MATHS - Raffaele, Eleonora, Camilla and Livia (1st liceo scientifico)

rules

100

What rule derives from the first principle of equivalence: “if you add or subtract the same numbers from the two members, the solution will be the same”?

The transport rule

200

What does the first congruence postulate?

Two triangoles are congruent if they have the two sides and angle between them congruent

300

What‘s equale to the median in a isosceles triangle?

The height and the bisector 

400

How can you factorise the subtraction between two cubes? (A³ - B³)

(A - B)(A² + AB + B²)

500

What is definition of the polynomial zero? 

The polynomial zero it is a number, which makes the polynomial null  

equation

100

3 + 2x = 13

x = 5 

200

2 + 3x = 2x + 1 

x = -1

300

2a + 3 = 1/2a - 1

^{tips use a piece of paper}

a = - 8/3

400

x (x + 7) + 9 = x + (x + 3)² 

^{tips use a piece of paper} 

0x = 0 (undeterminated)

500

(5x/4 - 11/4) - (5x/16 + 3/16) = (50/8 - 3x/8)

^{tips use a piece of paper}

x = 7

factorising polynomials

100

2x - 2y 

2(x - y)

200

16g² - 1

(4g + 1)(4g - 1)

300

2xy⁴ - 8y²x + 4y⁴ - 16y² 

^{tips use a piece of paper} 

(2y²(x + 2))(y - 2)(y + 2)

400

3a³ - 18a²b + 27ab²

^{tips use a piece of paper} 

3a(a - 3b)²

500

t⁴ - 4t² - 77

(t² - 11)(t² + 7)

potpourri

100

I earn 4.000 gross euro, the goverment takes the 38% of my salary every month. How much do I earn net yearly? (without other acquisitions)

18.240 euro 

200

Does the negative greek py belong to the “Z” numbers?

No

300

What does “Q“ mean in a set?

Rational number

400

What do you mean for “C.E.“ in an algebric fraction?

Find the value for the variable which canceles the denominator

500

(2 + x + 3x² + x³) : (2 + x²)

Q = x + 3

R = - x + 4