# Complete AP Physics 1 & C, AP Statistics & AP Computer Science A Study Guide

> Complete AP STEM exam preparation for AP Physics 1 & C (kinematics, dynamics, rotational motion, E&M), AP Statistics (probability, sampling distributions, confidence intervals, hypothesis testing), and AP Computer Science A & Principles (Java OOP, recursion, sorting, networking)

- **Canonical URL:** https://flashcards.world/guides/en/pillar-ap-physics-1-c-ap-statistics-ap-computer-science-a-study-guide/
- **Markdown URL:** https://flashcards.world/guides/en/pillar-ap-physics-1-c-ap-statistics-ap-computer-science-a-study-guide.md
- **Topic / Curriculum:** AP Physics 1 & C, AP Statistics & AP Computer Science A / Principles
- **Language:** en

# Complete AP Physics 1 & C, AP Statistics & AP Computer Science A Study Guide

Master AP Physics 1, AP Physics C (Mechanics & E&M), AP Statistics, and AP Computer Science A (Java) with our 192-card progressive flashcard curriculum, formula & Java quick-reference tables, FRQ rubrics, and 8-week spaced-repetition study plan.

> **[Explore All Flashcard Sets for This Exam on flashcards.world](https://flashcards.world/flashcards/?q=AP%20Physics%201%20%26%20C%2C%20AP%20Statistics%20%26%20AP%20Computer%20Science%20A%20High-Yield%20Review&back_lng=en)**

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## 1. Complete 6-Deck Progressive Curriculum Matrix (192 Flashcards)

| Module | Mastery Level | Curated Flashcard Deck | Cards | Direct Study Link |
| :--- | :--- | :--- | :--- | :--- |
| **Module 1** | `basic` | **[AP Physics 1 & C: Kinematics, Newton's Laws, Work-Energy Theorem & Linear Momentum](/flashcards/sets/19ab42ba-e89c-40cd-a0a9-bad7a9037bdd/)** | 32 | [Study Set →](https://flashcards.world/flashcards/sets/19ab42ba-e89c-40cd-a0a9-bad7a9037bdd/) |
| **Module 2** | `intermediate` | **[AP Physics 1 & C: Rotational Dynamics, Simple Harmonic Motion, Electrostatics & DC Circuits](/flashcards/sets/f3c4718a-70d7-4672-a5e0-c4b55041f0b1/)** | 32 | [Study Set →](https://flashcards.world/flashcards/sets/f3c4718a-70d7-4672-a5e0-c4b55041f0b1/) |
| **Module 3** | `basic` | **[AP Statistics: Exploring Data, Normal Distribution, Linear Regression & Experimental Design](/flashcards/sets/d4547d81-4507-4bd2-a49c-4b61243f5810/)** | 32 | [Study Set →](https://flashcards.world/flashcards/sets/d4547d81-4507-4bd2-a49c-4b61243f5810/) |
| **Module 4** | `intermediate` | **[AP Statistics: Probability, Sampling Distributions, Confidence Intervals & Hypothesis Tests (z, t, Chi-Square)](/flashcards/sets/67e66f7a-28d0-4bb9-a16d-0fc1fa1c4c6e/)** | 32 | [Study Set →](https://flashcards.world/flashcards/sets/67e66f7a-28d0-4bb9-a16d-0fc1fa1c4c6e/) |
| **Module 5** | `advanced` | **[AP Computer Science A: Java Primitives, Control Flow, Classes, Objects, Strings, 1D/2D Arrays & ArrayLists](/flashcards/sets/c2f1ae27-6687-4cc1-aa6c-63704efbf2ca/)** | 32 | [Study Set →](https://flashcards.world/flashcards/sets/c2f1ae27-6687-4cc1-aa6c-63704efbf2ca/) |
| **Module 6** | `advanced` | **[AP Computer Science A: Inheritance, Polymorphism, Recursion & Searching/Sorting Algorithms](/flashcards/sets/8d91cdd4-8a64-4e4e-ab42-f7b73843a91d/)** | 32 | [Study Set →](https://flashcards.world/flashcards/sets/8d91cdd4-8a64-4e4e-ab42-f7b73843a91d/) |

---

## 2. Module-by-Module High-Yield Reference Tables & Sample Flashcards

### Module 1 (BASIC): [AP Physics 1 & C: Kinematics, Newton's Laws, Work-Energy Theorem & Linear Momentum](/flashcards/sets/19ab42ba-e89c-40cd-a0a9-bad7a9037bdd/)

**Overview**: High-yield AP Physics 1 & AP Physics C: Mechanics review covering 1D/2D kinematics, calculus kinematics, Newton's Laws, inclined planes, friction, circular motion, universal gravitation, Work-Energy Theorem, conservative forces, and impulse-momentum collisions.

- **Direct Set Link**: [AP Physics 1 & C: Kinematics, Newton's Laws, Work-Energy Theorem & Linear Momentum (32 Cards)](https://flashcards.world/flashcards/sets/19ab42ba-e89c-40cd-a0a9-bad7a9037bdd/) (`/flashcards/sets/19ab42ba-e89c-40cd-a0a9-bad7a9037bdd`)
- **Level Search**: [BASIC Sets on flashcards.world](https://flashcards.world/flashcards/?q=AP%20Physics%201%20%26%20C%2C%20AP%20Statistics%20%26%20AP%20Computer%20Science%20A%20/%20Principles&back_lng=en&expertise_level=basic)

| Term / Concept | Key Rule / Formula | Exam Application |
| :--- | :--- | :--- |
| **Constant-Acceleration ('Big 4') & Calculus Kinematics** | v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx; Δx = ½(v₀ + v)t; Calculus: v(t) = dx/dt, a(t) = dv/dt, Δx = ∫v dt, Δv = ∫a dt | Object speeds up when v(t) and a(t) have the SAME sign; in 2D projectile motion, at the apex vy = 0 but acceleration is still g = 9.8 m/s² downward. |
| **Newton's Laws, Inclined Planes & Friction** | ∑F = ma; on an incline of angle θ: Fg∥ = mg sin θ, Fg⊥ = mg cos θ, fk = μk mg cos θ, a = g(sin θ - μk cos θ); Angle of repose: tan θmax = μs | Valid Newton's 3rd Law pairs ALWAYS act on two different objects and involve the exact same type of force (never normal force and weight on the same block). |
| **Atwood Machines, Elevators & Linear Drag (Physics C)** | Atwood acceleration: a = (m₂ - m₁)g / (m₁ + m₂), Tension T = 2m₁m₂g / (m₁ + m₂); Elevator scale reading: FN = m(g + ay); Drag F = -bv -> vT = mg/b, v(t) = vT(1 - e^(-bt/m)) | Always set up the differential equation m(dv/dt) = mg - bv and separate variables carefully on AP Physics C Mechanics FRQs. |
| **Uniform Circular Motion & Universal Gravitation** | ac = v²/r = ω²r; Min speed at top of vertical loop: vmin = √(gR) (fromhmin = 2.5R); Orbital speed: vorb = √(GM/r); Kepler's 3rd Law: T² = (4π²/GM)r³; Escape speed: vesc = √(2GM/R) | Never draw 'centripetal force' as a separate arrow on a Free-Body Diagram—it is the radial net force ∑Fr = mv²/r supplied by gravity, tension, or normal/friction forces. |
| **Work-Energy Theorem & Potential Energy Curves U(x)** | W = F d cos θ = ∫Fx dx (area under F–x graph); Wnet = ΔK; Fx = -dU/dx; Us = ½kx²; Bound circular orbit: K = +GMm/(2r), Ug = -GMm/r, Etotal = -GMm/(2r) | On a U(x) curve, equilibrium occurs where slope dU/dx = 0: local minima (concave up) are stable equilibria; local maxima (concave down) are unstable. |
| **System Selection & Conservation of Mechanical Energy** | Single-object system: ΔU = 0, Wext = ΔK; Object–Earth–Spring system: Ki + Ugi + Usi + Wnc = Kf + Ugf + Usf (where friction work Wf = -fk d = -ΔEthermal) | For a mass dropped onto a vertical spring, maximum speed occurs at the equilibrium compression y = mg/k where net force is zero, NOT when it first touches the spring. |
| **Impulse-Momentum Theorem & Center of Mass Velocity** | p = mv; Impulse J = ∫F dt = Favg Δt = Δp (area under F–t graph); vcm = (∑mi vi)/Mtotal; if ∑Fext = 0, vcm remains strictly constant during any internal collision or explosion | Comparing a light mass m and heavy mass 4m via K = p²/(2m): if both have equal kinetic energy K, the heavier mass 4m has 2× the momentum. |
| **1D/2D Collisions (Elastic vs. Inelastic) & Ballistic Pendulum** | Momentum ∑p is conserved in ALL collisions where ∑Fext = 0; Kinetic energy K is conserved ONLY in elastic collisions (v1i - v2i = -(v1f - v2f)) | In a 2-stage Ballistic Pendulum, use Conservation of Momentum ONLY during the collision (mv₀ = (m+M)v) and Conservation of Energy ONLY during the upward swing (½(m+M)v² = (m+M)gh). |

