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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 | |
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