Free VCE Year 11 Specialist Mathematics Flashcard Review
Review 20 public cards with spaced repetition. Flip a card, then grade your recall. Cards you miss return today. Your schedule stays in this browser.
Loading your review schedule…
Browse the free cards
What are the number systems in order of inclusion?
N ⊂ Z ⊂ Q ⊂ R ⊂ C: natural numbers, integers, rationals, reals, complex numbers.
How many elements are in the power set of a 5-element set?
2⁵ = 32.
When does a simplified fraction p/q have a terminating decimal?
When the only prime factors of q are 2 and 5.
Write 0.7̇ = 0.777… as a fraction.
Let x = 0.777…; 10x − x = 7, so x = 7/9.
State the fundamental theorem of arithmetic.
Every integer greater than 1 is a product of primes, uniquely apart from order.
Why is 1 not prime?
A prime has exactly two positive divisors; 1 has only one. Excluding 1 keeps factorisations unique.
What is the contrapositive of P ⇒ Q?
¬Q ⇒ ¬P, which is logically equivalent to P ⇒ Q.
How do you disprove a ‘for all’ statement?
Give one counter-example.
What is the negation of ‘for all x, P(x)’?
There exists an x such that P(x) is false.
What are the steps of a proof by contradiction?
Assume the statement is false, deduce a logical impossibility, then conclude the statement is true.
List the parts of an induction proof.
Define P(n); prove the base case; assume P(k) and prove P(k + 1); write the conclusion.
Define a | b.
a divides b if b = ak for some integer k.
What is a simple graph?
A graph with no loops and no multiple edges.
Name the four broad types of graph problems.
Existence, construction, counting and optimisation.
State the handshaking lemma.
Σ deg(v) = 2e: the degrees add to twice the number of edges.
Why is the number of odd vertices always even?
The degree sum 2e is even, so the odd degrees must add to an even number, needing an even count of them.
How many edges does Kₙ have?
n(n − 1)/2
What is the complement of a simple graph G?
Same vertex set; two vertices are adjacent exactly when they are not adjacent in G.
How many edges does an r-regular graph on n vertices have?
nr/2
How many edges does Kₘ,ₙ have?
mn