| # | Front (Active Recall Prompt) | Back (Verified Exam Answer & Explanation) |
| :--- | :--- | :--- |
| **1** | What four equations describe one-dimensional motion with constant acceleration? | For elapsed time t, signed displacement Δx, initial velocity v0 and constant acceleration a: v = v0 + at; Δx = v0t + ½at²; v² = v0² + 2aΔx; Δx = ½(v0 + v)t. These respectively omit Δx, v, t and a. |
| **2** | How do position, velocity and acceleration relate through calculus and motion graphs? | In one dimension, v = dx/dt and a = dv/dt. Signed areas give Δx = ∫v dt and Δv = ∫a dt over the time interval. Where v ≠ 0, speed increases if va > 0 and decreases if va < 0; the sign of acceleration alone does not determine speeding up. |
| **3** | What are the apex properties, flight time, height and range of an ideal level-ground projectile? | With uniform downward g, no air resistance, launch speed v0 and angle 0 < θ < 90°, the apex has vx = v0 cosθ, vy = 0, ax = 0 and ay = −g. Returning to launch height takes T = 2v0 sinθ/g. Height above launch is H = v0² sin²θ/(2g), and range is R = v0² sin(2θ)/g. At fixed v0, range is greatest at 45°; complementary angles give equal ranges. |
| **4** | What do Newton’s three laws say in an inertial frame, and what is a third-law pair? | Zero net force gives constant velocity. For a particle of constant mass, ΣF = dp/dt = ma, with vector quantities. For an interaction between A and B, F_AonB = −F_BonA. These equal and opposite forces act on different bodies. Weight and normal force on the same book are not a third-law pair. |
| **5** | What forces and acceleration apply to a block sliding down a fixed rough incline? | For slope angle θ above horizontal, gravity has components mg sinθ down the slope and mg cosθ into it. With no other applied force and no normal acceleration, N = mg cosθ. In the kinetic-friction model, fk = μkN acts uphill. Taking downhill as positive, a = g(sinθ − μk cosθ) while the block slides downhill; a may be negative. |
| **6** | How do static and kinetic friction differ, and what is the ideal angle of repose? | In the simple friction model, 0 ≤ fs ≤ μsN while surfaces do not slide; during sliding, fk = μkN opposes relative motion. μk is often below μs, but this is not a universal identity, nor is fk constant if N changes. For a block on an incline acted on only by gravity, normal force and friction, impending slip gives tanθ_max = μs. |

### Module 2 (INTERMEDIATE): [AP Physics 1 & C: Rotational Dynamics, Simple Harmonic Motion, Electrostatics & DC Circuits](/flashcards/sets/f3c4718a-70d7-4672-a5e0-c4b55041f0b1/)

**Overview**: High-yield AP Physics 1 & C review covering rotational kinematics, torque, rotational inertia, parallel-axis theorem, rolling without slipping, angular momentum, SHM (springs and pendulums), Coulomb's Law, Gauss's Law, electric potential, capacitors, and DC RC circuits.

- **Direct Set Link**: [AP Physics 1 & C: Rotational Dynamics, Simple Harmonic Motion, Electrostatics & DC Circuits (32 Cards)](https://flashcards.world/flashcards/sets/f3c4718a-70d7-4672-a5e0-c4b55041f0b1/) (`/flashcards/sets/f3c4718a-70d7-4672-a5e0-c4b55041f0b1`)
- **Level Search**: [INTERMEDIATE Sets on flashcards.world](https://flashcards.world/flashcards/?q=AP%20Physics%201%20%26%20C%2C%20AP%20Statistics%20%26%20AP%20Computer%20Science%20A%20/%20Principles&back_lng=en&expertise_level=intermediate)

| Term / Concept | Key Rule / Formula | Exam Application |
| :--- | :--- | :--- |
| **Rotational Kinematics, Torque & Static Equilibrium** | s = rθ, vt = rω, at = rα, ac = rω²; Torque τ = r × F = rF sin θ = r⊥F; Static equilibrium requires BOTH ∑F = 0 and ∑τ = 0 about any pivot | When solving static beam/hinge problems, always place your pivot point at the hinge or unknown support force to eliminate its torque from ∑τ = 0. |
| **Rotational Inertia (I), Parallel-Axis Theorem & Rolling Race** | I = ∑mr² = ∫r² dm; Parallel-Axis Theorem: I = Icm + Md² (Rod center = 1/12 ML², Rod end = 1/3 ML²); Rolling without slipping: vcm = Rω, Ktotal = ½Mvcm² + ½Icmω² | In the downhill rolling race (a = g sin θ / (1 + c) where I = cMR²), mass M and radius R cancel out: Solid Sphere (c=2/5) beats Solid Disk (c=1/2) beats Thin Hoop (c=1). |
| **Angular Momentum (L = Iω and L = r × p) & Conservation** | Rigid body: L = Iω; Point particle moving in straight line: L = mvr sin θ = mvr⊥; If ∑τext = 0, Li = Lf (I₁ω₁ = I₂ω₂) | When a skater pulls her arms in (I decreases by ½), angular speed ω doubles AND rotational kinetic energy Krot = L²/(2I) doubles due to internal work. |
| **Simple Harmonic Motion (SHM): Springs & Pendulums** | d²x/dt² = -ω²x; Mass-spring period: Ts = 2π√(m/k); Simple pendulum: Tp = 2π√(L/g); Physical pendulum: T = 2π√(I/mgd); Etotal = ½kA² = ½mvmax² | In SHM, kinetic and potential energy are equal (K = Us = ½Etotal) at x = ±A/√2 ≈ ±0.707A (at x = A/2, Us is 25% and K is 75%). |
| **Coulomb's Law, Electric Fields & Gauss's Law (Physics C)** | Fe = k\|q₁q₂\|/r²; E = Fe/q₀; Gauss's Law: ∮E·dA = Qenc/ε₀; Conducting sphere: E = 0 inside (r < R) and V = kQ/R (constant non-zero!) inside; Insulating uniform sphere: E ∝ r inside | Remember that Electric Field E is a vector (use trig components and symmetry) whereas Electric Potential V = ∑kqi/ri is a scalar (keep +/- signs, no trig components!). |
| **Electric Potential (V), Potential Energy (UE) & Equipotentials** | UE = kq₁q₂/r; ΔU = qΔV = -Wfield; Ex = -dV/dx and ΔV = -∫E·dr; Electric field lines are always perpendicular to equipotential contours and point from high V to low V | At the center of a square with two +q and two -q charges at the corners, V = 0 always, but E = 0 ONLY if like charges are diagonally opposite each other. |
| **Capacitors, Dielectrics & Equivalent Capacitance** | C = Q/ΔV = κε₀A/d; UC = ½QΔV = ½C(ΔV)² = Q²/(2C); Parallel: Ceq = C₁ + C₂ (same ΔV); Series: 1/Ceq = 1/C₁ + 1/C₂ (same Q) | If battery remains CONNECTED, ΔV stays constant; if battery is DISCONNECTED (isolated capacitor), charge Q stays constant when plate separation d or dielectric κ changes. |
| **DC Resistor Circuits, Kirchhoff's Rules & RC Transients** | R = ρL/A; ΔV = IR; P = IΔV = I²R = ΔV²/R; Junction Rule: ∑Iin = ∑Iout (Conservation of Charge); Loop Rule: ∑ΔV = 0 (Conservation of Energy); RC time constant τ = RC | In any RC circuit, an uncharged capacitor at t = 0⁺ acts like a bare wire (short circuit, ΔVC = 0), and a fully charged capacitor as t -> ∞ acts like an open switch (IC = 0). |

