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25 Cards in this Set
- Front
- Back
The remainder theorem |
When polynomial f(x) is divided by (ax - b) then the remainder is f(b/a) |
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The sine rule |
a/SinA = b/SinB = c/SinC or SinA/a = SinB/b = SinC/c |
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The cosine rule |
a² =b² + c² - 2bc CosA and CosA = (b² + c² - a²) / (2bc) |
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The area of a triangle |
1/2 abSinC |
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The multiplication law (logs) |
LOGaXY = LOGaX + LOGaY |
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The division law (logs) |
LOGa(X/Y) = LOGaX - LOGaY |
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The power law (logs) |
LOGa(X)^k = kLOGaX and LOGa(1/X) = -LOGaX |
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Change of base rule (logs) |
LOGaX= LOGbX / LOGbA |
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The mid-point of a line |
( (X1 + X2) / 2, (Y1 + Y2) / 2 )
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The length of a line |
√ (X2 - X1)² + (Y2 - Y1)² |
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Equation of a circle |
Centre (a, b), radius = r, (X - a)² + (Y - b)² = r² |
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Pascals Triangle |
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 |
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The binomial expansion |
(a + bx)^n = nC0 a^n + nC1 a^n-1 bx + nC2 a^n-2 b^2 x^2 + ... nCn b^n x^n |
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Radians into degrees |
1r = 180d / Pi |
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Length of arc |
l = rθ |
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Area of a sector |
A = 1/2 r² |
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Area of a segment |
A = 1/2 r² (θ - sinθ) |
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Sum to n of a series |
Sn = a(1-r^n) / (r - 1) |
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Sum to infinity |
S ∞ = a / (1 - r) |
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sin θ, cos θ, tan θ |
sin θ = y/r cos θ = x/r tan θ = y/x |
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Trig quadrant rule |
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Increasing / decreasing functions differentiation |
f ' (x) > 0 increasing f ' (x) < 0 decreasing |
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Stationary points |
f ' (x) = 0 f ''(x) < 0 max point f ''(x) > 0 min point |
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Trig identities - rule 1 |
tan θ = sin θ / cos θ |
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Trig identities - rule 2 |
sin² θ + cos² θ = 1 |