Terms

Linear expression of x

ax + b, a and b are constants - a≠0

Quadratic expression of x

ax² + bx + c, a and b and c are constant - a≠0.

Expression for difference between two squares

x² - y² or (x-y)(x+y)

Rational number

A number of the form a/b where a and b are integers - b≠0

N (double line)

Natural numbers, positive integers - 1, 2, 3 …

Z (double line)

Integer numbers, whole numbers -2, -1, 0, 1 …

Q (double line)

Quotients, rational numbers expressed as fractions - 3/20, 1/16 …

R (double line)

Real numbers, any possible number like rational and irrational - π, 1.5, 12/15 …

Even number

2n, 2a, 2m, etc.

Odd number

2n+1, 2a+1, 2m+1, etc.

Multiple of k

Kn

Consecutive numbers

n, n+1, n+2, etc.

Proof by deduction

Using known facts to support your argument to show a statement must be true, e.g. prove that the product of 2 rational numbers is also rational: a/b x c/d = ac/bd

Proof by exhaustion

Proof by breaking something down into all possible scenarios and proving each one to be true, e.g. show sum of two consecutive square numbers will be an odd number: 1+4=5 → odd, 4+9=13 → odd, etc.

Disproof by counter example

Give an example which shows the statement is not true, e.g. disprove statement: “product of two prime numbers is always odd” → 2 is prime, 5 is prime → 2×5=10 which is not odd ∴ not true.