Master Gaokao Math: 102 Formula Flashcards from the Sine Rule to De Moivre
Every formula the gaokao maths paper assumes you know: 102 flashcards across algebra, trigonometry, calculus, conics, vectors and probability.
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In a gaokao maths paper, a formula you half-remember is worth nothing. The Gaokao Math Formulas deck (code ZP1212, 102 cards) on Flip It is the recall layer: every identity and equation the paper assumes you already have, one per card — front = name, back = the formula.
Study this deck: Gaokao Math Formulas
1 / 10Quadratic formula
Tap the card for the answer · swipe right if you knew it, left if not
The 102 formulas, by block
- Algebra and sequences (20 cards) — quadratic formula, discriminant, sum and product of roots, binomial expansion with C(n,k), difference of squares, sum and difference of cubes, arithmetic and geometric general terms and sums, sums of the first n squares and cubes.
- Trigonometry (19) — sine rule with 2R, cosine rule, area by sine and by Heron, Pythagorean and tangent identities, reciprocal identities, double angle, half angle, sum and difference of angles, product-to-sum.
- Calculus (15) — derivatives of xⁿ, eˣ, ln x, sin, cos, tan, cot; product, quotient and chain rules; the matching integrals; the fundamental theorem; area under a curve.
- Analytic geometry (17) — distance in 2D and 3D, midpoint, slope, point-slope, slope-intercept and two-point forms, parallel and perpendicular conditions, circle, ellipse, hyperbola and parabola with foci and directrix.
- Vectors and solids (8) — magnitude, dot and cross product, parallel and perpendicular conditions, sphere equation, volume of sphere, cylinder and cone.
- Probability and statistics (12) — classical probability, complement, addition and multiplication rules, conditional probability, permutations, combinations, mean, variance, standard deviation, binomial probability.
- Logs, exponentials, complex numbers, inequalities (11) — log product, quotient and power rules, change of base, exponent laws, complex modulus and multiplication, De Moivre, AM-GM, Cauchy-Schwarz.
Ten cards as they appear:
| Front | Back |
|---|---|
| Discriminant of quadratic | Delta = b² - 4ac; > 0: two real roots; = 0: one; < 0: none |
| Sine rule | a/sin A = b/sin B = c/sin C = 2R |
| Double angle: cosine | cos 2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ |
| Chain rule | d/dx(f(g(x))) = f'(g(x)) × g'(x) |
| Integral power rule | ∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ -1) |
| Hyperbola equation (horizontal) | x²/a² - y²/b² = 1; foci at (±c, 0), c² = a² + b² |
| Conditional probability | P(A given B) = P(A ∩ B) / P(B) |
| De Moivre's theorem | (cos θ + i sin θ)ⁿ = cos(nθ) + i sin(nθ) |
How to drill it
Two weeks at eight new cards a day, but block order beats pace: algebra and sequences first, then trigonometry, analytic geometry, calculus, probability last. Review both directions — naming an identity you are shown is a different skill from recalling it cold.
Two traps in this deck
1. Learn the conditions, not just the formulas. Several backs carry a restriction that is exactly where marks are lost: the infinite geometric sum needs |r| < 1, the finite sum needs r ≠ 1, the integral power rule excludes n = -1, the half-angle formulas keep a ± that your quadrant decides, AM-GM requires a, b ≥ 0. The condition is part of the answer.
2. Separate the conic pair. The ellipse card gives c² = a² - b², the hyperbola card gives c² = a² + b². One sign, and the foci land in the wrong place for the whole question. Drill those two back to back, and do the same with the three forms of cos 2θ.
Efficiency note: roughly fifteen cards are derivable in seconds from others — product-to-sum falls out of the sum and difference formulas, double angle is the sum formula with α = β, the sum of the first n cubes is the square of the sum of the first n.
Sign in to Flip It and find Gaokao Math Formulas (ZP1212) in the library. New to the exam itself? Start with how the gaokao works.
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