| # | Front (Active Recall Prompt) | Back (Verified Exam Answer & Explanation) |
| :--- | :--- | :--- |
| **1** | For a point at fixed radius r > 0 rotating about a fixed axis, how do angular and linear quantities relate? | With angles in radians, ω = dθ/dt and α = dω/dt. Signed arc displacement is Δs = rΔθ; tangential velocity is vₜ = rω, while speed is r\|ω\|. Tangential acceleration is aₜ = rα; inward radial acceleration has magnitude aᵣ = rω². The total acceleration magnitude is √(aₜ² + aᵣ²). |
| **2** | What is torque, and what conditions keep an initially stationary rigid body in static equilibrium? | Torque is the vector cross product τ = r × F. Its magnitude is rF sin φ = Fℓ, where ℓ is the perpendicular lever arm in metres; torque is measured in N·m. Net external force and net external torque must both be zero. With force balance, torque balance holds about any fixed origin. |
| **3** | How are moment of inertia and the parallel-axis theorem defined, and how do four standard shapes compare? | I = Σmᵢrᵢ² = ∫r² dm, with r measured perpendicular to the chosen axis. For an axis parallel to a centre-of-mass axis at separation d, I = Icm + Md². For equal M and R, uniform bodies rank: thin hoop MR² > thin spherical shell 2MR²/3 > solid disk/cylinder MR²/2 > solid sphere 2MR²/5. Use the hoop/disk axis through its centre and normal to its plane, the cylinder’s central longitudinal axis, and sphere diameters. |
| **4** | What acceleration does a hanging mass m have when its string unwinds a uniform solid-disk pulley of mass M and radius R? | Assume a fixed frictionless axle, a massless inextensible string and no slip. For fixed-axis rotation, net torque = Iα, with I = MR²/2. Downward force balance gives mg − T = ma; pulley rotation gives TR = I(a/R). Thus a = mg/(m + M/2), downward. |
| **5** | What determines motion down an incline for a rigid body with Icm = cMR² rolling without slipping from rest? | On a stationary incline of angle θ, v = Rω and K = Mv²(1 + c)/2. With sufficient static friction and negligible rolling resistance, a = g sin θ/(1 + c); after dropping height h, v = √[2gh/(1 + c)]. Smaller c gives faster descent: solid sphere, disk, thin spherical shell, then hoop. A frictionless sliding block is faster still. Ideal static friction does no work at the stationary contact point. |
| **6** | How is angular momentum defined, and when is it conserved? | For a particle about a fixed origin, L = r × p. For rotation about a principal axis, the axial component is L = Iω. Zero net external torque about a fixed inertial origin conserves total angular momentum. Constant straight-line momentum can give constant nonzero L about an off-line origin. At fixed nonzero L, reducing I increases angular speed \|ω\| and rotational energy L²/(2I); internal work can supply that energy. |

### Module 3 (BASIC): [AP Statistics: Exploring Data, Normal Distribution, Linear Regression & Experimental Design](/flashcards/sets/d4547d81-4507-4bd2-a49c-4b61243f5810/)

**Overview**: High-yield AP Statistics Units 1–3 review covering CUSS univariate distributions, outliers, mean vs. median under skewness, z-scores and Empirical Rule, least-squares linear regression, r and R-squared, residual plots, transformations, sampling methods, and experimental design.

- **Direct Set Link**: [AP Statistics: Exploring Data, Normal Distribution, Linear Regression & Experimental Design (32 Cards)](https://flashcards.world/flashcards/sets/d4547d81-4507-4bd2-a49c-4b61243f5810/) (`/flashcards/sets/d4547d81-4507-4bd2-a49c-4b61243f5810`)
- **Level Search**: [BASIC Sets on flashcards.world](https://flashcards.world/flashcards/?q=AP%20Physics%201%20%26%20C%2C%20AP%20Statistics%20%26%20AP%20Computer%20Science%20A%20/%20Principles&back_lng=en&expertise_level=basic)

| Term / Concept | Key Rule / Formula | Exam Application |
| :--- | :--- | :--- |
| **Univariate Data (CUSS), Skewness & Outlier Rules** | Describe distributions in context using Center, Unusual features, Shape, Spread; Skewed right -> Mean > Median; Skewed left -> Mean < Median; Outlier fences: Q₁ - 1.5(IQR) and Q₃ + 1.5(IQR) or μ ± 2σ | Always pair Median & IQR for skewed data or data with outliers (because they are resistant), and use Mean & SD for symmetric data; use comparative words ('higher than') when comparing two groups. |
| **Linear Transformations, z-Scores & Empirical Rule** | Adding +a shifts Center/Position ONLY (Spread SD, IQR, Range unchanged!); Multiplying by ×b multiplies BOTH Center and Spread by \|b\|; z = (x - μ)/σ; Empirical Rule: 68% (±1σ), 95% (±2σ), 99.7% (±3σ) | On Normal distribution FRQs, always write 'Normal(μ = ..., σ = ...)' and show the z-score or shaded curve rather than naked calculator syntax. |
| **Correlation (r) & Least-Squares Regression Line (LSRL)** | ŷ = a + bx where slope b = r(sy/sx) and intercept a = ȳ - b x̄ (passes through (x̄, ȳ)); standardized prediction: zŷ = r · zx; -1 ≤ r ≤ 1 (unitless, unchanged by swapping x and y) | When interpreting slope b or y-intercept a, ALWAYS include the word 'predicted' or 'on average' in context (otherwise you lose credit for deterministic language). |
| **Residuals, Residual Plots, r² & Standard Deviation of Residuals (s)** | Residual e = y - ŷ (Actual minus Predicted); Linear model is appropriate iff the residual plot shows random scatter with no curved pattern; r² = % of variation in y explained by linear model with x | From computer regression tables, take r = ±√(R-Sq) and give r the exact same sign (+ or -) as the slope coefficient b. |
| **Outliers vs. High-Leverage / Influential Points & Transformations** | High-leverage points have extreme x-values (far from x̄) and strongly pull the slope b; Exponential model linearizes via log(y) vs. x; Power model linearizes via log(y) vs. log(x) | When predicting ŷ from a log-transformed LSRL (log ŷ = a + bx), remember to exponentiate (10^(a+bx) or e^(a+bx)) at the final step. |
| **Two-Way Contingency Tables & Conditional Distributions** | Marginal = Row/Col total ÷ Grand total; Joint = Cell ÷ Grand total; Conditional = Cell ÷ Row (or Col) total; Two categorical variables are independent iff conditional distributions match across categories | To justify whether an association exists between two categorical variables on an FRQ, always calculate and compare explicit conditional percentages. |
| **Sampling Methods & Survey Biases** | SRS (every group of size n equally likely); Stratified (sample SOME from ALL homogeneous strata); Cluster (sample ALL from SOME heterogeneous clusters); Systematic (every k-th); Biases: Voluntary Response, Undercoverage, Nonresponse, Response wording | Stratified sampling reduces sampling variability for a given sample size; increasing sample size n reduces random sampling variability but NEVER fixes bias. |
| **Experimental Design, Blocking, Matched Pairs & Scope of Inference** | 4 Principles: Comparison, Random Assignment, Control, Replication (many units per group); Block by variable strongly tied to response; Scope: Random Selection -> Generalize to population; Random Assignment -> Cause-and-Effect | Never claim cause-and-effect from an observational study; explain that random assignment balances unobserved confounding variables across treatment groups. |

