Complete AP Physics 1 & C, AP Statistics & AP Computer Science A / Principles 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

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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	32	Study Set →
Module 2	intermediate	AP Physics 1 & C: Rotational Dynamics, Simple Harmonic Motion, Electrostatics & DC Circuits	32	Study Set →
Module 3	basic	AP Statistics: Exploring Data, Normal Distribution, Linear Regression & Experimental Design	32	Study Set →
Module 4	intermediate	AP Statistics: Probability, Sampling Distributions, Confidence Intervals & Hypothesis Tests (z, t, Chi-Square)	32	Study Set →
Module 5	advanced	AP Computer Science A: Java Primitives, Control Flow, Classes, Objects, Strings, 1D/2D Arrays & ArrayLists	32	Study Set →
Module 6	advanced	AP Computer Science A: Inheritance, Polymorphism, Recursion & Searching/Sorting Algorithms	32	Study Set →

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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

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) (/flashcards/sets/02924399-2209-49df-ae6b-3a1ab0b6ced1)
• Level Search: BASIC Sets on flashcards.world

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^)	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 = -)	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 are the four Constant-Acceleration ('Big 4') Kinematic Equations, and which variable is missing from each?	1. $v = v_0 + at$ (missing displacement $\Delta x$) 2. $\Delta x = v_0 t + \frac{1}{2}at^2$ (missing final velocity $v$) 3. $v^2 = v_0^2 + 2a\Delta x$ (missing time $t$) 4. $\Delta x = \frac{1}{2}(v_0 + v)t$ (missing acceleration $a$)
2	How do Position $x(t)$, Velocity $v(t)$, and Acceleration $a(t)$ relate via Calculus (AP Physics C) and Graph Slopes/Areas (AP Physics 1)?	• Derivatives (Slopes): $v(t) = \frac{dx}{dt}$ (slope of $x\text{–}t$ graph) and $a(t) = \frac{dv}{dt} = \frac{d^2x}{dt^2}$ (slope of $v\text{–}t$ graph). • Integrals (Signed Areas): $\Delta x = \int_{t_1}^{t_2} v(t),dt$ (area under $v\text{–}t$ graph) and $\Delta v = \int_{t_1}^{t_2} a(t),dt$ (area under $a\text{–}t$ graph). • An object speeds up when $v(t)$ and $a(t)$ have the SAME sign, and slows down when $v(t)$ and $a(t)$ have OPPOSITE signs.
3	In 2D Projectile Motion (neglecting air resistance) launched at speed $v_0$ and angle $\theta$ above horizontal, what are the horizontal and vertical components of velocity and acceleration at the highest point (apex), plus the Time of Flight and Range formulas?	• Horizontal: $a_x = 0$, $v_x = v_0 \cos\theta = \text{constant}$ throughout flight. • Vertical: $a_y = -g$ downward everywhere; at the apex, $v_y = 0$, $v_{\text{total}} = v_0 \cos\theta$, and $a_{\text{total}} = g$ downward (acceleration is NEVER zero at the top!). • Level-Ground Time of Flight: $T = \frac{2v_0 \sin\theta}{g}$; Max Height: $H = \frac{v_0^2 \sin^2\theta}{2g}$; Horizontal Range: $R = \frac{v_0^2 \sin(2\theta)}{g}$ (maximized at $\theta = 45^\circ$; complementary angles $\theta$ and $90^\circ - \theta$ give equal range).
4	State Newton's Three Laws of Motion and identify what constitutes a valid Newton's Third Law Action-Reaction Pair.	1. First Law (Inertia): If $\sum \vec{F} = 0$, an object remains at rest or moves at constant velocity ($\vec{a} = 0$, translational equilibrium). 2. Second Law: $\vec{a} = \frac{\sum \vec{F}}{m}$ (or $\sum \vec{F} = \frac{d\vec{p}}{dt} = m\vec{a}$). 3. Third Law: $\vec{F}{A\text{ on }B} = -\vec{F}{B\text{ on }A}$. A valid Third Law pair ALWAYS acts on two DIFFERENT objects and involves the exact same type of force (e.g., Earth's gravitational pull down on a book and the book's gravitational pull up on the Earth—NEVER normal force and weight on the same book!).
5	For a block of mass $m$ on an Inclined Plane angled at $\theta$ above the horizontal with coefficient of kinetic friction $\mu_k$, what are the parallel and perpendicular components of gravity, the Normal Force $F_N$, and the acceleration down the ramp?	• Parallel component of gravity: $F_{g\parallel} = mg\sin\theta$ (pulls down the incline). • Perpendicular component of gravity: $F_{g\perp} = mg\cos\theta$ (into the incline). • Normal Force (with no other vertical forces): $F_N = mg\cos\theta$. • Kinetic Friction: $f_k = \mu_k F_N = \mu_k mg\cos\theta$ (opposes direction of sliding). • Acceleration sliding down the incline: $a = g(\sin\theta - \mu_k\cos\theta)$ (independent of mass $m$!).
6	Contrast Static Friction ($f_s$) and Kinetic Friction ($f_k$), and find the maximum angle $\theta_{\max}$ of an incline before a stationary block begins to slide.	• Static Friction: $f_s \le \mu_s F_N$ (a self-adjusting force that matches the applied parallel force up to the threshold $f_{s,\max} = \mu_s F_N$). • Kinetic Friction: $f_k = \mu_k F_N$ (constant while sliding; $\mu_k < \mu_s$). • Angle of Repose ($\theta_{\max}$): At the verge of slipping on an incline, $mg\sin\theta_{\max} = \mu_s mg\cos\theta_{\max} \implies \tan\theta_{\max} = \mu_s \implies \theta_{\max} = \arctan(\mu_s)$.

