syllabus dot points ME Flashcards
Methods
understand the notion of a combination as a set of π objects taken from a set of π distinct objects
A
use the notation (
π
π
) and the formula (
π
π
) =
π!
π!(πβπ)!
for the number of combinations of π objects
taken from a set of π distinct objects
A
investigate Pascalβs triangle and its properties to link (
π
π
) to the binomial coefficients of the
expansion of (π₯ + π¦)
π
for small positive integers
A
review the concepts and language of outcomes, sample spaces, and events, as sets of outcomes
A
use set language and notation for events, including:
a. π΄Μ
(or π΄
β²
) for the complement of an event π΄
b. π΄ β© π΅ and π΄ βͺ π΅ for the intersection and union of events π΄ and π΅ respectively
c. π΄ β© π΅ β© πΆ and π΄ βͺ π΅ βͺ πΆ for the intersection and union of the three events π΄, π΅ and πΆ
respectively
d. recognise mutually exclusive events.
A
use everyday occurrences to illustrate set descriptions and representations of events and set
operations
A
review probability as a measure of βthe likelihood of occurrenceβ of an event
A
review the probability scale: 0 β€ π(π΄) β€ 1 for each event π΄, with π(π΄) = 0 if π΄ is an impossibility
and π(π΄) = 1 if π΄ is a certainty
A
review the rules: π(AΜ ) = 1 β π(π΄) and π(π΄ βͺ π΅) = π(π΄) + π(π΅) β π(π΄ β© π΅)
use relative frequencies obtained from data as estimates of probabilities
understand the notion of a conditional probability and recognise and use language that indicates
conditionality
1.1.12. use the notation π(π΄|π΅) and the formula π(π΄ β© π΅) = π(π΄|π΅)π(π΅)
1.1.13. understand the notion of independence of an event A from an event B, as defined by
π(π΄|π΅) = π(π΄)
establish and use the formula π(π΄ β© π΅) = π(π΄)π(π΅) for independent events π΄ and π΅, and
recognise the symmetry of independence
use relative frequencies obtained from data as estimates of conditional probabilities and as
indications of possible independence of events
recognise features of the graph of π¦ = ππ₯ + π, including its linear nature, its intercepts and its slope
or gradient
determine the equation of a straight line given sufficient information; including parallel and
perpendicular lines
examine examples of quadratically related variables
recognise features of the graphs of π¦ = π₯
2
, π¦ = π(π₯ β π)
2 + π, and π¦ = π(π₯ β π)(π₯ β π), including
their parabolic nature, turning points, axes of symmetry and intercepts
solve quadratic equations, including the use of quadratic formula and completing the square
determine the equation of a quadratic given sufficient information
determine turning points and zeros of quadratics and understand the role of the discriminant
recognise features of the graph of the general quadratic π¦ = ππ₯
2 + ππ₯ + οΏ½