.

物理

Specific Heat and Phase Change

Specific heat and phase change

See why the same energy pulse changes different materials by different temperature amounts, and why a phase-change shelf can absorb or release energy without changing temperature on one compact thermal bench.

物理

Circular Orbits and Orbital Speed

Orbital speed

See why a circular orbit needs the right sideways speed, how gravity supplies the centripetal acceleration, and how source mass and radius together set orbital speed and period on one bounded live model.

物理

Electric Fields

E-fields

See how source-charge sign, distance, and superposition set the electric field at one probe, then watch a test charge turn that field into a force without changing the field itself.

物理

Kepler's Third Law and Orbital Periods

Orbital periods

Compare circular orbits around one source mass and see why larger orbits take longer: the path is longer, the circular speed is lower, and the same live model makes the period law visible without hiding the gravity-speed link.

物理

Electric Potential

Potential

Map how source-charge sign and distance shape electric potential, compare potential differences across one honest scan line, and connect the downhill slope of V to the electric field.

物理

Capacitance and Stored Electric Energy

Capacitance

Keep one parallel-plate capacitor on screen so geometry, stored charge, field strength, and stored electric energy stay tied to the same bounded battery-and-plates model.

物理

Escape Velocity

Escape speed

Launch outward from one bounded gravity source and see how source mass, launch radius, and total specific energy decide whether the object escapes or eventually returns.

物理

Basic Circuits

Circuits

Keep one battery and two resistors in view while current, voltage, resistance, Ohm's law, and the contrast between series and parallel all stay tied to one honest circuit.

物理

Light as an Electromagnetic Wave

Light and spectrum

Connect electromagnetic waves to visible light, color, frequency, and the broader spectrum while one compact stage keeps the spectrum rail, field-pair sketch, and medium-linked wavelength changes tied together.

物理

Polarization

Use one compact polarizer bench to see polarization as the orientation story of transverse waves, how angle mismatch sets transmitted light, and why one ideal polarizer makes unpolarized light emerge with one chosen axis.

物理

Power and Energy in Circuits

Circuit power

Keep one source and one resistive load in view while current, power, and accumulated energy over time stay tied to the same honest circuit.

物理

Diffraction

Watch a wave spread after one narrow opening, see why diffraction grows when wavelength competes with slit width, and build the wave-optics bridge toward double-slit interference.

物理

Double-Slit Interference

Double slit

Use two coherent slits and one screen to connect path difference, phase difference, and fringe spacing to wavelength, slit separation, and screen distance on one compact optics bench.

物理

Refraction / Snell's Law

Refraction

Watch one light ray cross a boundary, connect refractive index to speed change, and see Snell's law set the refracted angle, bending direction, and critical-angle limit on the same live diagram.

物理

Series and Parallel Circuits

Series / Parallel

Switch the same two loads between one loop and two branches, then track how current, voltage, brightness, and charge flow reorganize without changing the battery.

物理

Dispersion / Refractive Index and Color

Dispersion and color

Use one compact thin-prism bench to see how refractive index can depend on wavelength, why different colors bend by different amounts, and how a bounded prism model separates colors without widening into a full spectroscopy subsystem.

物理

Total Internal Reflection

TIR

Push a ray from a higher-index medium toward a lower-index boundary, watch the critical angle emerge, and see the same live diagram hand off from ordinary refraction to full internal reflection.

物理

Kirchhoff Loop and Junction Rules

Kirchhoff rules

Write one current-balance equation at a junction and one voltage-balance equation around a loop on the same bounded grouped circuit, then see those equations match the live branch currents and drops.

物理

Mirrors

Use plane, concave, and convex mirrors to track equal-angle reflection, signed image distance, and magnification on the same live ray diagram.

物理

Equivalent Resistance

R_eq

Reduce one highlighted resistor group into an equivalent block, then collapse the whole mixed circuit honestly and watch how the total current and grouped behavior change together.

物理

Magnetic Fields

B-fields

See how current direction, wire spacing, distance, and superposition set the magnetic field around one or two long straight wires, with the stage arrows and scan graphs tied to the same live source pattern.

