Math Igcse Study Cards

Front 1

Solving Simultaneous Equations: Elimination Method

Back 1

Multiple one, or both, of the equations by suitable multiplier, until they have a matching number of x's or y's2 variants of method:If the matching terms have one + and one - signs, then use add equations.If signs are the same then subtract equations.Remember: DASS : Different, Add; Same, Subtract!

Front 2

Solving Simultaneous Equations: Graphical Method

Back 2

*system of equationsUse if answers are whole numbers.Example: 4x + y = 6 equation(1)5x-4y = 18 equation(2)Use equation(1),when x=0 then 4x0 +y =6, giving y=6.Thus graph passes through (0,6).When y=0 then 4x + 0 = 6, giving x =1.5Thus graph passes through (1.5,0)Repeat above with equation(2) then plot lines, where they cross is the solution.

Front 3

Probability: Number of likely outcomes

Back 3

Probability = no. of favourable outcomes/ total no. of possible outcomes

Front 4

Probability: With test data

Back 4

Probability = no. of tests with favourable outcome/ total number of tests conducted

Front 5

Probability of an event not happening

Back 5

Probability Event(x) doesn't happen = 1- Probability Event(x) does happen

Front 6

Combined Probability of 2 events happening, when they can't happen at the same time.

Back 6

P [A or B] = P [A] + P [B]

Front 7

Combined Probability of 2 events happening when they are independent.

Back 7

P [A or B] = P[A] x P [B]

Front 8

Probabilities with multiple tests

Back 8

Use tree diagrams

Front 9

Differentiation: General Rule

Back 9

y = ax^ndy/dx = anx^n-1

Front 10

Differentiation: Useful Examples

Back 10

1/x becomes -1/x^21/x^2 becomes -2/x^3

Front 11

Differentiation: Finding Max, Min values of Graphs

Back 11

Max, min values are known as turning points and occur when dy/dx = 0

Front 12

Surds: √ab =

Back 12

√ab = √a x √b

Front 13

Surds: (√a)^2 =

Back 13

(√a)^2 = a

Front 14

Surds: Rules

Back 14

When multiplying or dividing: calculate whole numbers first then surdsWhen adding and subtracting: only collect like terms

Front 15

Surds: Special products: (a+b)^2 =

Back 15

(a+b)^2 = a^2 + 2ab + b^2first term squared + double the product +second term squared

Front 16

Surds: Special products: (a+b)(a-b)

Back 16

*Roots (a+b)(a-b) = a^2 - b^21st term squared - 2nd term squared(√a+√b)(√a-√b) = a - b

Front 17

Surds: Rationalising the denominator

Back 17

With a fraction:To get rid of surd on the bottom, multiple top and bottom by the surdwith (√a+√b) at the bottom, multiple by the conjugate, i.e (√a-√b) top and bottom

Front 18

Polygons

Back 18

There are two types of angle when dealing with Polygons - internal and external.regular polygon with sides 'n', external angle: 360/ninternal angle: 180 - 360/n

Front 19

Simple Interest

Back 19

I = principal amount invested(P) x percentage rate of interest(R) x no. of years (T) / 100I = PRT/100

Front 20

Mean

Back 20

the total of all the values , divided by how many there are

Front 21

Median

Back 21

the middle number in an ordered data set

Front 22

Mode

Back 22

the value that occurs most often

Front 23

range

Back 23

the difference between the highest and lowest values

Front 24

interquartile range

Back 24

range of the middle 50% of the data

Front 25

Upper and Lower quartile

Back 25

values located one-quarter and three quarters of the way through the data sets, once it has been ordered

Front 26

Frequency density

Back 26

frequency density = frequency / group width

Front 27

Negative Powers

Back 27

x^-n=1/x^n

Front 28

Natural Number

Back 28

A whole number from 1 to infinity, sometimes called "counting numbers". 0 is not included.

Front 29

Integer

Back 29

Any of the negative and positive whole numbers including 0.

Front 30

Prime Number

Back 30

A whole number greater than 1 which has only two factors: the number itself and 1.

Front 31

Symbol

Back 31

A short way of writing mathematical information, such as "=" which means is equal to.

Front 32

Multiple

Back 32

The result of multiplying a number by an integer.

Front 33

Factor

Back 33

A number that divides exactly into another number with no remainder.

Front 34

Composite Number

Back 34

Integer with more than two factors i.e. it has more factors than just 1 and itself.

Front 35

Prime Factor

Back 35

A prime number that divides exactly into another number with no remainder.

Front 36

Root

Back 36

A number that when multiplied by itself a certain number of times will result in another number. i.e. 2 is the square root of 4.

Front 37

Power

Back 37

Another word for exponent or index, indicating how many times a base number is multiplied by itself.

Front 38

Square root

Back 38

A number that, multiplied by itself gives a square.

Front 39

Cube

Back 39

A cube is the result obtained when a number is multiplied by itself and then multiplied by itself again.

Front 40

Directed numbers

Back 40

Numbers that have a (positive or negative) direction; once a direction is taken to be positive, the opposite direction is negative e.g. -4 degrees C is a directed number.

Front 41

Order of operations (BODMAS)

Back 41

When more than one arithmetic operation appears in a sum, the mnemonic indicates the order in which the operations should take place. Brackets, Of, Division, Multiplication, Addition, Subtraction.

Front 42

Addition

Back 42

+

Front 43

Subtraction

Back 43

-

Front 44

multiplication

Back 44

*or x

Front 45

Division

Back 45

/

Front 46

Sum

Back 46

The result of addition

Front 47

Difference

Back 47

The result of subtraction

Front 48

Product

Back 48

The result of multiplication

Front 49

Quotient

Back 49

The result of division

Front 50

Brackets

Back 50

( ),[],or {}

Front 51

Even

Back 51

Numbers such as 2, 4, 6, 8 that can be divided by two.

Front 52

Odd

Back 52

Numbers such as 1, 3, 5, 7 that can not be divided by two.