Free Practice Questions for Math 30-2 Diploma

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Key Facts: Math 30-2 Diploma Exam

The Mathematics 30-2 Diploma Exam has 32 machine-scored questions worth 75% and 2 written-response questions worth 25% (Alberta Education).

The machine-scored section is split into 24 multiple-choice and 8 numerical-response questions (Alberta Education).

The diploma exam counts for 30% of the final blended course mark; the school-awarded mark counts for 70% (Alberta Education).

Exam content is weighted Logical Reasoning 15-20%, Probability 30-35%, and Relations and Functions 45-55% (Math 30-2 Information Bulletin 2025-2026).

Students have 3 hours to write, with up to 3 additional hours permitted (Alberta Education).

The acceptable standard is a final course mark of 50% and the standard of excellence is 80% (Alberta Education).

Mathematics 30-2 diploma exams are offered in January, April, June, and August sessions (Alberta Education).

Alberta's Grade 12 Mathematics 30-2 Diploma Exam runs 3 hours with 32 machine-scored questions (75%) and 2 written-response questions (25%), counting for 30% of the final course mark.

Sample Math 30-2 Diploma Practice Questions

Try these sample questions to review concepts for the Math 30-2 Diploma exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 116+ question experience with AI tutoring.

1In the Math 30-2 outcome on logical reasoning, what is the purpose of a counterexample when investigating a conjecture?

A.To prove the conjecture is always true

B.To restate the conjecture in symbolic form

C.To provide a single case where the conjecture is false, disproving it

D.To estimate how often the conjecture holds

Explanation: A conjecture is a general statement believed to be true. A single counterexample, an instance for which the statement fails, is sufficient to disprove the conjecture entirely. One example can never prove a conjecture, but one exception can disprove it.

2A conjecture states: 'The sum of two odd numbers is always odd.' Which choice is a valid counterexample?

A.3 + 5 = 8

B.Both 3 + 5 = 8 and 1 + 1 = 2 disprove it

C.1 + 1 = 2

D.2 + 4 = 6

Explanation: The sum of two odd numbers is actually always even. Both 3 + 5 = 8 and 1 + 1 = 2 use two odd numbers and give an even sum, so each disproves the conjecture. Either valid counterexample is enough, and both listed pairs qualify.

3Inductive reasoning is best described as reaching a conclusion by:

A.Translating a statement into set notation

B.Applying a proven general rule to a specific case

C.Disproving a statement with a counterexample

D.Generalizing from specific observations or patterns

Explanation: Inductive reasoning draws a general conclusion (a conjecture) from specific cases or observed patterns. It is the reasoning used to form conjectures, though the conclusion is not guaranteed true until proven.

4Which scenario is an example of deductive reasoning?

A.Noticing the first five terms increase by 3 and predicting the sixth

B.Knowing all squares have four equal sides and concluding a given square has four equal sides

C.Observing several swans are white and concluding all swans are white

D.Testing many odd numbers and conjecturing their squares are odd

Explanation: Deductive reasoning applies an accepted general rule to a specific case to reach a guaranteed conclusion. Using the definition that all squares have four equal sides to conclude a particular square does is deductive.

5When analyzing a game or puzzle to develop a winning strategy, the most reliable approach is to:

A.Play randomly until you win once

B.Work backward from a winning end position to identify required moves

C.Assume the first player always loses

D.Ignore the opponent's possible responses

Explanation: A common Math 30-2 strategy for analyzing games is to reason backward from a winning (or losing) position to determine the moves that force that outcome. This identifies the key positions a player must reach.

6Let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8}. If A = {2, 4, 6, 8}, what is the complement A'?

A.{1, 2, 3, 4, 5, 6, 7, 8}

B.{2, 4, 6, 8}

C.{1, 3, 5, 7}

D.{ }

Explanation: The complement A' consists of every element of the universal set U that is NOT in A. Removing {2, 4, 6, 8} from U leaves {1, 3, 5, 7}.

7Given A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A ∩ B?

A.{1, 2, 3, 4, 5, 6}

B.{3, 4}

C.{1, 2, 5, 6}

D.{ }

Explanation: The intersection A ∩ B contains only the elements common to both sets. Both 3 and 4 appear in A and in B, so A ∩ B = {3, 4}.

