## 32 terms · Theta junk you need to know

###
Number of digits in x^y

(Ex. 7^43)

y(logx)+1

43(log7)+1

36.339...+1

37.339...

37 (Eliminate the decimal part)

### What is the determinant of a singular matrix?

0

That is why singular matrices have no inverses.

###
For any square matrix A,

A • A^(-1)

The Identity Matrix

| 1 0 |

| 0 1 | For a 2x2 matrix,

| 1 0 0 |

| 0 1 0 |

| 0 0 1 | For a 3x3 matrix, etc.

###
For any square matrix A,

|A| - |A^T|

(A^T is the transverse of the matrix A)

0

The determinant of any square matrix is equal to the determinant of its transverse matrix.

### Area of a Triangle Using Matrices

1 | x(1) y(1) 1 |

±— | x(2) y(2) 1 |

2 | x(3) y(3) 1|

1/2 is indicated as ± so that you can multiply whichever number would result in a positive value, depending on the situation, because area must be positive.

x(n) or y(n) means x "sub-n" or y "sub-n"

### Number of Positive Integral Factors of a Number (Ex. 3240)

Find the prime factorization of the number and multiply the exponents of the prime factors after adding one to each of them.

3240 = 2^3 • 3^4 • 5

(3+1)(4+1)(1+1)

4 • 5 • 2

40

### Binomial Theorem

Sorry, again, I don't know how to explain this one on here you just have to know it.

### √n+√(n+√(n+...=x

Square both sides

Set the radical junk equal to x

Solve the quadratic equation

The positive solution is the solution to the entire equation

### Sum of the Reciprocals of the Roots of a Quadratic Equation

ax^2 + bx + c = 0

-b/c

Sum of Roots/Product of Roots

(-b/a)/(c/a)

-b/c

### Sum of the Squares of the Reciprocals (or the Reciprocals of the Squares) of the Roots of a Quadratic Equation

ax^2 + bx + c = 0

(b^2 - 2ac)/c^2

### Product of the Roots of Other Polynomial Equations

Ax^n + Bx^(n-1) + Cx^(n-2) +...+ Jx + K=0

If n is even, K/A

If n is odd, -K/A

### Sum of the Reciprocals of the Roots of Other Polynomial Equations

Ax^n + Bx^(n-1) + Cx^(n-2) +...+ Jx + K=0

-J/K

### Sum of the Squares of the Roots of Other Polynomial Equations

Ax^n + Bx^(n-1) + Cx^(n-2) +...+ Jx + K=0

(B^2 - 2AC)/A^2

###
Number of Zeroes at the End of a Specific Number Factorial

Ex. 1000

Divide the number by the largest integral power of 5 less than the original number

Continue dividing by decreasing integral powers of 5 until you reach 5

Add the quotients

Ex.

1000÷625=1

1000÷125=8

1000÷25=40

1000÷5=200

1+8+40+200=249

249 zeroes

### In a rectangle with the dimensions x by y, the number of distinct paths from one corner to the other

(x+y)!/x!y!