This page holds a finished MAT-FPX2051 Assessment 2 proof portfolio with each method named and executed, definitions unpacked on their own lines, and every induction's hypothesis visibly used. Searches like "mat fpx 2051 assessment 2 assignment example", "matfpx2051 assessment 2 sample" and "mat-fpx2051 assessment 2 example" land here.
What a finished MAT-FPX2051 Assessment 2 proof portfolio looks like
The finished portfolio is a set of short arguments, each complete in itself. A proof opens with what is assumed and what will be shown, stated separately so the two can never trade places. Definitions are unpacked the moment they are needed, an even integer becoming two k on its own line, a subset claim becoming an element argument, because in this course the definition is the working tool. The inductions carry their skeleton openly: base case verified with arithmetic shown, hypothesis stated for k, and the step containing the line where that hypothesis is substituted in, marked so a reader can find it. Set proofs choose an arbitrary element and follow it. Each proof ends by stating that the original claim now stands.
How a MAT-FPX2051 Assessment 2 example is structured
The portfolio is organized by technique because the assessment usually is. The direct proofs come first, modeling the base skill: hypothesis written, definition opened, algebra pushed through, conclusion matched against the claim. Contrapositive and contradiction proofs follow with their setup lines made explicit, what is being assumed and why that assumption is the right one for the method, since naming contradiction and then writing the contrapositive is a recognized way to lose the method criterion. The induction section is the largest, and each induction is annotated at its hinge, the exact line where the assumption about k produces the statement about k plus one. Counterexample problems are handled as their own genre, one concrete case exhibited and checked, because a false universal needs a witness, not an essay. Notation stays disciplined throughout, and no step claims more than the one before it proved.
Assumed and shown, kept separate
Every proof declares its starting point and its target in different sentences, which is the structural guard against arguing in a circle.
Definitions opened on their own lines
Even, divisible, subset and relation properties are rewritten in working form the moment they arrive, because the definition is the tool that moves each proof.
The named method is the used method
A proof labeled contradiction derives a contradiction; one labeled contrapositive proves the contrapositive, and the criteria check for exactly this match.
Inductions that spend their hypothesis
Each inductive step marks the line where the assumption for k is used, since a step that never touches it proved nothing.
Counterexamples given as witnesses
False claims are settled with one concrete case computed in full, because examples in any quantity cannot settle a claim made about every case.
Where marks go in MAT-FPX2051 Assessment 2
Proof portfolios lose points in ways prose can never see. The circular argument leads, the claim assumed somewhere in the middle, usually smuggled through notation, and once found it forfeits the problem regardless of the surrounding polish. The unused hypothesis is the induction version: a step that arrives at k plus one by direct algebra, never touching the assumption for k, has abandoned induction while wearing its uniform. Method mismatches cost the criterion that watches for them, and examples offered where a general argument was demanded earn the sympathy of a grader and nothing else. Smaller drains include base cases checked at the wrong value, arbitrary elements that quietly acquire special properties, and conclusions that state something adjacent to the claim rather than the claim. The portfolio shows the discipline that prevents each.
Get a MAT-FPX2051 Assessment 2 example written to your instructions
Send the Assessment 2 problems and the scoring guide from your MAT-FPX2051 courseroom, and a complete worked portfolio returns within 24 to 48 hours, the first request free. Every proof is written at grading granularity, with methods named, definitions unpacked and induction hinges marked, matched to the problems your section actually assigned.
MAT-FPX2051 Assessment 2 questions, answered
I understand the proofs I read but freeze writing my own. Does the example address that?
Its most useful feature for that problem is the visible first move: every proof shows what gets written before any insight arrives, the assumption stated, the definition unpacked, the target recorded. That opening is mechanical, and doing it reliably is what dissolves the blank page. The clever middle, where one exists, is always shorter than stuck students expect.
How long should each proof in the portfolio be?
As long as its logic requires and no longer, which for this course's claims is usually a handful of lines at full granularity. Length is not graded; gaplessness is. A six-line proof with every step justified outscores a page that waves across the one gap that mattered. The example's proofs are short precisely because each line does stated work.
What does the induction hypothesis actually do in the step?
It is the engine: the statement about k that gets substituted into the expression for k plus one to produce the target. The example marks that substitution in every induction so the moment is unmissable, because writing inductions without it, deriving the step from scratch, is the most common serious error in this assessment.