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52 Cards in this Set
- Front
- Back
Solving Simultaneous Equations: Elimination Method |
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! |
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Solving Simultaneous Equations: Graphical Method |
*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. |
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Probability: Number of likely outcomes |
Probability = no. of favourable outcomes/ total no. of possible outcomes |
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Probability: With test data |
Probability = no. of tests with favourable outcome/ total number of tests conducted |
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Probability of an event not happening |
Probability Event(x) doesn't happen = 1- Probability Event(x) does happen |
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Combined Probability of 2 events happening, when they can't happen at the same time. |
P [A or B] = P [A] + P [B] |
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Combined Probability of 2 events happening when they are independent. |
P [A or B] = P[A] x P [B] |
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Probabilities with multiple tests |
Use tree diagrams |
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Differentiation: General Rule |
y = ax^ndy/dx = anx^n-1 |
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Differentiation: Useful Examples |
1/x becomes -1/x^21/x^2 becomes -2/x^3 |
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Differentiation: Finding Max, Min values of Graphs |
Max, min values are known as turning points and occur when dy/dx = 0 |
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Surds: √ab = |
√ab = √a x √b |
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Surds: (√a)^2 = |
(√a)^2 = a |
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Surds: Rules |
When multiplying or dividing: calculate whole numbers first then surdsWhen adding and subtracting: only collect like terms |
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Surds: Special products: (a+b)^2 = |
(a+b)^2 = a^2 + 2ab + b^2first term squared + double the product +second term squared |
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Surds: Special products: (a+b)(a-b) |
*Roots (a+b)(a-b) = a^2 - b^21st term squared - 2nd term squared(√a+√b)(√a-√b) = a - b |
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Surds: Rationalising the denominator |
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 |
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Polygons |
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 |
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Simple Interest |
I = principal amount invested(P) x percentage rate of interest(R) x no. of years (T) / 100I = PRT/100 |
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Mean |
the total of all the values , divided by how many there are |
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Median |
the middle number in an ordered data set |
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Mode |
the value that occurs most often |
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range |
the difference between the highest and lowest values |
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interquartile range |
range of the middle 50% of the data |
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Upper and Lower quartile |
values located one-quarter and three quarters of the way through the data sets, once it has been ordered |
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Frequency density |
frequency density = frequency / group width |
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Negative Powers |
x^-n=1/x^n |
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Natural Number |
A whole number from 1 to infinity, sometimes called "counting numbers". 0 is not included. |
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Integer |
Any of the negative and positive whole numbers including 0. |
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Prime Number |
A whole number greater than 1 which has only two factors: the number itself and 1. |
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Symbol |
A short way of writing mathematical information, such as "=" which means is equal to. |
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Multiple |
The result of multiplying a number by an integer. |
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Factor |
A number that divides exactly into another number with no remainder. |
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Composite Number |
Integer with more than two factors i.e. it has more factors than just 1 and itself. |
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Prime Factor |
A prime number that divides exactly into another number with no remainder. |
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Root |
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. |
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Power |
Another word for exponent or index, indicating how many times a base number is multiplied by itself. |
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Square root |
A number that, multiplied by itself gives a square. |
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Cube |
A cube is the result obtained when a number is multiplied by itself and then multiplied by itself again. |
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Directed numbers |
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. |
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Order of operations (BODMAS) |
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. |
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Addition |
+ |
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Subtraction |
- |
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multiplication |
*or x |
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Division |
/ |
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Sum |
The result of addition |
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Difference |
The result of subtraction |
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Product |
The result of multiplication |
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Quotient |
The result of division |
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Brackets |
( ),[],or {} |
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Even |
Numbers such as 2, 4, 6, 8 that can be divided by two. |
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Odd |
Numbers such as 1, 3, 5, 7 that can not be divided by two. |