Maths - number

x² × x³

x⁵

(x²)³

x²×³ = x⁶

x⁵ ÷ x²

x³

x⁰

1 (anything to the 0 power is 1)

x⁻²

-1/x²

what do negative indices mean?

you take the reciprocal (flip it)

x^½

√x

x^¾

⁴√x³

Formula for total interest earned

Interest = final amount - initial amount

Formula for compound interest

final amount = initial amount × (1+ (interest rate/100)) ^no of years

How are bound ranges shown as

0.5 ≤ x ≤ 1.5

Formula for direct proportion

y = kx

Formula for indirect proportion

y = k/x

Finding the nth term in a sequence

(common difference) n + (first term - common difference)

e.g, 2n + 3

How to check if a number is in a sequence example

e.g, is 101 in the sequence 3n+2

- 3n+2 = 101

- 3n = 99

- n = 33

- 33 is an interger, so 101 is in the sequence

How to check if a number is in a sequence

1. Set the formula to the number (e.g, 3n+2 = 101)

2. solve

3. if "n" is an interger, then it is in the sequence

Finding a specific term in a sequence

1. set "n" to the term (e.g, 3n + 2 → 3(20) + 2)

2. solve e.g, 3(20) +2 = 60 + 2 = 62

The 20th term is 62

Finding the term of a number

1. Set the formula to the number (e.g, 3n+2 = 101)

2. solve

- 3n+2 = 101

- 3n = 99

- n = 33

101 is the 33rd term

sum of terms when the last term is known

n/2 (first term - last term)

formula for the sum of terms when the last term is unknown

n/2(2a+(n-1)d)

What does "a" represent in sequences

first term

What does "d" represent in sequences

common difference

What does "n" represent in sequences formula

number of terms

What does "Un" represent in sequences formula

nth term

What does "Sn" represent in sequences formula

sum of the first n terms

What is the upper bound

largest possible number

What is the lower bound

smallest possible number

How to find bounds

above or below half the rounding unit