物理

Faraday's Law and Lenz's Law

Faraday / Lenz

Track one magnet passing one coil and see how changing magnetic flux linkage creates induced emf while Lenz's law fixes the response direction, with the stage, galvanometer, and graphs all driven by the same bounded motion.

物理

Maxwell's Equations Synthesis

Maxwell synthesis

See what each Maxwell equation says physically, how sources and circulation differ, and why changing electric and magnetic fields together unify electricity, magnetism, and light.

物理

Electromagnetic Waves

EM waves

See how changing electric and magnetic fields travel together as one rightward wave, with the local field pair, source-to-probe delay, and propagation cue all tied to the same compact live stage.

物理

Magnetic Force on Moving Charges and Currents

Magnetic force

Launch one moving charge through a uniform magnetic field, compare it with a same-direction current segment, and connect force direction, curvature, and current-based force on one bounded live stage.

物理

Lens Imaging

Lens imaging

Trace principal rays through converging and diverging lenses, connect the signed thin-lens equation to the diagram, and watch image distance and magnification respond to the same object setup.

物理

RC Charging and Discharging

RC response

Keep one resistor-capacitor loop on screen so capacitor voltage, current, stored energy, and the time constant all stay tied to the same charging or discharging setup.

物理

Optical Resolution / Imaging Limits

Optical resolution

Image two nearby point sources through one finite aperture and see why diffraction, wavelength, and aperture diameter limit how sharply an optical system can separate them.

物理

Photoelectric Effect

Photoelectric effect

Use one compact lamp-to-metal bench to see why light frequency sets electron emission, why intensity alone fails below threshold, and how stopping potential reads the electron energy honestly.

物理

Internal Resistance and Terminal Voltage

Internal resistance

Keep one non-ideal source and one load on screen so emf, internal drop, terminal voltage, current, and wasted power stay tied to the same one-loop circuit.

物理

Atomic Spectra

Atomic spectra

Link discrete emission and absorption lines to allowed energy-level gaps with one compact ladder-and-spectrum bench that keeps transitions, wavelengths, and mode changes tied together.

物理

de Broglie Matter Waves

Matter waves

Use one compact matter-wave bench to see how particle momentum sets wavelength, why heavier or faster particles get shorter wavelengths, and how whole-number loop fits form a bounded bridge toward early quantum behavior.

物理

Bohr Model

Bohr model

Use a compact hydrogen bench to connect quantized energy levels, allowed transitions, and named spectral-line series while staying clear that Bohr is a useful historical model rather than the final quantum description.

物理

Radioactivity and Half-Life

Half-life

Use one compact decay bench to see why each nucleus decays unpredictably, why large samples still follow a regular half-life curve, and how to read remaining-count graphs honestly.

數學

Graph Transformations

Graph transforms

Move one parent curve with honest controls so shifts, vertical scale, and reflections stay tied to the same overlaid graph and landmark points.

數學

Rational Functions / Asymptotes and Behavior

Rational functions

Vary one shifted reciprocal family so domain breaks, vertical and horizontal asymptotes, intercepts, and removable-hole behavior stay tied to the same graph.

數學

Exponential Change / Growth, Decay, and Logarithms

Exponential change

Change one starting value, one rate, and one target so growth, decay, doubling or half-life, and logarithmic target time all stay tied to the same live curve.

數學

Derivative as Slope / Local Rate of Change

Derivative as slope

Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.

數學

Limits and Continuity / Approaching a Value

Limits and continuity

Move one target-distance slider inward from both sides, compare the finite-limit guide with the actual point, and separate continuous, removable-hole, jump, and blow-up behavior on one graph-first bench.

數學

Optimization / Maxima, Minima, and Constraints

Optimization and constraints

Move one rectangle width under a fixed 24 meter perimeter and watch height, area, and local slope respond together so the square maximum emerges from the same bench.

數學

Integral as Accumulation / Area

Integral as area

Drag one upper bound across a source curve, watch signed area and the accumulation graph update together, and separate current source height from the running total.

數學

Vectors in 2D

2D vectors

Combine, subtract, and scale vectors on one plane so magnitude, direction, and components stay tied to the same live object.

