Assalomu alaykum aziz obunachilarim! Bugundan boshlab siz ushbu kanalda matematikaga materiallar va chet el universitetlari matematika imtihoniga kerak bolgan narsalar bilan taminlanib borasizlar.
_________________________________
Hello dear subscribers! From today, you will be provided with materials for mathematics on this channel and what you need for the math exam of foreign universities.
_________________________________
Hello dear subscribers! From today, you will be provided with materials for mathematics on this channel and what you need for the math exam of foreign universities.
Westminster_International_University.pdf
174.1 MB
Westminster international university's Math book in English
@math_emperor
@math_emperor
Qisqa ko'paytirish formulalari / Short multiplication formulas
1.Yig'indining kvadrati / Square of sum:
(a+b)²=a²+2ab+b²
2. Ayirmaning kvadrati / Square of difference:
(a-b)²=a²-2ab+b²
3. Kvadratlar ayirmasi / Difference of squares:
a²-b²=(a-b)(a+b)
4. Yig'indining kubi / Cube of sum:
(a+b)³=a³+3a²b+3ab²+b³
5. Ayirmaning kubi / Cube of difference:
(a-b)³=a³-3a²b+3ab²-b³
6. Kublar yig'indisi / Sum of cubes:
a³+b³=(a+b)(a²-ab+b²)
7. Kublar ayirmasi / Cube of difference:
a³-b³=(a-b)(a²+ab+b²)
@Math_Emperor
1.Yig'indining kvadrati / Square of sum:
(a+b)²=a²+2ab+b²
2. Ayirmaning kvadrati / Square of difference:
(a-b)²=a²-2ab+b²
3. Kvadratlar ayirmasi / Difference of squares:
a²-b²=(a-b)(a+b)
4. Yig'indining kubi / Cube of sum:
(a+b)³=a³+3a²b+3ab²+b³
5. Ayirmaning kubi / Cube of difference:
(a-b)³=a³-3a²b+3ab²-b³
6. Kublar yig'indisi / Sum of cubes:
a³+b³=(a+b)(a²-ab+b²)
7. Kublar ayirmasi / Cube of difference:
a³-b³=(a-b)(a²+ab+b²)
@Math_Emperor
If n is a natural number / Agar n natural son bo'lsa:
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k) / Agar n juft son bo'lsa (n= 2k) :
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1) / Agar n toq son bo'lsa (n=2k+1) :
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
@Math_Emperor
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k) / Agar n juft son bo'lsa (n= 2k) :
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1) / Agar n toq son bo'lsa (n=2k+1) :
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
@Math_Emperor
Hello everyone. What's up? I have a great news for you. From today i am going to share useful materials and vocabulary for international universities in Tashkent! / Hammaga salom. Yaxshimisizlar? Siz uchun ajoyib yangilik bor. Bugundan boshlab men Toshkentdagi xalqaro universitetlarning matematika fanidan bo'lib o;tadigan imtihon uchun foydali materiallar va so'z boyliklari bilan ulashmoqchiman!
@Math_Emperor
@Math_Emperor
Theme : Basic operations with numbers, HCD and LCM
Terms
To add - qo'shmoq,
To subtract - ayirmoq,
To multiply - ko'paytirmoq,
To divide - bo'lmoq,
To compute = to calculate = to work out - hisoblamoq
A natural number - natural son,
Whole number - nomanfiy butun son,
Integer number - butun son,
Rational number - ratsional son,
Irrational number - irratsional son,
Mixed number - aralash sonlar, Negative number - manfiy son, Positive number - musbat son,
Prime number - tub son,
Composite number- murakkab son
@Math_Emperor
Terms
To add - qo'shmoq,
To subtract - ayirmoq,
To multiply - ko'paytirmoq,
To divide - bo'lmoq,
To compute = to calculate = to work out - hisoblamoq
A natural number - natural son,
Whole number - nomanfiy butun son,
Integer number - butun son,
Rational number - ratsional son,
Irrational number - irratsional son,
Mixed number - aralash sonlar, Negative number - manfiy son, Positive number - musbat son,
Prime number - tub son,
Composite number- murakkab son
@Math_Emperor
Continue of terms / terminlarni davomi
An ordinary fraction - oddiy kasr,
Proper fraction - to'g'ri kasr,
Improper fraction - noto'g'ri kasr, Decimal fraction - o'nli kasr,
Factor-ko'paytuvchi,
Prime factorization - tub koʻpaytuvchilarga ajratmoq
The highest (greatest) common divisor (HCD) - katta eng umumiy bo'luvchi (EKUB)
The lowest (least) common multiply (LCM) - eng kichik umumiy karrali (EKUK)
@Math_Emperor
An ordinary fraction - oddiy kasr,
Proper fraction - to'g'ri kasr,
Improper fraction - noto'g'ri kasr, Decimal fraction - o'nli kasr,
Factor-ko'paytuvchi,
Prime factorization - tub koʻpaytuvchilarga ajratmoq
The highest (greatest) common divisor (HCD) - katta eng umumiy bo'luvchi (EKUB)
The lowest (least) common multiply (LCM) - eng kichik umumiy karrali (EKUK)
@Math_Emperor
Learning terms / terminlarni yodlash
Natural numbers
1, 2, 3, 4, 5, 6, 7, ... ( used for counting / sanash uchun ishlatiladigan)
Whole numbers
0, 1, 2, 3, 4, 5, 6, 7, ...
Integers numbers
-3, -2, -1, 0, 1, 2, 3
Rational numbers
m/n (m = integers, n= natural) such as 7/11, 1/2, -4/5
Irrational numbers
√m such as √2, √5, √24,
Negative numbers
-1 -2 -3 ... -n (n= natural numbers)
Positive numbers
1 2 3 4 ... n (n= natural numbers)
Prime numbers
2 3 5 7 11
@Math_Emperor
Natural numbers
1, 2, 3, 4, 5, 6, 7, ... ( used for counting / sanash uchun ishlatiladigan)
Whole numbers
0, 1, 2, 3, 4, 5, 6, 7, ...
Integers numbers
-3, -2, -1, 0, 1, 2, 3
Rational numbers
m/n (m = integers, n= natural) such as 7/11, 1/2, -4/5
Irrational numbers
√m such as √2, √5, √24,
Negative numbers
-1 -2 -3 ... -n (n= natural numbers)
Positive numbers
1 2 3 4 ... n (n= natural numbers)
Prime numbers
2 3 5 7 11
@Math_Emperor