Module 2 (INTERMEDIATE): AP Physics 1 & C: Rotational Dynamics, Simple Harmonic Motion, Electrostatics & DC Circuits

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) (/flashcards/sets/db23d541-2a61-4254-a1ed-27830e95d7bc)
• Level Search: INTERMEDIATE Sets on flashcards.world

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	How do Rotational Kinematic variables ($\theta, \omega, \alpha$) connect to Linear (Translational) variables ($s, v_t, a_t, a_c$) for a point at radius $r$ from the axis of rotation?	Using radians ($\theta$ in $\text{rad}$, $\omega = d\theta/dt$ in $\text{rad/s}$, $\alpha = d\omega/dt$ in $\text{rad/s}^2$): • Arc Length: $s = r\theta$ • Tangential Speed: $v_t = r\omega$ • Tangential Acceleration: $a_t = r\alpha$ (changes the magnitude of speed) • Centripetal (Radial) Acceleration: $a_c = \frac{v_t^2}{r} = r\omega^2$ (points toward axis) • Total Linear Acceleration: $a_{\text{total}} = \sqrt{a_t^2 + a_c^2}$.
2	Define Torque ($\vec{\tau}$) and state the two conditions required for Complete Static Equilibrium of a rigid body.	• Torque: $\vec{\tau} = \vec{r} \times \vec{F}$, with magnitude: $$\tau = r F \sin\theta = r F_{\perp} = r_{\perp} F$$ (where $r_{\perp} = r\sin\theta$ is the lever arm / moment arm, measured in $\text{N}\cdot\text{m}$). • Complete Static Equilibrium: 1. Translational Equilibrium: $\sum \vec{F} = 0$ ($\sum F_x = 0$ and $\sum F_y = 0$). 2. Rotational Equilibrium: $\sum \tau = 0$ about ANY chosen pivot point (choose the pivot at the location of an unknown force to eliminate its torque!).
3	Define Rotational Inertia (Moment of Inertia, $I$), state the Parallel-Axis Theorem, and rank common shapes of equal mass $M$ and radius $R$.	• Definition: $I = \sum m_i r_i^2 = \int r^2,dm$ (measures resistance to angular acceleration; increases when mass is distributed farther from the axis of rotation). • Parallel-Axis Theorem: If $I_{\text{cm}}$ is the moment of inertia about an axis through the center of mass, then about any parallel axis a distance $d$ away: $$I = I_{\text{cm}} + Md^2$$ • Common Shapes ($I = cMR^2$): - Thin Hoop / Cylindrical Shell: $I = MR^2$ ($c = 1$, largest $I$) - Thin Spherical Shell: $I = \frac{2}{3}MR^2$ - Solid Disk / Cylinder: $I = \frac{1}{2}MR^2$ - Solid Sphere: $I = \frac{2}{5}MR^2$ ($c = 0.4$, smallest $I$).
4	State Newton's Second Law for Rotation ($\sum \tau = I\alpha$) and find the linear acceleration $a$ of a mass $m$ hanging from a string wound around a solid pulley disk of mass $M$, radius $R$, and $I = \frac{1}{2}MR^2$.	1. Hanging Mass $m$ (downward positive): $mg - T = ma$. 2. Pulley $M$ (with no slipping, $\alpha = a/R$): $\tau = TR = I\alpha = \left(\frac{1}{2}MR^2\right)\left(\frac{a}{R}\right) \implies T = \frac{1}{2}Ma$. 3. Substitute $T$ into the first equation: $$mg - \frac{1}{2}Ma = ma \implies a = \frac{mg}{m + \frac{1}{2}M}$$
5	What are the conditions for Rolling Without Slipping, the Total Kinetic Energy of a rolling object, and the winner of the 'Great Downhill Race' down an incline?	• Rolling Without Slipping Conditions: $v_{\text{cm}} = R\omega$ and $a_{\text{cm}} = R\alpha$ (the bottom contact point is instantaneously at rest, $v_{\text{bottom}} = 0$, while $v_{\text{top}} = 2v_{\text{cm}}$; static friction provides the torque to roll without doing any dissipative work!). • Total Kinetic Energy: $$K_{\text{total}} = K_{\text{trans}} + K_{\text{rot}} = \frac{1}{2}Mv_{\text{cm}}^2 + \frac{1}{2}I_{\text{cm}}\omega^2$$ • Race Down an Incline of Height $h$ (for $I = cMR^2$): $$Mgh = \frac{1}{2}Mv^2(1 + c) \implies v = \sqrt{\frac{2gh}{1 + c}} \quad \text{and} \quad a = \frac{g\sin\theta}{1 + c}$$ Independent of mass $M$ and radius $R$! The shape with the smallest shape factor $c$ wins: Frictionless block ($c=0$) $>$ Solid Sphere ($c=2/5$) $>$ Solid Disk ($c=1/2$) $>$ Hollow Sphere ($c=2/3$) $>$ Hoop ($c=1$).