數學

Matrix Transformations / Stretch, Shear, Reflection

Matrix transforms

Let one 2 by 2 matrix act on a grid, the basis vectors, and a sample shape so stretch, shear, reflection, and combined plane changes stay visual instead of symbolic-only.

數學

Dot Product / Angle and Projection

Dot product

Keep two vectors, their angle, the signed projection of one onto the other, and the dot product visible together so alignment reads geometrically instead of as memorized cases.

數學

Complex Numbers on the Plane

Complex numbers

Read complex numbers as points and vectors on one plane, then keep addition and multiplication geometric instead of symbolic-only.

數學

Unit Circle / Sine and Cosine from Rotation

Unit circle rotation

Keep one rotating point, its x and y projections, and the sine-cosine traces linked so the unit circle becomes the live source of both functions.

數學

Polar Coordinates / Radius and Angle

Polar coordinates

Keep one point visible in polar and Cartesian views at the same time so radius and angle turn directly into x and y on the plane.

數學

Parametric Curves / Motion from Equations

Parametric curves

Keep x(t), y(t), the traced path, and the moving point visible together so shape and traversal stay distinct.

數學

Trig Identities from Unit-Circle Geometry

Trig identities

Keep one rotating point and its projections visible so the core trig identities stay tied to geometry instead of detached symbol rules.

數學

Inverse Trig / Angle from Ratio

Inverse trig

Keep one polar point and its coordinate signs visible so inverse trig becomes angle-from-ratio reasoning with quadrant checks instead of a calculator-only output.

化學

Reaction Rate / Collision Theory

Reaction rate

Keep one chemistry box visible so temperature, concentration, activation threshold, and catalysts can be read as changes in successful collisions instead of chemistry slogans.

化學

Dynamic Equilibrium / Le Chatelier's Principle

Dynamic equilibrium

Watch a reversible chemistry bench keep changing microscopically while the mixture settles toward a new balance after each disturbance.

化學

Stoichiometric Ratios and Recipe Batches

Recipe ratios

Keep one reaction recipe visible so stoichiometric ratios read as complete batches, not detached worksheet proportions.

化學

Limiting Reagent and Leftover Reactants

Limiting reagent

Use one recipe bench to see which reactant caps the output first and why the other reactant can remain in excess.

化學

Percent Yield and Reaction Extent

Percent yield

Compare actual output with the same theoretical recipe cap so percent yield stays visual and honest on one shared bench.

化學

Concentration and Dilution

Concentration

Use one beaker to separate how concentration changes when you add solvent from how it changes when you add more solute.

化學

Solubility and Saturation

Solubility

Keep dissolved amount, excess solid, and current capacity in one beaker so saturation reads like a visible limit instead of a slogan.

化學

Acid-Base / pH Intuition

pH intuition

Keep acid amount, base amount, water, and the pH strip visible together so acidity and basicity stay intuitive rather than memorized.

化學

Buffers and Neutralization

Buffers

Keep neutralization, buffer reserve, and the pH strip visible together so steady pH does not look like unchanged chemistry.

電腦科學

Sorting and Algorithmic Trade-offs

Sorting trade-offs

Watch sorting as visible work on a live list so input order, comparisons, and writes stay concrete instead of collapsing into one final answer.

電腦科學

Binary Search / Halving the Search Space

Binary search

Keep an ordered list, the low-mid-high markers, and the shrinking interval visible together so binary search feels visual instead of procedural.

電腦科學

Graph Representation and Adjacency Intuition

Graph adjacency

Keep one live graph, one local neighborhood, and one frontier cue visible together so graph structure feels readable before traversal rules get formal.

電腦科學

Breadth-First Search and Layered Frontiers

BFS

Keep the queue frontier, visited count, and graph layers visible together so breadth-first search reads as a layered process instead of a procedure list.

電腦科學

Depth-First Search and Backtracking Paths

DFS

Keep the stack frontier, current depth, and branch order visible together so depth-first search feels like disciplined backtracking instead of random wandering.

電腦科學

Frontier and Visited State on Graphs

Frontier and visited

Keep repeat skips, waiting frontier nodes, and already-expanded nodes visible together so cycle handling feels like honest bookkeeping on one graph bench.