Maths Flashcards
Sine, cosine rule, area of triangle, ambigious case
Sin(A)/a= Sin(B)/b= Sin(C)c
a^2= b^2 + c^2-2bCos(A)
Area= 1/2 ab sin(C)
Ambiguous case: 180- value if the angle is obtuse so sin(67)= sin(113)
Quadratic formula
x = [-b ± √(b2 - 4ac)]/2a.
(remember to use brackets when substituting)
Percentage profit/loss, Compound changes/interest(depreciation & growth), rate of pay
New= original x (multiplier representing percentage change) ^ number of times repeated/years. For unknown lengths of time, use trial and error on calculator.
Rate of pay= total wages/number of hours worked ( £/$ per hour)
Gradient of linear graph
y= mx + c
OR
y1-y2= m(x1-x2)
Exponential function
y=ka^x
Conversion graph
conversion graph: used to change one unit into another. This could be changing between miles and kilometres. directly proportional graph
proportion
direct proportion: y=kx (straight line passing through the origin)
inverse proportion: y= k/x (recipricol graph)
When there are two proportionalities, deal with them separately and use different letters. But if P~q and q~r, P~r.
Two way table, probability (mutually exclusive & independent events), counting by multiplying (product rule) , sample space diagram
Two way table: A frequency table used for organising data for categorical variables.
Probability= no. successful outcomes/ total no. possible outcomes
P(not A)= 1-P(A)
Mutually exlusive (A or B) = P(A) + P(B)
Independent events (A and B)= P(A) x P(B)
When counting by multiplying and using product rule, check if the data is non ordered or ordered and if it is repeated or non-repeated.
A sample space diagram is a way of listing all of the outcomes of two events which can then be used to calculate probabilities.
Probability- set notations
Set= collection of items e.g. {4,3,2}
no duplicates and order does not matter
Empty set:∅
Subset: sets that make up a set {{1,2},{3,4}}
AcB means A is a subset of B
2∈{1,2} means 2 is a member of the set
and 2 ∉ {1,2 } means its not.
Universal set:all numbers we are interested in.
Intersection of A and B (what numbers are both in A and B)= A n B
Union of A and B (everything that’s in A aand B)= A u B
P(Not A)= P(A’)
Conditional probability: likelihood of an event happening GIVEN THAT another event is already known to have occured.
P(A/B)= P(AnB)/ P(B)
Naming parts of a circle
Centre, circunference, sector, diameter, radius, tangent, major segment, minor segment, chord, arc
Circle Theorems
- Angle at the cetnre is twice angle at the circumference (centre involved)
- The angle in a semi-circle is 90%(centre involved)
- Angles in the same segment are equal (no centre involved)
- Opposite angle in a cyclic quadrilateral sum to 180 degrees
- A perpendicular to a chord through the centre bisects the chord
- A tangent is perpendicular to a radius
- Tangents from a point are equal
Angles in alternate segments are equal.
Surds
Similar to algebra; can collect lie terms
√’a x √’b= √’ab
√’a/√’b= √’(a/b)
Simplifying surds: Take the highest factor which is also a square number out of the surd.
Rationalising the denominator:
if it is √’(a/b), multiply the top and bottom by √’b
recurring decimals to fractions
if there are 2 recurring decimal points then make x= that value and find 100x. Then subtract 100x- x to find 99x= an integer, and rearrange so that x= a fraction.
Inequalities
When dealing with 2 inequalities, do them separately and then put them together at the end. WHEN MULTIPLYING/DIVIDING BY A NEGATIVE NUMBER, FLIP THE SIGN
If there are 2 solutions put it as one inequality or say x=… OR x=…
< > - non coloured circle, dotted line
≤ ≥ -coloured circle and normal straight line
Draw quadratic graph when solving quadratic inequalities.
error intervals and upper and lower bounds
findthe value of the percentage and then add and subtract it from the original value using these symbols:≤ ≥
Bounds:
Subtraction:
-miniumum: a LB - b UB max: a UB- b LB
Multiplication:
-miniumum: a LB x b LB max: a UB x b UB
Division:
min: a LB / b UB max: aUb /b LB
