Every Formula and Identity to Memorise for IGCSE Add Math

0606 effectively assumes you carry the formula book in your head. Here is the complete memorise list, organised by topic, with the highest-frequency items marked. Print it, blank-page test yourself weekly, and use our memorisation method to make it stick.

Quadratics ★ (every paper)

• Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• Discriminant: $b^2 - 4ac$, $> 0$ two real roots; $= 0$ repeated; $< 0$ no real roots
• Completed square form: $a(x + p)^2 + q$, vertex at $(-p, q)$
• Line–curve intersection: substitute, form quadratic, apply discriminant, see quadratic functions

Logarithms & exponentials ★

• log rules: $\log a + \log b = \log ab$; $\log a - \log b = \log\frac{a}{b}$; $n \log a = \log a^n$
• Change of base: $\log_b a = \frac{\log a}{\log b}$
• Definitions: $y = a^x \Leftrightarrow x = \log_a y$; $e$ and $\ln$ as inverse pair: $e^{\ln x} = x$
• Linear-form reductions: $y = ax^n \to \log y = \log a + n \log x$; $y = Ab^x \to \log y = \log A + x \log b$, see logs & exponentials

Trigonometry ★ (the most-tested identities in 0606)

• $\tan\theta = \frac{\sin\theta}{\cos\theta}$
• $\sin^2\theta + \cos^2\theta = 1$, and its rearrangements
• $1 + \tan^2\theta = \sec^2\theta$; $1 + \cot^2\theta = \csc^2\theta$
• $\sec\theta = \frac{1}{\cos\theta}$, $\csc\theta = \frac{1}{\sin\theta}$, $\cot\theta = \frac{1}{\tan\theta}$
• R-formula: $a \sin\theta \pm b \cos\theta = R \sin(\theta \pm \alpha)$, $R = \sqrt{a^2 + b^2}$, $\tan\alpha = \frac{b}{a}$
• Exact values table: $\sin$/$\cos$/$\tan$ of $0°$, $30°$, $45°$, $60°$, $90°$ (and radian equivalents), see trigonometry

Circular measure ★

• $\pi$ radians $= 180°$
• Arc length: $s = r\theta$ ($\theta$ in radians)
• Sector area: $A = \frac{1}{2}r^2\theta$, see circular measure

Straight lines & the circle

• Gradient: $\frac{y_2 - y_1}{x_2 - x_1}$; midpoint; length $\sqrt{(\Delta x)^2 + (\Delta y)^2}$
• Perpendicular gradients: $m_1 m_2 = -1$
• Circle: $(x - a)^2 + (y - b)^2 = r^2$, centre $(a, b)$, radius $r$; general form $x^2 + y^2 + 2gx + 2fy + c = 0$ with centre $(-g, -f)$, $r = \sqrt{g^2 + f^2 - c}$, see circle geometry

Series ★

• Binomial: $(a + b)^n = \sum {}^nC_r \, a^{n-r} b^r$; ${}^nC_r = \frac{n!}{r!(n-r)!}$
• AP: $u_n = a + (n-1)d$; $S_n = \frac{n}{2}(2a + (n-1)d)$
• GP: $u_n = ar^{n-1}$; $S_n = \frac{a(1 - r^n)}{1 - r}$; $S_\infty = \frac{a}{1 - r}$ for $|r| < 1$, see series

Permutations & combinations

• ${}^nP_r = \frac{n!}{(n-r)!}$, order matters; ${}^nC_r = \frac{n!}{r!(n-r)!}$, order doesn’t, see permutations & combinations

Calculus ★★ (largest topic in the syllabus)

• Power rule: $\frac{d}{dx}(x^n) = nx^{n-1}$
• Product rule: $(uv)' = u'v + uv'$
• Quotient rule: $\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$
• Chain rule: $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$
• Standard derivatives: $\sin x \to \cos x$; $\cos x \to -\sin x$; $\tan x \to \sec^2 x$; $e^x \to e^x$; $\ln x \to \frac{1}{x}$
• Integration as reverse: $\int x^n \,dx = \frac{x^{n+1}}{n+1} + c$ ($n \ne -1$); $\int (ax+b)^n$, $\int e^{ax+b}$, $\int \sin$/$\cos$ forms
• Definite integral $=$ area under curve between limits
• Kinematics chain: differentiate displacement to get velocity, differentiate velocity to get acceleration, integrate to go back, see calculus

Vectors

• Magnitude: $|x\mathbf{i} + y\mathbf{j}| = \sqrt{x^2 + y^2}$; unit vector: $\frac{\mathbf{v}}{|\mathbf{v}|}$
• Position vector of point dividing $AB$; relative velocity setup, see vectors

How to actually memorise this list

Reading it nightly does almost nothing. What works: blank-page recall (write the whole list from memory twice a week, check, drill the gaps) plus use in context, every formula gets cemented by the questions that need it. The full routine is in how to memorise Add Math formulae, and the 8-week revision plan schedules recall drills automatically.

Students in our 1-to-1 online classes get this list drilled as a standing warm-up, by exam week it’s reflex. If that structure would help, Teacher Rig offers a free 1-hour trial class over WhatsApp.