Free WACE Year 11 Mathematics Methods Flashcard Review
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What does C(n,r) count?
Unordered selections of r distinct objects from n.
Combination formula?
C(n,r) = n!/[r!(n − r)!].
How is a Pascal entry formed?
Add its two neighbours in the row above.
Coefficient of xⁿ⁻ʳyʳ in (x + y)ⁿ?
C(n,r).
What is an event?
A subset of the sample space.
Meaning of A ∪ B?
A or B or both.
Meaning of A ∩ B?
Both A and B.
Complement rule?
P(A′) = 1 − P(A).
Addition rule?
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Conditional multiplication rule?
P(A ∩ B) = P(A|B)P(B).
Independence criterion?
P(A|B) = P(A), when P(B) > 0.
Relative-frequency estimate?
Event count divided by relevant total; use the subgroup total when conditioning.
What defines a function?
Exactly one output for every permitted input.
What is gradient?
Change in output divided by change in input.
How are perpendicular gradients related?
Their product is −1, except the horizontal/vertical pair.
What does quadratic vertex form reveal?
a(x − b)² + c has vertex (b, c) and axis x = b.
What does the discriminant tell you?
Positive: two real zeros; zero: one repeated zero; negative: no real zeros.
What stays constant in inverse proportion?
The product xy = k.
Asymptotes of a/(x − b)?
x = b and y = 0, for a ≠ 0.
Even versus odd positive power end behaviour?
Even: both ends rise. Odd: fall left, rise right.