| # | Front (Active Recall Prompt) | Back (Verified Exam Answer & Explanation) |
| :--- | :--- | :--- |
| **1** | What does the acronym CUSS (or SOCS) stand for when describing a Univariate Quantitative Distribution on an AP Statistics FRQ, and when should you use Mean/SD vs. Median/IQR? | Always describe a quantitative distribution **in context** using **CUSS**: • **C — Center**: Mean ($\bar{x}$) or Median. • **U — Unusual Features**: Outliers, gaps, or clusters. • **S — Shape**: Symmetric/bell-shaped, skewed right (tail to the right), skewed left (tail to the left), uniform, or bimodal. • **S — Spread (Variability)**: Standard Deviation ($s_x$), Interquartile Range ($\text{IQR} = Q_3 - Q_1$), or Range. • **Choice of Summary Statistics**: Because the **Median and IQR are resistant** to outliers and skewness, ALWAYS use **Median and IQR for skewed distributions or data with outliers**, and use **Mean and Standard Deviation for roughly symmetric distributions**. |
| **2** | How do the Mean and Median compare in a Right-Skewed, Left-Skewed, and Symmetric distribution? | The non-resistant **Mean is always pulled in the direction of the longer tail (and outliers)**: • **Skewed Right (positively skewed)**: $\text{Mean} > \text{Median}$. • **Skewed Left (negatively skewed)**: $\text{Mean} < \text{Median}$. • **Symmetric**: $\text{Mean} \approx \text{Median}$. |
| **3** | State the two standard mathematical rules used on AP Statistics to test for Outliers in a dataset. | 1. **$1.5 \times \text{IQR}$ Rule** (used for boxplots):    - $\text{IQR} = Q_3 - Q_1$.    - **Lower Fence**: $Q_1 - 1.5 \times \text{IQR}$.    - **Upper Fence**: $Q_3 + 1.5 \times \text{IQR}$.    Any observation strictly below the Lower Fence or above the Upper Fence is an outlier. 2. **$2\text{ SD}$ Rule**: Any observation more than $2$ standard deviations away from the mean ($< \bar{x} - 2s_x$ or $> \bar{x} + 2s_x$). |
| **4** | How does a Linear Transformation of every data point ($y_i = a + b x_i$, i.e., multiplying by $b$ and adding a constant $a$) affect Measures of Center and Position vs. Measures of Spread? | • **Adding/Subtracting a Constant ($+a$)**:   - Shifts **Center and Position** (Mean, Median, Quartiles $Q_1, Q_3$, Min, Max, Percentiles) by **$+a$**.   - Does **NOT change Measures of Spread** (Standard Deviation $s$, IQR, and Range remain completely unchanged! Variance $s^2$ is also unchanged). • **Multiplying/Dividing by a Constant ($\times b$)**:   - Multiplies **BOTH** Center/Position AND Spread (Mean, Median, Quartiles, SD $s$, IQR, Range) by **$\|b\|$** (and multiplies Variance $s^2$ by $b^2$).   - **Shape and $z$-scores never change** under linear transformations ($b > 0$). |
| **5** | How do you calculate and interpret a Standardized $z$-Score, and what is the Empirical (68–95–99.7) Rule for a Normal Distribution $N(\mu, \sigma)$? | • **$z$-Score Formula**:   $$z = \frac{x - \mu}{\sigma}$$   (Measures how many standard deviations an observation $x$ lies above or below the mean $\mu$). • **Empirical (68–95–99.7) Rule** for any Normal Distribution $N(\mu, \sigma)$:   - Approximately **$68\%$** of observations fall within **$\mu \pm 1\sigma$** ($z \in [-1, 1]$).   - Approximately **$95\%$** of observations fall within **$\mu \pm 2\sigma$** ($z \in [-2, 2]$).   - Approximately **$99.7\%$** of observations fall within **$\mu \pm 3\sigma$** ($z \in [-3, 3]$). |
| **6** | How do you check whether a dataset is approximately Normally Distributed, and what must you write to earn full credit on a Normal probability calculation FRQ? | • **Checking Normality**: Plot a histogram/dotplot/stemplot (check for unimodal symmetry with no outliers), check if proportions match $68\text{–}95\text{–}99.7\%$, or inspect a **Normal Probability Plot (Q-Q Plot)**—if the points follow a ** roughly straight diagonal line**, the data are approximately Normal. • **Full-Credit Normal FRQ Setup**: Always state the distribution and parameters (**'Normal with $\mu = \dots, \sigma = \dots$'**), write the probability statement or $z$-score ($P(X > x) = P(Z > z)$), OR draw and shade a labeled Normal curve (avoid 'calculator-speak' like `normalcdf(70, 1e99, 65, 3)` without labeling parameters!). |

### Module 4 (INTERMEDIATE): [AP Statistics: Probability, Sampling Distributions, Confidence Intervals & Hypothesis Tests (z, t, Chi-Square)](/flashcards/sets/67e66f7a-28d0-4bb9-a16d-0fc1fa1c4c6e/)

**Overview**: High-yield AP Statistics Units 4–9 review covering probability rules, Bayes' Theorem, discrete/binomial/geometric random variables, CLT and sampling distributions, 4-step STATE-PLAN-DO-CONCLUDE inference, 1/2-sample z and t procedures, Type I/II errors, Power, Chi-Square tests, and regression slope t-tests.

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| Term / Concept | Key Rule / Formula | Exam Application |
| :--- | :--- | :--- |
| **Probability Rules, Independence vs. Mutually Exclusive & Bayes** | P(A ∪ B) = P(A) + P(B) - P(A ∩ B); P(A \| B) = P(A ∩ B) / P(B); Mutually Exclusive (Disjoint): P(A ∩ B) = 0; Independent: P(A \| B) = P(A) and P(A ∩ B) = P(A)P(B) | Two events with non-zero probabilities can NEVER be both mutually exclusive and independent; use a tree diagram or Bayes' Rule for reverse conditional probabilities. |
| **Discrete, Binomial & Geometric Random Variables + Combining RVs** | Discrete: μX = ∑xi P(xi), σX = √∑(xi - μ)²P(xi); Combining Independent RVs: μ(X±Y) = μX ± μY and σ(X±Y) = √(σX² + σY²) (Variances ALWAYS add!); Binomial B(n,p): μ = np, σ = √(np(1-p)); Geometric Geom(p): μ = 1/p | Watch the classic distinction: multiplying a single variable by 3 gives σ(3X) = 3σX, whereas summing 3 independent copies gives σ(X₁+X₂+X₃) = √3 σX. |
| **Sampling Distributions of p̂ and x̄ & Central Limit Theorem (CLT)** | Proportions (p̂): μp̂ = p, σp̂ = √(p(1-p)/n), Normal if np ≥ 10 & n(1-p) ≥ 10; Means (x̄): μx̄ = μ, σx̄ = σ/√n, Normal if population is Normal OR n ≥ 30 by the Central Limit Theorem | Always check the 10% Condition (n < 0.10N) when sampling without replacement from a finite population, but do NOT check it for randomized experiments without sampling. |
| **4-Step Inference Framework (STATE – PLAN – DO – CONCLUDE)** | 1. STATE: H₀, Ha in parameter symbols (p, μ, β), define parameter in context, α; 2. PLAN: Name procedure & check Random, 10%, Large Counts/Normal; 3. DO: Test statistic, df, p-value / CI; 4. CONCLUDE: Link p-value < α -> Reject H₀ -> convincing evidence of Ha in context | Never use sample statistics (p̂, x̄, b) in H₀ or Ha, and never say 'accept H₀' or 'prove H₀' when p-value > α. |
| **1-Sample & 2-Sample z-Procedures for Proportions** | 1-Prop CI: p̂ ± z*√(p̂(1-p̂)/n); 1-Prop Test (H₀: p = p₀): z = (p̂ - p₀)/√(p₀(1-p₀)/n); 2-Prop Test (H₀: p₁ = p₂) uses POOLED p̂c = (X₁+X₂)/(n₁+n₂); 2-Prop CI is unpooled | When solving for minimum sample size n for a target Margin of Error ME, use p̂ = 0.50 if no prior estimate is given and always round n UP to the next integer. |
| **1-Sample, Paired & 2-Sample t-Procedures for Means** | 1-Sample / Paired t (df = n - 1): x̄ ± t*(s/√n) and t = (x̄ - μ₀)/(s/√n); 2-Sample Independent t: (x̄₁ - x̄₂) ± t*√(s₁²/n₁ + s₂²/n₂) | Always check whether two sets of quantitative data are Paired (dependent measurements on same/matched units -> 1-sample t-test on differences d) or Independent (2-sample t-test). |
| **Type I Error (α), Type II Error (β) & Power of a Test (1 - β)** | Type I Error (prob = α): Rejecting H₀ when H₀ is true; Type II Error (prob = β): Failing to reject H₀ when Ha is true; Power (1 - β): Probability of correctly rejecting a false H₀ | Power increases (and β decreases) when you increase sample size n, increase significance level α, have a larger true effect size, or reduce σ. |
| **Chi-Square Tests (GOF, Homogeneity, Independence) & Slope t-Test** | χ² = ∑(O - E)²/E (Condition: ALL Expected counts ≥ 5); GOF: 1 sample, 1 var, df = k - 1; Homogeneity (2+ samples, 1 var) & Independence (1 sample, 2 vars): E = (Row × Col)/Total, df = (r-1)(c-1); Slope t-test: t = (b - 0)/SEb with df = n - 2 | Distinguish Chi-Square Homogeneity (separate random samples from multiple populations or randomized treatment groups) from Independence (one random sample cross-classified by two variables). |

