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
119 tricks- High school๐คAlgebra0๏ธโฃ
Zero product equation: A ร B = 0 in 2 seconds
If a product equals 0, at least one factor is 0. The rule that cracks every factored equation.
- 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.
- High school๐ฒProbability๐
Variance and standard deviation: dispersion in 2 formulas
How to measure a data set's spread. Variance = mean squared deviation. Standard deviation = square root of variance.
- High school๐Geometryโก๏ธ
Vector coordinates: AB = (xB โ xA, yB โ yA)
A vector's coordinates are 'arrival minus departure'. Easy to remember, works everywhere.
- Middle school๐Geometry๐บ
Volumes of cone, pyramid, and sphere: the 3 formulas
Cone/pyramid = (base ร height) / 3. Sphere = 4/3ยทฯยทrยณ. Three formulas for every middle-school solid.
- 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.
- High school๐Geometry๐บ
Triangle area with sine: ยฝยทaยทbยทsin(C)
Two sides and the included angle are enough. One formula for any triangle, no height needed.
- 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
Trigonometric equations: the unit circle method
cos(x) = a, sin(x) = a, tan(x) = a. All solutions on โ using the unit circle.
- Middle school๐Geometry๐
Thales contrapositive: prove two lines are NOT parallel
If ratios aren't equal, lines aren't parallel. The contrapositive of the theorem.
- 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.
- Middle school๐Geometryโก๏ธ
Translation by a vector: the transformation that 'slides' everything
Every point moves by the same vector. No fixed point. Preserves everything (distances, angles, areas, orientation).