6	Define Angular Momentum ($\vec{L}$) for a Point Particle vs. a Rigid Body, and state the Law of Conservation of Angular Momentum.	• Rigid Body rotating about symmetry axis: $L = I\omega$. • Point Particle moving with linear momentum $\vec{p} = m\vec{v}$ relative to a pivot: $$\vec{L} = \vec{r} \times \vec{p} \implies L = m v r \sin\theta = m v r_{\perp}$$ (Yes, a particle moving in a straight line has constant non-zero angular momentum about any point not on its line of motion!). • Conservation of Angular Momentum (since $\sum \vec{\tau}{\text{ext}} = \frac{d\vec{L}}{dt}$): If **net external torque is zero ($\sum \tau{\text{ext}} = 0$)**, total angular momentum is conserved: $$L_i = L_f \implies I_i\omega_i = I_f\omega_f$$ (When a spinning figure skater pulls her arms inward, $I$ decreases $\rightarrow \omega$ increases, and rotational kinetic energy $K_{\text{rot}} = \frac{L^2}{2I}$ INCREASES due to internal work done by her muscles!).

Module 3 (BASIC): AP Statistics: Exploring Data, Normal Distribution, Linear Regression & Experimental Design

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) (/flashcards/sets/ac66a4a5-1eb4-465a-a06d-ff1edbe50d6d)
• Level Search: BASIC Sets on flashcards.world

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 ); 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)

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.

• Direct Set Link: AP Statistics: Probability, Sampling Distributions, Confidence Intervals & Hypothesis Tests (z, t, Chi-Square) (32 Cards) (/flashcards/sets/9d09dd39-a240-4625-ae9c-518d0bdc3918)
• Level Search: INTERMEDIATE Sets on flashcards.world

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); 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

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.

• Direct Set Link: AP Computer Science A: Java Primitives, Control Flow, Classes, Objects, Strings, 1D/2D Arrays & ArrayLists (32 Cards) (/flashcards/sets/595b333e-7fc8-4124-a2b3-1f329609bb19)
• Level Search: ADVANCED Sets on flashcards.world

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

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.

• Direct Set Link: AP Computer Science A: Inheritance, Polymorphism, Recursion & Searching/Sorting Algorithms (32 Cards) (/flashcards/sets/9bd6c35a-c4a3-4024-aa9a-0addaa57c3dc)
• Level Search: ADVANCED Sets on flashcards.world

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) + 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!

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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.

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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.

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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.

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