| # | Front (Active Recall Prompt) | Back (Verified Exam Answer & Explanation) |
| :--- | :--- | :--- |
| **1** | State the General Addition Rule, Conditional Probability Rule, and General Multiplication Rule, and distinguish Mutually Exclusive (Disjoint) Events from Independent Events. | • **General Addition Rule**: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. • **Conditional Probability**: $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$. • **General Multiplication Rule**: $P(A \cap B) = P(B) \cdot P(A \mid B)$. • **Mutually Exclusive (Disjoint) Events**: Cannot occur together, so **$P(A \cap B) = 0$**. • **Independent Events**: Knowing $B$ occurred does not change the probability of $A$, so **$P(A \mid B) = P(A)$** and **$P(A \cap B) = P(A) \cdot P(B)$**. • **Exam Trap**: Two events with positive probabilities ($P(A)>0, P(B)>0$) can **NEVER be both mutually exclusive and independent** (because if $A$ and $B$ are disjoint and $B$ occurs, $P(A \mid B) = 0 \ne P(A)$!). |
| **2** | How do you solve a Tree Diagram / Reverse Conditional Probability (Bayes' Theorem) problem (such as a medical diagnostic test with false positives)? | Use **Bayes' Theorem** (or a 2x2 table with a hypothetical population of $10,000$): $$P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)P(B \mid A)}{P(A)P(B \mid A) + P(A^c)P(B \mid A^c)}$$ For example, if $1\%$ of a population has a disease ($P(D)=0.01$), a test is $95\%$ sensitive ($P(+ \mid D)=0.95$), and has a $4\%$ false-positive rate ($P(+ \mid D^c)=0.04$), then: $$P(D \mid +) = \frac{(0.01)(0.95)}{(0.01)(0.95) + (0.99)(0.04)} = \frac{0.0095}{0.0491} \approx 0.1935$$ |
| **3** | Write the formulas for the Mean (Expected Value $\mu_X$) and Standard Deviation ($\sigma_X$) of a Discrete Random Variable $X$, and state how you must interpret $\mu_X$ in context. | • **Mean (Expected Value)**:   $$\mu_X = E(X) = \sum x_i P(x_i)$$   (Note: $\mu_X$ does NOT have to be a possible integer value of $X$!). • **Standard Deviation**:   $$\sigma_X = \sqrt{\sum (x_i - \mu_X)^2 P(x_i)}$$ • **Required AP Interpretation of $\mu_X$**: *'If we repeated [random process] **many, many times** (in the long run), the **average** [variable $X$, in context] would be about $\mu_X$ [units].'* |
| **4** | When you Combine two Independent Random Variables ($W = aX \pm bY$), what are the Mean $\mu_W$, Variance $\sigma_W^2$, and Standard Deviation $\sigma_W$? ('Variances ALWAYS Add!') | For any two random variables $X$ and $Y$: • **Mean**: $\mu_{aX + bY} = a\mu_X + b\mu_Y$ and $\mu_{aX - bY} = a\mu_X - b\mu_Y$. • **Variance & Standard Deviation** (ONLY if $X$ and $Y$ are **INDEPENDENT**—**VARIANCES ALWAYS ADD, EVEN WHEN SUBTRACTING $X - Y$!**):   $$\sigma_{X \pm Y}^2 = \sigma_X^2 + \sigma_Y^2 \implies \sigma_{X \pm Y} = \sqrt{\sigma_X^2 + \sigma_Y^2}$$   $$\sigma_{aX \pm bY} = \sqrt{a^2\sigma_X^2 + b^2\sigma_Y^2}$$ |
| **5** | In Combining Random Variables, what is the critical difference between $3X$ (multiplying a single observation by $3$, e.g., converting yards to feet) and $X_1 + X_2 + X_3$ (summing $3$ independent observations)? | Both have the exact same mean ($3\mu_X$), but their standard deviations differ! • **Linear Rescaling ($3X$)**: $\sigma_{3X} = \sqrt{3^2 \sigma_X^2} = \mathbf{3\sigma_X}$. • **Sum of $3$ Independent Observations ($X_1 + X_2 + X_3$)**:   $$\sigma_{X_1 + X_2 + X_3} = \sqrt{\sigma_X^2 + \sigma_X^2 + \sigma_X^2} = \mathbf{\sqrt{3}\,\sigma_X}$$ |
| **6** | What are the BINS conditions for a Binomial Random Variable $X \sim B(n, p)$, and what are its Probability Formula, Mean $\mu_X$, and Standard Deviation $\sigma_X$? | • **BINS Conditions**:   - **B — Binary**: Each trial results in 'Success' or 'Failure.'   - **I — Independent**: Trials are independent (or satisfy the $10\%$ condition $n < 0.10N$ if sampling without replacement).   - **N — Number**: Fixed number of trials $n$ is set in advance.   - **S — Same Probability**: Constant probability of success $p$ on every trial. • **Probability of exactly $k$ successes in $n$ trials**:   $$P(X = k) = \binom{n}{k}p^k(1 - p)^{n - k}$$ • **Mean & SD**: $\mu_X = np$ and $\sigma_X = \sqrt{np(1 - p)}$. |

### Module 5 (ADVANCED): [AP Computer Science A: Java Primitives, Control Flow, Classes, Objects, Strings, 1D/2D Arrays & ArrayLists](/flashcards/sets/c2f1ae27-6687-4cc1-aa6c-63704efbf2ca/)

**Overview**: High-yield AP Computer Science A Units 1–8 review covering Java primitive types, integer division, casting, Math.random(), De Morgan's Laws, short-circuit evaluation, OOP classes, String methods, 1D/2D arrays, ArrayLists, and traversal traps.

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| Term / Concept | Key Rule / Formula | Exam Application |
| :--- | :--- | :--- |
| **Java Primitives, Integer Division (`/`), Modulus (`%`) & Casting** | Primitives: int, double, boolean; int / int truncates toward 0 (7 / 2 == 3); n % 10 gets ones digit, n /= 10 drops ones digit; Cast (int) or (double) has HIGHER precedence than *, /, +, -; Round positive d: (int)(d + 0.5) | Watch `(double) 5 / 2` (= 2.5) vs. `(double)(5 / 2)` (= 2.0), and remember `Integer.MAX_VALUE + 1` silently overflows to `Integer.MIN_VALUE`. |
| **Math.random(), Boolean Short-Circuiting & De Morgan's Laws** | Random int in [min, max]: `(int)(Math.random() * (max - min + 1)) + min`; De Morgan: `!(A && B) <=> !A \|\| !B`, `!(A \|\| B) <=> !A && !B`; Negating `<` gives `>=` | Short-circuit evaluation (`&&` and `\|\|`) evaluates left-to-right and stops early, protecting `if (i < arr.length && arr[i] == x)` and `if (s != null && s.length() > 0)`. |
| **OOP Classes: Encapsulation, Constructors, `this`, Pass-by-Value & `static`** | Instance variables MUST be `private`; Constructor has exact class name and NO return type (not even `void`); Java is strictly Pass-by-Value (copies primitives; copies object references); `static` methods cannot access non-static fields/methods | Mutating an array or object via a parameter (`arr[0] = 9;`) modifies the caller's object, whereas reassigning the parameter (`arr = new int[5];`) does not. |
| **String Immutability & All 7 AP Quick Reference String Methods** | `length()`, `substring(from, to)` (to is exclusive; length = to - from), `substring(from)`, `indexOf(str)` (-1 if not found), `equals(other)`, `compareTo(other)` (<0, 0, >0); single char at i: `s.substring(i, i + 1)` | NEVER compare Strings with `==` (checks memory address alias); always use `s1.equals(s2)` and remember `s.substring(s.length())` returns `""` without error. |
| **1D Arrays (`int[]`), Default Values & Enhanced `for-each` Loops** | Length is `arr.length` (field, no parentheses); Default values: `0`, `0.0`, `false`, `null`; `for (int x : arr)` copies each element into local variable `x` | Never use an enhanced `for-each` loop to modify array elements (`x = 0` does nothing to `arr`), access indices, or remove from an `ArrayList`; initialize min/max to `arr[0]`, never `0`. |
| **1D Array Shifting & Reversing Algorithms** | Shift Left: loop forward `i = 0` to `length - 2` (`arr[i] = arr[i + 1]`); Shift Right: MUST loop BACKWARD `i = length - 1` down to `1` (`arr[i] = arr[i - 1]`); Reverse: loop `i = 0` to `length / 2` | If you loop forward while shifting right (`arr[i + 1] = arr[i]`), you overwrite every element in the array with `arr[0]`. |
| **Wrapper Classes (`Integer`, `Double`), `ArrayList<E>` & the Removal Trap** | 6 AP `ArrayList` methods: `size()`, `add(obj)` (returns true), `add(i, obj)` (void), `get(i)`, `set(i, obj)` (returns old element), `remove(i)` (shifts left & returns removed element) | Calling `list.remove(i)` in a forward `for` loop skips the next element when consecutive matches occur! Fix by either adding `i--;` after `remove(i)` OR looping backward from `list.size() - 1` down to `0`. |
| **2D Arrays (`int[][]`): Row-Major, Column-Major & `for-each` Traversal** | Rows = `mat.length`, Columns = `mat[0].length`; Row-major: outer loop `r`, inner loop `c` (`mat[r][c]`); Column-major: outer loop `c`, inner loop `r` (still `mat[r][c]`!); Enhanced `for-each`: `for (int[] row : mat) for (int val : row)` | In a square N×N matrix, main diagonal is `mat[i][i]` and minor (anti-) diagonal is `mat[i][mat.length - 1 - i]`. |

