KS Learning can provide extra lessons for maths from gcse maths tutors in London and help with gcse maths past papers, gcse maths revision notes, and gcse maths revision worksheets. Maths private tuition at its tuition centre can improve maths knowledge and performance through maths lessons, mathematics tutorials and maths tuition Twickenham.
natural numbers - positive whole numbers: 1, 2, 3, 4, to infinity
counting numbers - zero and positive whole numbers: 0, 1, 2, 3, 4, to infinity
integers - positive and negative whole numbers plus zero : negative infinity ... -3, -2, -1, 0, 1, 2, 3, 4, to positive infinity
real numbers - all numbers on a number line including decimals, fractions, and surds
even numbers - divide by two exactly e.g. 2, 4, 6, 8
odd numbers - do not divide by two exactly e.g. 11, 13, 15, 17
prime numbers - have only two factors, one and themselves e.g. 2, 3, 5, 7, 11. Note that 1 is not a prime number because it has only one factor
surds - the root of a prime number or the product of different primes
fractions - a portion of a whole
square numbers - a number multiplied by itself produces a square number e.g. 4, 9, 16
cube numbers - a number multiplied by itself three times produces a cube number e.g. 8, 27, 64
factor - a number that divides exactly into another number e.g. 3 is a factor of 6
multiple - a number in the timetable of another number e.g. 12 is a multiple of 6
highest common factor - the largest number that divides into two or more numbers exactly e.g. 6 is the HCF of 24 and 30 (HCF)
lowest common multiple - the smallest number that two or more numbers divide into exactly e.g. 120 is the LCM of 24 and 30 (LCM)
vulgar fraction - expressed as a whole number over another whole number, respectively numerator and denominator, in which the denominator
cannot be zero; also known as a simple or common fraction
proper fraction - a vulgar fraction where the numerator is smaller than the denominator
improper fraction - a vulgar fraction where the numerator is greater than the denominator; also called a top-heavy fraction
rational numbers - a rational number is any number that can be expressed as a fraction p/q where p and q are integers. Integers are rational numbers as
they can be
written over 1
irrational numbers - an irrational number cannot be written as a fraction. For example, the square root of 2 is an irrational number because it cannot
be written as a ratio of two integers
Maths makes use of the following symbols and terms
Symbol | Meaning |
---|---|
= | equal to |
≡ | equivalent to |
≠ | not equal to |
< | less than |
> | greater than |
≤ | less than or equal to |
≥ | greater than or equal to |
≈ | approximately equal to |
∑ | the sum of |
α | alpha |
β | beta |
γ | gamma |
θ | theta |
∞ | infinity |
∴ | therefore |
⇒ | therefore |
Sum | the result of adding |
Difference | the result of substracting |
Product | the result of multiplying |
Prefixes are added to the base unit so 9Gm (giga metres) means 9 x 109 m = 9 000 000 000 m
Index | Symbol | Name |
---|---|---|
1012 | T | tera |
109 | G | giga |
106 | M | mega |
103 | k | kilo |
102 | h | hecto |
101 | da | deca |
base unit | ||
10-1 | d | deci |
10-2 | c | centi |
10-3 | m | milli |
10-6 | µ | micro |
10-9 | n | nano |
10-12 | p | pico |
Title | Rule | Examples |
---|---|---|
Divisible by 2 | End with 0,2,4,6,8 | 254 and 4718 are divisible by 2 |
Divisible by 3 | Sum of digits is divisible by 3 | 549 =5 + 4 + 9 = 18 = 1 + 8 = 9 is divisible by 3 hence 549 is divisible by 3 |
Divisible by 4 | Last two digits divisible by 4 | 5648 here last 2 digits are 48 which is divisible by 4 hence 5648 is divisible by 4 |
Divisible by 5 | Ends with 0 or 5 | 225 or 330 here last digit digit is 0 or 5 that mean both the numbers are divisible by 5 |
Divisible by 6 | Divides by both 2 and 3 | 4536 here last digit is 6 so it divisible by 2 and 4+5+3+6=18=1+8=9 which is divisible by 3. Hence 4536 is divisible by 6 |
Divisible by 8 | Last 3 digits divide by 8 | 746848 here last 3 digit 848 is divisible by 8 hence 746848 is also divisible by 8 |
Divisible by 10 | End with 0 | 220,450,1450,8450 all numbers has a last digit zero it means all are divisible by 10 |
Term | Explanation | Illustration |
---|---|---|
semi-circle | half a circle | ![]() |
concentric circles | circles which share the same centre | ![]() |
circumference | the perimeter of a circle | ![]() |
arc | a portion of the circumference | ![]() |
minor arc | an arc that is less than half the circumference | ![]() |
major arc | an arc that is more than half the circumference | ![]() |
radius | the line from the centre of the cirle to the edge of the circle | ![]() |
diameter | the line from one side of the circle to the other through the centre | ![]() |
chord | a line from one side of the circle to the other side whose endpoints are on the edge of a circle | ![]() |
secant | a line that pass through both sides of the circle | ![]() |
tangent | a line that touches the circle at one point only | ![]() |
normal | a line at 90 degrees to the tangent at the point where it touches the circle | ![]() |
segment | the portion of a circle between a chord and an arc | ![]() |
sector | the portion of a circle between two radii and an arc | ![]() |
subtended angle | ![]() |
|
bisector | a line that cuts another line in half | ![]() |
Number | Theorem | Diagram |
---|---|---|
Theorem 1 | The angles on the cirumference of a circle are equal when subtended by the same arc | ![]() |
Theorem 2 | The angle at the centre of a circle, is twice the size of the angle at the circumference when subtended by the same arc | ![]() |
Theorem 3 | An angle on the circumference is 90 degrees when subtended by diameter of the circle | ![]() |
Theorem 4 | The opposite angles in a cycle quadrilateral always add up to 180 degrees. | ![]() |
Theorem 5 | A tangent to a circle is perpendicular to the radius at the point of contact | ![]() |
Theorem 6 | Tangents to a circle from the point they intersect to the points of contact are equal in length | ![]() |
Theorem 7 | The line joining the point where two tangents intersect to the centre of the circle, bisects the angle between the tangents | ![]() |
Theorem 8 | If a radius bisects a chord, the angle between them will be at 90 degrees | ![]() |
Theorem 9 | The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment | ![]() |
A good tutor can build the confidence of a learner enabling subject success
A private tutor can improve the skills a pupil needs to master a subject
Regular tutoring can drive progress and better results in school subjects
Support can help students and parents make the right academic decisions