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Bacalaureat Mathematics Key Formulas

26 flashcards with the main formulas of calculus, algebra, matrices, geometry and probability. Study material written for practice, not the official exam.

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Derivative of

x^{n}

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Derivative of

x^{n}

n x^{n - 1}

(the power rule).

Product rule

(uv)^{'} = u^{'} v + u v^{'}

Quotient rule

(\frac{u}{v})^{'} = \frac{u ^{'} v - u v ^{'}}{v ^{2}}

for

v \neq = 0

Chain rule

(f (g (x)))^{'} = f^{'} (g (x)) \cdot g^{'} (x)

Derivatives of

e^{x}

and

ln x

(e^{x})^{'} = e^{x}

and

(ln x)^{'} = \frac{1}{x}

for

x > 0

Derivatives of

sin x

and

cos x

(sin x)^{'} = cos x

and

(cos x)^{'} = - sin x

Discriminant of

a x^{2} + b x + c

Δ = b^{2} - 4 a c

: two real roots if

Δ > 0

, one double root if

Δ = 0

, none if

Δ < 0

Vieta's relations

For

a x^{2} + b x + c = 0

x_{1} + x_{2} = - \frac{b}{a}

and

x_{1} x_{2} = \frac{c}{a}

Fundamental theorem of calculus

\int_{a}^{b} f (x) d x = F (b) - F (a)

, where

F^{'} = f

Integration by parts

\int u d v = uv - \int v d u

Determinant of a

2 \times 2

matrix

det (a c b d) = a d - b c

Inverse of a

2 \times 2

matrix

A^{- 1} = \frac{1}{d e t A} (d - c - b a)

when

det A \neq = 0

Modulus of a complex number

∣ a + bi ∣ = a^{2} + b^{2}

Powers of

i

i, - 1, - i, 1

repeating with period

4

; use

n mod 4

Number of permutations of

n

objects

n! = n (n - 1) \dots 2 \cdot 1

Number of combinations of

k

from

n

(k n) = \frac{n !}{k ! ( n - k )!}

Number of arrangements of

k

from

n

A_{n}^{k} = \frac{n !}{( n - k )!}

n

-th term of an arithmetic progression

a_{n} = a_{1} + (n - 1) r

, with sum

S_{n} = \frac{n ( a _{1} + a _{n} )}{2}

n

-th term of a geometric progression

b_{n} = b_{1} q^{n - 1}

, with sum

S_{n} = b_{1} \frac{q ^{n} - 1}{q - 1}

for

q \neq = 1

Equation of a line through two points

\frac{y - y _{1}}{y _{2} - y _{1}} = \frac{x - x _{1}}{x _{2} - x _{1}}

Distance between two points

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Dot product of two vectors

a \cdot b = a_{1} b_{1} + a_{2} b_{2}

, and it is zero for perpendicular vectors.

Pythagorean identity

sin^{2} x + cos^{2} x = 1

Law of logarithms for a product

lo g_{b} (x y) = lo g_{b} x + lo g_{b} y

for

x, y > 0

Tangent line to

y = f (x)

x_{0}

y - f (x_{0}) = f^{'} (x_{0}) (x - x_{0})

Probability of independent events

P (A \cap B) = P (A) P (B)

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