| # | Front (Active Recall Prompt) | Back (Verified Exam Answer & Explanation) |
| :--- | :--- | :--- |
| **1** | What are the three Java Primitive Data Types tested on the AP Computer Science A exam, and how do Integer Division (`/`) and the Modulus Operator (`%`) work? | • **Three AP Java Primitives**: `int` (32-bit signed integers from `Integer.MIN_VALUE` $= -2^{31}$ to `Integer.MAX_VALUE` $= 2^{31} - 1$), `double` (64-bit floating-point numbers), and `boolean` (`true` or `false`). *(Note: `String` is a reference/object type, NOT a primitive!)* • **Integer Division (`/`)**: When BOTH operands are `int`, Java **truncates toward zero** (drops the decimal fraction completely): `7 / 2` evaluates to `3`, `-7 / 2` evaluates to `-3`, and `3 / 5` evaluates to `0`. • **Modulus (`%`)**: Returns the remainder: `17 % 5` is `2`, `5 % 17` is `5`, `n % 2 == 0` checks if `n` is even, and `n % 10` extracts the rightmost digit of a positive integer `n` (while `n /= 10` removes the rightmost digit!). |
| **2** | How does Type Casting (`(int)` and `(double)`) work in Java, including Operator Precedence and Rounding to the Nearest Integer? | • **Widening Conversion (`int` to `double`)**: Happens automatically (implicitly), e.g., `double x = 5;` sets `x` to `5.0`. • **Narrowing Conversion (`double` to `int`)**: Requires an explicit cast `(int)`, which **truncates toward zero**. • **High Precedence Trap**: The cast operator `(int)` or `(double)` has **HIGHER precedence than `*`, `/`, `+`, `-`**! Thus:   - `(double) 5 / 2` casts `5` to `5.0` FIRST, then computes `5.0 / 2` $= \mathbf{2.5}$.   - `(double) (5 / 2)` performs integer division `5 / 2` $= 2$ FIRST, then casts to $\mathbf{2.0}$! • **Rounding a `double d` to the Nearest `int`**:   - Positive `d`: `(int)(d + 0.5)`   - Negative `d`: `(int)(d - 0.5)`. |
| **3** | How do you use `Math.random()` to generate a random integer in the inclusive range `[min, max]`, and what do the AP Quick Reference `Math` methods return? | • `Math.random()` returns a `double` in the half-open interval **`[0.0, 1.0)`** ($0.0 \le r < 1.0$, never reaching $1.0$). • **Random `int` from `min` to `max` inclusive**:   ```java   int num = (int)(Math.random() * (max - min + 1)) + min;   ```   (Here `max - min + 1` is the **number of possible integers**, and `min` is the **starting value**). • **Other AP `Math` Methods**:   - `Math.abs(int x)` returns `int`; `Math.abs(double x)` returns `double`.   - `Math.pow(double base, double exp)` ALWAYS returns a **`double`**.   - `Math.sqrt(double x)` ALWAYS returns a **`double`**. |
| **4** | State De Morgan's Laws and Relational Operator Negations in Java Boolean Expressions. | • **De Morgan's Laws** (distribute `!` and flip `&&` $\leftrightarrow$ `\|\|`):   - `!(A && B)` is equivalent to **`!A \|\| !B`**   - `!(A \|\| B)` is equivalent to **`!A && !B`** • **Negating Relational Operators** (watch the `=` boundary!):   - `!(x > 5)` $\Longleftrightarrow$ **`x <= 5`**   - `!(x >= 5)` $\Longleftrightarrow$ **`x < 5`**   - `!(x == 5)` $\Longleftrightarrow$ **`x != 5`**   *(Example: `!(x > 0 && y <= 10)` simplifies to `x <= 0 \|\| y > 10`.)* |
| **5** | What is Short-Circuit Evaluation in Java (`&&` and `\|\|`), and how does it prevent `ArithmeticException` (division by zero), `NullPointerException`, and `IndexOutOfBoundsException`? | Java evaluates boolean expressions from **left to right** and stops as soon as the truth value is determined: • **`A && B`**: If `A` is **`false`**, Java does **NOT evaluate `B`** because `false && anything` is guaranteed to be `false`. • **`A \|\| B`**: If `A` is **`true`**, Java does **NOT evaluate `B`** because `true \|\| anything` is guaranteed to be `true`. • **Safe Guard Idioms** (guard MUST come FIRST on the left!):   - `if (count != 0 && sum / count > 80)` (prevents division by zero)   - `if (str != null && str.length() > 0)` (prevents `NullPointerException`)   - `if (i >= 0 && i < arr.length && arr[i] == target)` (prevents `ArrayIndexOutOfBoundsException`). |
| **6** | Why must you NEVER use `==` to compare two `String` objects (or any Objects) for value equality in Java, and how does `==` differ from `.equals()`? | • **`==` on Object References**: Compares **memory addresses (references)**—returning `true` ONLY if both variables point to the **exact same object instance in memory** (**aliases**). While Java's string literal pool may sometimes make `"hi" == "hi"` evaluate to `true`, `new String("hi") == "hi"` is **`false`**! • **`.equals(Object other)`**: Compares the **actual character contents / state** of the two objects (`s1.equals(s2)` returns `true` if `s1` and `s2` contain the exact same sequence of characters). Always use `.equals()` for Strings and Wrapper objects! |

### Module 6 (ADVANCED): [AP Computer Science A: Inheritance, Polymorphism, Recursion & Searching/Sorting Algorithms](/flashcards/sets/8d91cdd4-8a64-4e4e-ab42-f7b73843a91d/)

**Overview**: High-yield AP Computer Science A Units 9–10 review covering inheritance (`extends`, `super`), method overriding, compile-time vs. run-time polymorphism, `Object` class, recursion tracing, base cases, Linear/Binary Search, and Selection/Insertion/Merge Sort.

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| Term / Concept | Key Rule / Formula | Exam Application |
| :--- | :--- | :--- |
| **Inheritance (`extends`), IS-A vs. HAS-A & Encapsulation** | `public class Sub extends Super` establishes an IS-A relationship; HAS-A = composition (field of another class type); Subclasses do NOT inherit constructors and CANNOT directly access `private` superclass fields/methods | To read or modify a superclass's `private` field from a subclass, you MUST call the superclass's `public` getter/setter or pass arguments to `super(...)`. |
| **Subclass Constructors & `super(...)` vs. `super.method(...)`** | `super(args);` calls the superclass constructor and MUST be the very first statement in the subclass constructor; if omitted, Java implicitly inserts no-arg `super();` on line 1 | If the superclass has only a parameterized constructor and no default `Super()` constructor, omitting an explicit `super(args);` in the subclass causes a compile-time error. |
| **Polymorphism: Compile-Time Check vs. Run-Time Dynamic Dispatch** | For `Super a = new Sub();`: 1. At COMPILE TIME, compiler checks that the called method exists in `Super` (left-side declared type); 2. At RUN TIME, JVM executes the overridden method in `Sub` (right-side actual object type) | #1 AP CS A MCQ trap: if `a.method1()` (defined in `Super`) calls `method2()` (which is overridden in `Sub`), `Sub`'s version of `method2()` executes at run time! |
| **Type Compatibility, Upcasting, Downcasting & `Object` Class** | Upcasting (`Super a = new Sub();`) is always valid; Downcasting (`((Sub) a).subOnlyMethod()`) requires explicit parentheses and throws `ClassCastException` at run time if `a` is not actually a `Sub`; all classes extend `Object` (`toString()`, `equals(Object)`) | Note operator precedence: the dot operator `.` has higher precedence than a cast, so you must write `((Dog) a).bark()`, NOT `(Dog) a.bark()`. |
| **Recursion Fundamentals, Call Stack Unwinding & Base Cases** | Every recursive method needs a Base Case (stops recursion) and a Recursive Call (progresses toward base case); missing base case throws `StackOverflowError`; statements AFTER the recursive call execute in reverse (LIFO) order as the stack unwinds | For recursive String reversal `rev(s.substring(1)) + s.substring(0, 1)`, trace small inputs of length 3–4 by writing out each stack frame. |
| **Linear Search vs. Binary Search (`O(N)` vs. `O(log N)`)** | Linear Search works on any array/list (max N comparisons); Binary Search REQUIRES a sorted array (`mid = (low + high) / 2`, updates `low = mid + 1` or `high = mid - 1`), taking at most ⌊log₂ N⌋ + 1 comparisons | Doubling the size N of a sorted array adds only +1 maximum comparison to Binary Search (e.g., N = 1,000 takes ≤ 10 comparisons; N = 2,000 takes ≤ 11). |
| **Selection Sort vs. Insertion Sort (Mechanics & Pass Identification)** | Selection Sort: finds global min in unsorted suffix and swaps into `arr[i]` (always N(N-1)/2 comparisons, ≤ N-1 swaps); Insertion Sort: starts at `i = 1`, shifts larger elements right in a `while` loop (`O(N)` best case on already-sorted array, `O(N²)` worst case on reverse-sorted) | After k passes: Selection Sort has locked the k smallest elements of the ENTIRE array at indices `0..k-1`; Insertion Sort has sorted the first `k+1` elements relative to each other while leaving indices `k+1..N-1` untouched. |
| **Merge Sort (`O(N log N)` Divide-and-Conquer)** | Recursively splits array in half (`mergeSort(left)`, `mergeSort(right)`), then merges the two sorted halves using a temporary array (`O(N)` extra space) | Merge Sort always runs in `O(N log N)` time regardless of whether the input array is already sorted, reverse-sorted, or random. |

