- 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.
- High school๐Geometry๐บ
Triangle area with sine: ยฝยทaยทbยทsin(C)
Two sides and the included angle are enough. One formula for any triangle, no height needed.
- 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.
- High school๐คAlgebraโ
1 + 2 + 3 + ... + n = n(n+1)/2: Gauss's formula
Young Gauss found it at age 8 by folding the series on itself. One of the most elegant results in math.
- High school๐Functions๐ฏ
Sum and product of roots: S = โb/a, P = c/a
For axยฒ+bx+c=0, the roots satisfy xโ+xโ = โb/a and xโยทxโ = c/a. Handy without the discriminant.
- High school๐Functions๐
Tangent line equation: y = f'(a)(x โ a) + f(a)
The tangent at a has slope f'(a) and passes through (a, f(a)). One formula, everything's in it.
- High schoolโซCalculus๐ฎ
Squeeze theorem: sandwich to conclude
If v_n โค u_n โค w_n and v_n, w_n both tend to โ, so does u_n. A classic for tricky limits.
- High school๐Functions๐
Successive percentage changes: the +10% then โ10% trap
+10% then โ10% does NOT bring you back to the starting price. The multiplier trick that fixes this in 3 seconds.
- 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.