- High school📊Trigonometry🔵
Trig circle: the 4 values to memorize (0°, 30°, 45°, 60°, 90°)
One raised hand, five fingers, five angles. The mnemonic to remember cos and sin of all usual angles.
- High school📈Functions🧮
Quadratic equation: the discriminant in 5 seconds
$\Delta = b^2 - 4ac$. Three cases, three scenarios. The universal method for all $ax^2 + bx + c = 0$.
- High school📈Functions📊
Sign table: the method that organizes everything
Study the sign of $f(x)$, solve $f(x) > 0$, understand inequalities: one tool for all these questions.
- High school📊Trigonometry🔵
cos²(x) + sin²(x) = 1: Pythagoras in disguise
The most-used trig identity of high school is nothing but Pythagoras applied to the unit circle. Proof in 30 seconds.
- High school∫Calculus📈
Product rule derivative: the « u'v + uv' » mnemonic
A little phrase to chant so you never mix it up again, and an example that clicks.
- High school🔤Algebra⚡
Spot a notable identity in 2 seconds flat
$(a+b)^2$, $(a-b)^2$, $a^2-b^2$: three patterns to recognize with your eyes closed. The 3 reflexes that speed up the whole chapter.
- High school∫Calculus🔓
The 5 logarithm properties to know 100%
$\ln$ turns products into sums, powers into products. Five formulas that unlock terminal-year calculus.
- High school∫Calculus⚠️
Spot an indeterminate form: the 4 classics
$\infty - \infty$, $\dfrac{0}{0}$, $\dfrac{\infty}{\infty}$, $0 \times \infty$. The 4 traps to catch so you never say « the limit exists » too fast.
- High school∫Calculus🚀
Limit at ±∞: keep only the dominant powers
At ±∞, only the highest-degree term matters. The rest gets crushed. A trick that simplifies 90% of polynomial and rational function limits.
- High school🔤Algebra🔨
Factor a trinomial when you know its roots
If $x_1$ and $x_2$ solve $ax^2 + bx + c = 0$, then $ax^2 + bx + c = a(x - x_1)(x - x_2)$. Free factorization.
- High school∫Calculus📋
The 8 derivatives to know by heart for the exam
A short table, memorizable in 10 minutes, that covers 90% of high school derivative calculations.
- High school∫Calculus🚀
Exponential beats all powers (at +∞)
No matter the power $x^n$, $e^x$ eventually surpasses it. The rule that settles all $e^x / x^n$ limits.