| # | Front (Active Recall Prompt) | Back (Verified Exam Answer & Explanation) |
| :--- | :--- | :--- |
| **1** | In Java Inheritance (`public class SubClass extends SuperClass`), what defines an 'IS-A' relationship vs. a 'HAS-A' relationship, and can a subclass directly access `private` instance variables of its superclass? | • **IS-A Relationship (Inheritance via `extends`)**: `Dog extends Animal` means every `Dog` **IS-A** `Animal`. Java supports single inheritance only (a class can `extend` only ONE direct superclass, though hierarchies can be multi-level). • **HAS-A Relationship (Composition)**: A class contains an instance variable that is a reference to another object (e.g., `Car` has a `private Engine eng;`). • **Crucial Encapsulation Rule**: A subclass **CANNOT directly access `private` instance variables or `private` methods of its superclass**! It must use the superclass's `public` (or `protected`) accessor/mutator methods or pass arguments to `super(...)`. |
| **2** | How do Constructors work in a Subclass, and what happens if a Subclass Constructor does NOT explicitly call `super(...)` on its very first line? | • **Constructors are NEVER inherited** by subclasses. • **Explicit `super(...)` Call**: To call a superclass constructor, `super(args);` **MUST be the very first statement** in the subclass constructor. • **Implicit `super()` Rule**: If a subclass constructor does NOT explicitly write `super(...)` on line 1, the Java compiler automatically inserts a no-argument call **`super();`** as the first line. **Compile-Time Error Trap**: If the superclass has a parameterized constructor (e.g., `public Animal(String name)`) and **NO no-arg constructor `public Animal()`**, omitting `super(name)` in the subclass constructor causes a **compile-time error**! |
| **3** | Distinguish between Method Overriding (across superclass/subclass) and Method Overloading, and explain how `super.methodName(...)` works. | • **Method Overriding**: A subclass defines a method with the **exact same method signature** (name, parameter types, and compatible return type) as an inherited method in its superclass, replacing its behavior for instances of the subclass. • **Calling the Superclass Version**: Inside a subclass method, writing **`super.methodName(args)`** invokes the superclass's version of that method (avoiding infinite recursion when extending superclass behavior, e.g., `return super.getPay() + bonus;`). |
| **4** | In Polymorphism (`SuperClass obj = new SubClass();`), state the Golden Rule for Compile-Time Type Checking vs. Run-Time Dynamic Method Dispatch (Late Binding). | Consider `Animal a = new Dog();` (where **Declared/Compile-Time Type** is `Animal` and **Actual/Run-Time Object Type** is `Dog`): 1. **At COMPILE TIME, the Compiler checks the DECLARED TYPE (`Animal`, Left Side)**:    - The method being called (`a.speak()` or `a.wagTail()`) **MUST exist in the `Animal` class (or its superclasses)**! If `wagTail()` is defined ONLY in `Dog` and NOT in `Animal`, then `a.wagTail();` causes a **COMPILE-TIME ERROR** (unless explicitly downcast via `((Dog) a).wagTail()`). 2. **At RUN TIME, the JVM executes the OVERRIDDEN method of the ACTUAL OBJECT TYPE (`Dog`, Right Side)**:    - If `a.speak()` compiles, Java uses **Dynamic Method Dispatch** to run `Dog`'s overridden `speak()` method! |
| **5** | Wait—in `SuperClass a = new SubClass();`, if `a.methodA()` (inherited from `SuperClass` and NOT overridden in `SubClass`) internally calls `methodB()` (which IS overridden in `SubClass`), WHICH version of `methodB()` runs? | **`SubClass`'s overridden `methodB()` runs!** This is the #1 AP CS A Inheritance MCQ trap: inside `SuperClass`'s `methodA()`, an unqualified call to `methodB()` is implicitly `this.methodB()`. Because at run time the implicit object `this` is actually an instance of **`SubClass`**, dynamic method dispatch invokes **`SubClass.methodB()`**! |
| **6** | Which Reference Assignments and Downcasts are valid at Compile Time vs. Run Time in an Inheritance Hierarchy (`GradStudent extends Student extends Person`)? | • **Upcasting (Subclass assigned to Superclass reference)**: Always legal without a cast:   - `Person p = new Student();` (Valid: a `Student` IS-A `Person`).   - `ArrayList<Person> list = new ArrayList<Person>(); list.add(new GradStudent());` (Valid). • **Assigning Superclass to Subclass without a cast**:   - `Student s = new Person();` $\rightarrow$ **COMPILE-TIME ERROR** (a `Person` is not necessarily a `Student`). • **Explicit Downcasting (`(SubClass) ref`)**:   - If `Person p = new GradStudent();`, then `Student s = (Student) p;` compiles AND succeeds at run time.   - If `Person p = new Person();`, then `Student s = (Student) p;` compiles, but throws a **`ClassCastException` at RUN TIME**! |

---

## 3. 8-Week Spaced Repetition Exam Prep Schedule

| Phase | Daily Action Plan |
| :--- | :--- |
| **Weeks 1–2: Foundation Tier (`basic`)** | Complete Modules 1 & 2 (32 new cards/day). Focus on instant recall of core definitions, rules, and foundational formulas. Review due cards daily (15–20 mins). |
| **Weeks 3–5: Core Application Tier (`intermediate`)** | Advance to Modules 3 & 4 (20–25 new cards/day) while maintaining daily spaced reviews of Basic sets. Practice applying rules and formulas to multi-step exam problems. |
| **Weeks 6–7: Advanced Mastery Tier (`advanced`)** | Complete Modules 5 & 6 (15–20 new cards/day). Interleave all 6 sets to sharpen discrimination between subtle distractors under timed conditions. |
| **Week 8: Final Exam Consolidation** | Pause new cards 7 days before exam day; clear all daily review queues on flashcards.world and drill any leech cards missed twice or more. |

