A-Level Maths Flashcards (AQA Year 13 KA1)

A comprehensive vocabulary review of core formulas and concepts for AQA Year 13 KA1 A-Level Mathematics, spanning Statistics, Calculus, Trigonometry, and Mechanics.

Mean (Formula)

Calculated as $\bar{x} = \frac{\sum x}{n}$.

Standard Deviation (Ungrouped Data)

Calculated as $s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}}$.

Correlation Coefficient

Given by $r = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sqrt{\sum (x - \bar{x})^2 \sum (y - \bar{y})^2}}$, where $-1 \le r \le 1$.

Probability of Independent Events

The probability of two independent events occurring together: $P(A \text{ and } B) = P(A) \times P(B)$.

Conditional Probability Formula

The formula defined as $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$.

Geometric Distribution Formula

The probability mass function given by $P(X = r) = (1 - p)^{r-1} p$, for $r = 1, 2, 3, \dots$.

Binomial Distribution Formula

The probability formula given by $P(X = r) = \binom{n}{r} p^r (1 - p)^{n-r}$.

Normal Distribution Rule

States that approximately $68\%$ of values lie within $1\sigma$, $95\%$ within $2\sigma$, and $99.7\%$ within $3\sigma$.

Power Rule

The differentiation rule stating that $\frac{d}{dx}(x^n) = n x^{n-1}$.

Product Rule

The differentiation rule stating that $\frac{d}{dx}(uv) = u \frac{dv}{dx} + v \frac{du}{dx}$.

Chain Rule

The differentiation rule stating that $\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}$.

Implicit Differentiation

The process of differentiating both sides of an equation with respect to $x$ and solving for $\frac{dy}{dx}$.

Integral of $x^n$

Given by $\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$, where $n \ne -1$.

Integral of $\frac{1}{x}$

Given by $\int \frac{1}{x}\,dx = \ln(|x|) + C$.

Integration by Parts

The integration formula given by $\int u\,dv = uv - \int v\,du$.

Integration by Substitution

The rule stating that if $x = g(t)$, then $\int f(x)\,dx = \int f(x(t)) \frac{dg}{dt}\,dt$.

Double Angle Formula for Sine

The trigonometric identity given by $\sin(2x) = 2 \sin(x) \cos(x)$.

Double Angle Formula for Cosine

The trigonometric identities given by $\cos(2x) = \cos^2(x) - \sin^2(x) = 1 - 2\sin^2(x) = 2\cos^2(x) - 1$.

Small Angle Approximations

For $x$ in radians: $\sin(x) \approx x$ and $\cos(x) \approx 1 - \frac{x^2}{2}$.

Sine Rule

The relationship given by $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$.

SUVAT (Displacement)

The kinematic formula relating displacement to initial velocity, time, and acceleration: $s = ut + \frac{1}{2} a t^2$.

Velocity Equation (SUVAT)

The kinematic equation given by $v = u + at$.

Final Velocity Equation (SUVAT)

The kinematic equation relating velocities, acceleration, and displacement: $v^2 = u^2 + 2as$.

Momentum Equation

The formula defining linear momentum: $p = mv$.

Projectile Velocity Components

The initial horizontal and vertical velocity components given by $u_x = u \cos(\theta)$ and $u_y = u \sin(\theta)$.

Time of Flight (Projectiles)

The duration of flight for same-height launch and landing: $T = \frac{2u \sin(\theta)}{g}$.

Maximum Height (Projectiles)

The maximum vertical displacement of a projectile: $H = \frac{u^2 \sin^2(\theta)}{2g}$.

Range (Projectiles)

The total horizontal distance traveled for a launch and landing at the same height: $R = \frac{u^2 \sin(2\theta)}{g}$.