All flashcard decks Matura Shtetërore (Albania) syllabus →

26 cardsMatura Shtetërore (Albania)

Key Formulas for Matura Mathematics

26 flashcards with the main algebra, calculus, geometry, sequence and probability formulas. Study material written for practice, not an official test.

Start studying Play Match

PDF study sheet

Free account needed to save, copy or download. We bring you back here.

1 / 26

0 known

TermClick or press Space to flip

Quadratic formula

GetMyMockTestQuestion side

Full list

Terms in this deck (26)

Matura Shtetërore (Albania) mock tests →

Quadratic formula

For

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

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

Discriminant and number of real roots

D = b^{2} - 4 a c

D > 0

: two real roots;

D = 0

: one double root;

D < 0

: no real roots.

Vieta's formulas

For

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

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

and

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

Difference of squares

a^{2} - b^{2} = (a - b) (a + b)

Laws of logarithms

lo g (x y) = lo g x + lo g y

lo g \frac{x}{y} = lo g x - lo g y

lo g x^{n} = n lo g x

Definition of a logarithm

lo g_{a} b = c

means

a^{c} = b

, with

a > 0

a \neq = 1

b > 0

Power rule for derivatives

(x^{n})^{'} = n x^{n - 1}

Product rule

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

Quotient rule

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

Chain rule

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

Derivative of

e^{x}

and

ln x

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

and

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

for

x > 0

Derivatives of sine and cosine

(sin x)^{'} = cos x

and

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

Condition for a local maximum or minimum

Solve

f^{'} (x) = 0

. If

f^{'}

changes from

+

-

it is a maximum; from

-

+

it is a minimum.

Power rule for integrals

\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C

for

n \neq = - 1

Area under a curve

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

when

f (x) \geq 0

[a, b]

Pythagorean identity

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

Double-angle formulas

sin 2 x = 2 sin x cos x

and

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

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos C

Law of sines

\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C} = 2 R

Arithmetic sequence

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

and

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

Geometric sequence

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

and

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

for

q \neq = 1

Sum of an infinite geometric series

S = \frac{a _{1}}{1 - q}

, valid only when

∣ q ∣ < 1

Combinations

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

Equation of a circle

(x - a)^{2} + (y - b)^{2} = r^{2}

has centre

(a, b)

and radius

r

Distance from a point to a line

d = \frac{∣ A x _{0} + B y _{0} + C ∣}{A ^{2} + B ^{2}}

for the line

A x + B y + C = 0

Volume of a cone and a sphere

Cone:

V = \frac{1}{3} π r^{2} h

. Sphere:

V = \frac{4}{3} π r^{3}

More Matura Shtetërore (Albania) practice

Matura Shtetërore (Albania) mock tests

All Matura Shtetërore (Albania) practice →