---

## 4. High-Yield Exam Traps & Strategic Tips

- **Distinguish AP Physics 1 (Algebra-Based) from AP Physics C (Calculus-Based) Efficiently**: Both exams share the exact same physical principles for Kinematics, Newton's Laws, Work-Energy, Momentum, Rotation, and Simple Harmonic Motion (**Modules 1 & 2**). On **AP Physics 1**, focus on proportional reasoning, area/slope of graphs, and qualitative-quantitative translation (QQT); on **AP Physics C (Mechanics & E&M)**, apply derivatives ($v = dx/dt, F = -dU/dx, E = -dV/dx, I = dQ/dt$), integrals ($W = \int F\,dx, I = \int r^2\,dm, \text{Gauss's Law}$), and separation of variables for first-order differential equations ($F_{\text{drag}} = -bv$ and $RC$ circuits).
- **Linearize Non-Linear Data Using $Y = mX + b$ on Physics Experimental FRQs**: When asked what quantities to graph so the slope yields an unknown constant (e.g., finding $g$ from pendulum period $T = 2\pi\sqrt{L/g}$), square both sides ($T^2 = \frac{4\pi^2}{g}L$), plot $T^2$ vs. $L$, and calculate the slope using **two points on the best-fit line** (never raw data table points!).
- **Always Write Context and Comparative Words on AP Statistics FRQs**: AP Statistics graders score on a holistic rubric (E = Essentially Correct, P = Partially Correct, I = Incorrect). You will automatically drop from **E to P** if you omit **context** (variable names and units), omit **comparative words** (*'higher than,' 'less variable than'*) when comparing distributions, or omit the word **'predicted'** when interpreting regression slopes and intercepts.
- **Follow the 4-Step STATE–PLAN–DO–CONCLUDE Blueprint for AP Statistics Inference**: On every confidence interval or hypothesis test FRQ (especially Question 4 or 6), explicitly write: (1) **STATE** parameter definition in context and $H_0, H_a$ using parameter symbols ($\mu, p, \beta$); (2) **PLAN** exact procedure name and verify Random, $10\%$, and Large Counts/Normal conditions with numbers; (3) **DO** test statistic, $df$, and $p$-value; (4) **CONCLUDE** compare $p$-value to $\alpha$, state 'reject $H_0$' or 'fail to reject $H_0$,' and state conclusion about $H_a$ in context.
- **Never Confuse `==` with `.equals()` or Length Syntax in AP Computer Science A**: Memorize the three length/size syntaxes in Java: **`arr.length`** (field, NO parentheses for 1D/2D arrays: `mat.length` rows, `mat[0].length` cols), **`str.length()`** (method with parentheses for `String`), and **`list.size()`** (method for `ArrayList`). Always use `.equals()`—never `==`—to compare `String` or `Integer` objects.
- **Watch the `ArrayList.remove(i)` Shifting Trap and `for-each` Mutation Trap (AP CS A)**: Whenever you remove elements from an `ArrayList` inside a forward loop (`for (int i = 0; i < list.size(); i++)`), calling `list.remove(i)` shifts subsequent elements left by 1—so you MUST either execute **`i--;`** immediately after `remove(i)` or loop **backward** (`for (int i = list.size() - 1; i >= 0; i--)`). And never use an enhanced `for-each` loop when removing elements or modifying array slots.
- **Use the Two-Step Polymorphism Rule on AP CS A Inheritance Questions**: For any polymorphic reference `SuperClass obj = new SubClass();`, check **Compile Time** using the **left-hand declared type (`SuperClass`)**—if the method does not exist in `SuperClass`, it is a compile-time error! If it compiles, determine **Run-Time behavior** using the **right-hand actual object type (`SubClass`)**—even for helper methods called internally via `this` inside inherited `SuperClass` methods.
- **Protect Partial Credit on AP CS A FRQs**: On the 4 Java Free-Response Questions (Methods/Control Structures, Class Design, Array/`ArrayList`, and 2D Array), graders do not deduct points for minor syntax typos (like a missing semicolon) as long as your intent is unambiguous, **provided** you do not violate method preconditions, mutate input parameters that must remain unchanged, or forget to `return` a value matching the method's return type.

---

## 5. Frequently Asked Questions (FAQ)

### How do the AP Physics 1, AP Physics C: Mechanics, and AP Physics C: E&M exam formats compare?
Under the updated College Board AP Physics exam structure, all AP Physics exams are **3 hours long** and consist of **40 Multiple-Choice Questions** (80 minutes, 50% of score) and **4 Free-Response Questions** (100 minutes, 50% of score: Mathematical Routines, Translation Between Representations, Experimental Design and Analysis, and Qualitative/Quantitative Translation). A graphing or scientific calculator and the official AP Physics Equation Sheet are permitted throughout the entire exam.

### What is the format of the AP Statistics exam, and how is Question 6 ('The Investigative Task') scored?
The AP Statistics exam is **3 hours long**: **Section I** has 40 Multiple-Choice Questions in 90 minutes (50% of score); **Section II** has 6 Free-Response Questions in 90 minutes (50% of score). **Questions 1–5** take ~12–13 minutes each and collectively account for **75% of the FRQ score** (37.5% of total exam score), while **Question 6 (The Investigative Task)** takes ~25 minutes, asks you to apply statistical reasoning to a novel problem beyond standard classroom templates, and is worth **25% of the FRQ score** (12.5% of total exam score). Always budget at least 25 minutes for Question 6!

### What is the format of the AP Computer Science A exam, and what are the 4 Free-Response Question types?
The AP Computer Science A exam is **3 hours long** and tests the official AP Java Subset: **Section I** consists of 40 Multiple-Choice Questions in 90 minutes (50% of score); **Section II** consists of 4 Free-Response Questions in 90 minutes (50% of score, 12.5% each): **FRQ 1: Methods and Control Structures** (loops, conditionals, `String`/`Math`), **FRQ 2: Class Design** (writing a complete Java class or subclass from scratch), **FRQ 3: Array / `ArrayList`** (1D array and `ArrayList` traversal/mutation), and **FRQ 4: 2D Array** (row-major/column-major nested loop algorithms). You are given the official 1-page **Java Quick Reference** sheet on both sections.

### How should I sequence these 6 flashcard decks on flashcards.world?
If you are taking one or more of these STEM AP exams, complete the **Basic** and **Intermediate** decks for your subject during Weeks 1–4 (32 new cards/day) to lock in core formulas, conditions, and syntax, then drill the **Advanced** decks in Weeks 5–7 while writing timed practice FRQs. In the final 7 days before your AP exam, pause new cards and clear your daily spaced-repetition review queue on flashcards.world.

---
**[Explore All Flashcard Sets for This Exam on flashcards.world →](https://flashcards.world/flashcards/?q=AP%20Physics%201%20%26%20C%2C%20AP%20Statistics%20%26%20AP%20Computer%20Science%20A%20High-Yield%20Review&back_lng=en)**

## Curated Flashcard Decks & Practice Sets

- **AP Physics 1 & C: Kinematics, Newton's Laws, Work-Energy Theorem & Linear Momentum**: [Interactive Deck](https://flashcards.world/flashcards/sets/19ab42ba-e89c-40cd-a0a9-bad7a9037bdd/) | [Markdown (.md)](https://flashcards.world/flashcards/sets/19ab42ba-e89c-40cd-a0a9-bad7a9037bdd.md)
- **AP Physics 1 & C: Rotational Dynamics, Simple Harmonic Motion, Electrostatics & DC Circuits**: [Interactive Deck](https://flashcards.world/flashcards/sets/f3c4718a-70d7-4672-a5e0-c4b55041f0b1/) | [Markdown (.md)](https://flashcards.world/flashcards/sets/f3c4718a-70d7-4672-a5e0-c4b55041f0b1.md)
- **AP Statistics: Exploring Data, Normal Distribution, Linear Regression & Experimental Design**: [Interactive Deck](https://flashcards.world/flashcards/sets/d4547d81-4507-4bd2-a49c-4b61243f5810/) | [Markdown (.md)](https://flashcards.world/flashcards/sets/d4547d81-4507-4bd2-a49c-4b61243f5810.md)
- **AP Statistics: Probability, Sampling Distributions, Confidence Intervals & Hypothesis Tests (z, t, Chi-Square)**: [Interactive Deck](https://flashcards.world/flashcards/sets/67e66f7a-28d0-4bb9-a16d-0fc1fa1c4c6e/) | [Markdown (.md)](https://flashcards.world/flashcards/sets/67e66f7a-28d0-4bb9-a16d-0fc1fa1c4c6e.md)
- **AP Computer Science A: Java Primitives, Control Flow, Classes, Objects, Strings, 1D/2D Arrays & ArrayLists**: [Interactive Deck](https://flashcards.world/flashcards/sets/c2f1ae27-6687-4cc1-aa6c-63704efbf2ca/) | [Markdown (.md)](https://flashcards.world/flashcards/sets/c2f1ae27-6687-4cc1-aa6c-63704efbf2ca.md)
- **AP Computer Science A: Inheritance, Polymorphism, Recursion & Searching/Sorting Algorithms**: [Interactive Deck](https://flashcards.world/flashcards/sets/8d91cdd4-8a64-4e4e-ab42-f7b73843a91d/) | [Markdown (.md)](https://flashcards.world/flashcards/sets/8d91cdd4-8a64-4e4e-ab42-f7b73843a91d.md)