Math, made clever
Tricks that make math click.
From middle school to college prep โ one short read + a mini exercise. Understand fast, remember longer.
All tricks
41 tricks- Middle school๐Geometry๐บ
Triangle area: half of the surrounding rectangle
Base ร height รท 2: the formula comes from a rectangle cut in half. The visual proof that makes the formula obvious.
- High school๐Trigonometry๐ต
Trig circle: the 4 values to memorize (0ยฐ, 30ยฐ, 45ยฐ, 60ยฐ, 90ยฐ)
One raised hand, five fingers, five angles. The mnemonic to remember cos and sin of all usual angles.
- Middle school๐Geometry๐บ
A triangle's angles always sum to 180ยฐ
Why 180ยฐ? Cut the angles out with scissors โ they form a straight line. Proof in 3 animated steps.
- Middle schoolโกMental math๐ฏ
Squaring a number ending in 5, without a calculator
Multiply the left part by itself + 1, stick 25 at the end. Done.
- Middle school๐Geometry๐ญ
Thales' theorem: when triangles zoom
Two lines from the same point, cut by parallels. The lengths stay proportional. The key to measuring without measuring.
- High school๐Functions๐งฎ
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 school๐Functions๐
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.
- College prepโซCalculus๐
Taylor expansions at 0: the 6 essentials for prep classes
$e^x$, $\ln(1+x)$, $\sin$, $\cos$, $(1+x)^\alpha$, $\dfrac{1}{1-x}$ to order 3. The table that unlocks all 0-limits.
- Middle school๐Geometry๐
Pythagoras' theorem, without formulas: the 3-squares proof
A right triangle, three squares drawn on its sides. The visual trick that makes the formula obvious.
- High school๐Trigonometry๐ต
cosยฒ(x) + sinยฒ(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.
- Middle school๐ขArithmetic๐งฎ
Powers of 2 to memorize (up to 1024)
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024โฆ A short list that unlocks tons of mental math โ and all of computing.
- High schoolโซCalculus๐
Product rule derivative: the ยซ u'v + uv' ยป mnemonic
A little phrase to chant so you never mix it up again, and an example that clicks.