Real Numbers

Fundamental Theorem of Arithmetic (1.2): name the 7 key ideas

• Theorem 1.1 statement • Does 4^n end in 0? • HCF by prime factors • LCM by prime factors • HCF × LCM = a×b • Composite number test • Real-life LCM problem

What is theorem 1.1 statement?

A composite number is a product of primes, unique apart from the order.

What is irrational meaning?

A number that cannot be written as p/q with integers and q not zero.

Revisiting Irrational Numbers (1.3): name the 5 key ideas

• Irrational meaning • Theorem 1.2 • Theorem 1.3: √2 irrational • √3 is irrational • Sum and product rules

Explain the step: “Prove √p irrational”

Standard 3-mark proof for √5 or similar primes.

What is introduction (1.1)?

The chapter revisits real numbers through two big ideas about primes.

Exam focus: name the 2 key ideas

• Prove √p irrational • HCF and LCM by factors

What is factor tree method?

Keep splitting a number until only prime branches remain.