Free Year 11 Proof & logic Quiz — 10 Questions, Instant Results

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What proof and logic covers in Year 11 Specialist Mathematics

Before the quiz, here is what the topic means at this level. In Units 1 and 2 proof covers the language of logic, direct proof, proof by contradiction, proof by contrapositive and simple number-theory results.

Every question on this page was written to a specific VCE study design reference for Year 11 and checked by an RHZ tutor before it could be served.

Where Year 11 students go wrong with proof and logic

Most errors in proof and logic are not random. When Year 11 students sit our Skills Check, the same handful of misunderstandings account for the majority of lost marks:

• A proof by contradiction assumes the conclusion rather than its negation.
• Examples are offered as proof.
• The converse of a statement is treated as equivalent.

Spotting which one applies is the useful part; the fix is usually quick once the misunderstanding is out in the open.

What to do if proof and logic needs work

Three things a parent or student can do this week:

1. Practise induction on sums and divisibility.
2. Identify the hypothesis and conclusion of every statement.
3. Rewrite proofs from the textbook in your own words.

For VCE maths, fluency in the foundations frees up working memory for the extended questions. Do a short mixed set daily and a timed paper each fortnight.

How the 10 questions are chosen

We keep 10 proof and logic questions for Year 11 that meet our standard, at the easy and at-level tiers, and this page serves 10 of them at a time. The default set is stable, so a teacher or parent can share the link; a fresh set is one click away. Marking happens on our server so the answer key cannot be read from the page.

Use this page to answer one question well: is proof and logic secure at Year 11 level? For the broader picture across every topic and every difficulty tier, the free Skills Check takes about fifteen minutes and produces a report a tutor walks you through.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 50526 · New set of questions →

Question 1

Proof & logic

The sum of two even numbers is always?

prime negative even odd

Question 2

Proof & logic

A student proves the statement P → Q by proving ¬P → ¬Q. Which of the following best describes the logical status of the student's proof?

The proof is invalid because ¬P → ¬Q is the inverse of P → Q, which is not logically equivalent to P → Q. The proof is valid because ¬P → ¬Q is the contrapositive of P → Q and is logically equivalent to it. The proof is invalid because only direct proof or proof by contradiction are accepted methods in mathematics. The proof is valid because ¬P → ¬Q is the converse of P → Q, and the converse has the same truth value.

Question 3

Proof & logic

Proof by contradiction begins by assuming the statement is?

false obvious unknown true

Question 4

Proof & logic

Which of the following is a valid proof technique to show that the statement 'For all integers n, if n² is even then n is even' is true?

Assume n is odd, write n = 2k + 1, then n² = 4k² + 4k + 1 which is odd, contradicting n² being even. Therefore n must be even. The statement is equivalent to its converse, so proving 'if n is even then n² is even' is sufficient. Choose n = 4, note that 4² = 16 is even and 4 is even, so the statement holds. Assume n² is even, write n² = 2m, then n = √(2m) which is even because 2 is a factor.

Question 5

Proof & logic

Consider the two statements below. Statement A: 'If n is divisible by 6, then n is divisible by 2.' Statement B: 'If n is divisible by 2, then n is divisible by 6.' Which of the following correctly describes the logical relationship between Statement A and Statement B?

B is the contrapositive of A, so B is logically equivalent to A. B is the inverse of A, and B is logically equivalent to A. A and B are logically equivalent because they involve the same numbers. B is the converse of A, and B is false (for example, n = 4 is divisible by 2 but not 6).

Question 6

Proof & logic

The symbol ∀ means?

implies for all not there exists

Question 7

Proof & logic

A single counterexample can?

disprove a general claim do nothing prove a claim prove sometimes

Question 8

Proof & logic

The sum of two odd numbers is always?

prime odd zero even

Question 9

Proof & logic

The converse of 'if P then Q' is?

if not Q then not P if not P then not Q if Q then P P and Q

Question 10

Proof & logic

The contrapositive of 'if P then Q' is?

if not P then not Q if not Q then not P P or Q if Q then P

Mark my answers →

Your result

0 / 10

Take the free full Skills Check →   Try another set

How to read a score out of 10

9 or 10 out of 10

The easy and at-level content is secure. The useful question now is how far above the year level the student can go, which a ten-item quiz cannot show. The free Skills Check adds stretch and challenge questions on every topic so you can see the ceiling as well as the floor.

7 or 8 out of 10

Solid, with one or two specific gaps. Look at which topic the incorrect answers came from (the results panel names the weakest topic) and spend a week on that topic before re-testing with a different seed.

5 or 6 out of 10

Some core ideas are shaky. The pattern matters more than the score: two misses in the same topic is a gap; misses scattered across topics usually means reading the question too fast. Either way, the Skills Check will tell you which.

4 or fewer out of 10

Foundations from an earlier year are probably missing, which is common and fixable. Try the quiz one year level down to confirm, then talk to a tutor about a short catch-up plan rather than more of the same practice.

What to do with the result

Questions? Call 03 9509 3293 or book a free consultation. RHZ Tutoring, 17/47 Apex Drive, Truganina VIC 3029.

Frequently asked questions

Other Specialist Mathematics topics for Year 11

Mixed Year 11 Specialist Mathematics quiz (all topics) →

All 3,261 free practice questions, Prep to Year 12 →