Math revision guide

Seite 1

Finding HCFs and LCMs of larger numbers

Example

Find the LCM 60 and 504

Find the largest power of each prime factor that appears in either number

Multiply these powers of primes together

60 = 2^2 x 3 x 5 and 504= 2^3 x 3^2 x 7

2^3 is the largest power of 2 that appears in either expression

3^2is the largest power of 3 that appears in either expression

5 is the largest er 5 that appears in either expression

7 is the largest power of 7 that appears in either expression

So the LCM of 60 and 504 = 2^3 x 3^2 x 5 x 7 = 2520

Rational and irrational numbers

a rational number is a number which can be expressed in the form of p/q where p and q are whole numbers all

decimals which recur are rational.

all decimals that terminate are rational

An irrational number is a number which it cannot be expressed as p/q where p and q are integers

A real number is a number that can be presented in a number line

Seite 2

Sequences

a sequence is a set of numbers which follow a certain pattern

the word term is used to refer o the various numbers in a sequence

working out

- 1st term = 4 = 3 x 1 + 1

- 2nd term = 7 = 3 x 2 + 1

- 3rd term = 10 = 3 x 3 + 1

- 4th term = 13 = 3 x 4 + 1

the pattern here can be seen and so we write nth term , t= 3 x n + 1 = 3n + 1

Sequences the same differences between terms

the pattern in the sequence 4, 7, 10, 13, ... is that the next term is always three more than the previous one.

the nth term of such sequences is t(n) = an + b.

the constants a and b need to be found. The easiest way to find b is as follows.

in this case a = 3 and b = 1. So t(n) = an + b = 3n + 1

example

(a) what is the nth term of 19, 13, 7, 1, ...

= -6n + 25

(b) which term of 19,