8In a class of 30 students, 18 take Biology, 15 take Chemistry, and 7 take both. How many students take Biology OR Chemistry (at least one of the two)?

A.33

B.40

C.26

D.23

Explanation: Use n(B ∪ C) = n(B) + n(C) − n(B ∩ C) = 18 + 15 − 7 = 26. Subtracting the 7 counted in both prevents double-counting, giving 26 students in at least one subject.

9Using the data from a survey of 30 students where 18 take Biology, 15 take Chemistry, and 7 take both, how many students take NEITHER subject?

A.11

B.7

C.0

D.4

Explanation: First, 18 + 15 − 7 = 26 take at least one subject. Of the 30 students, the number taking neither is 30 − 26 = 4. These 4 fall outside both circles of the Venn diagram.

10Set A = {2, 4} is a subset of set B = {1, 2, 3, 4, 5}. Which statement correctly uses set notation?

A.A ∩ B = ∅

B.B ⊂ A

C.A ⊂ B

D.A = B

Explanation: Every element of A (2 and 4) is also in B, so A is a subset of B, written A ⊂ B. The smaller set is contained within the larger set.

About the Math 30-2 Diploma Exam

The Mathematics 30-2 Diploma Examination is a Grade 12 provincial assessment set by Alberta Education and Childcare in Canada. The real exam consists of 32 machine-scored questions (24 multiple-choice and 8 numerical-response) worth 75% of the mark and 2 written-response questions worth 25%, completed in 3 hours. Mathematics 30-2 is the applied/conceptual pathway accepted by many non-STEM university programs, distinct from the pre-calculus Math 30-1 and the trades-oriented Math 30-3. Content spans Logical Reasoning (15-20%), Probability (30-35%), and Relations and Functions (45-55%). The diploma exam mark accounts for 30% of a student's final blended course mark.

Exam sponsor: Alberta Education and Childcare (Provincial Assessment Sector). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

100 questions

Time Limit

3 hours (up to 3 additional hours permitted)

Passing Score

Acceptable standard 50%; standard of excellence 80%. Exam is 30% of the final blended course mark.

Exam / Certification Fees

No fee for in-session school candidates; rewrite/mature-student fees may apply per Alberta Education's General Information Bulletin.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Alberta Education and Childcare (Provincial Assessment Sector): official exam information

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

15-20%

Logical Reasoning

Puzzles and games, problem-solving strategies, set theory, set notation, subsets, complements, and Venn diagrams.

30-35%

Probability

Counting methods, permutations and combinations, odds, mutually exclusive and non-mutually-exclusive events, conditional probability, and independent/dependent events.

45-55%

Relations and Functions

Polynomial functions, exponential and logarithmic functions and equations, sinusoidal and periodic functions, and rational expressions and equations.

Preparing for the Math 30-2 Diploma Exam

What You Need to Know

Passing score: Acceptable standard 50%; standard of excellence 80%. Exam is 30% of the final blended course mark.
Exam length: 100 questions
Time limit: 3 hours (up to 3 additional hours permitted)
Exam / certification fees: No fee for in-session school candidates; rewrite/mature-student fees may apply per Alberta Education's General Information Bulletin. Official sources

Using Our Practice Resources

Work through all 116 available questions
Review every answer and explanation
Track weak areas and revisit them
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Math 30-2 Diploma: Suggested Study Strategy

1Memorize the probability and counting formulas on the provided formula sheet (nPr, nCr, P(A or B), P(A and B)) so you can apply them quickly under time pressure.

2Practice translating word problems into set notation and Venn diagrams, since logical reasoning and probability both rely on careful counting of overlaps.

3Distinguish clearly between permutations (order matters) and combinations (order does not matter) before computing.

4Drill exponential and logarithmic equation solving by rewriting both sides with a common base; remember solving equations like log x + log 5 = 3 is beyond Math 30-2 scope.

5For sinusoidal questions, set up amplitude, midline, period, and vertical shift before reading off maximum and minimum values.

6Always state non-permissible values when simplifying rational expressions and check solutions against them in rational equations.

Frequently Asked Questions

How is the Math 30-2 Diploma Exam structured?

The exam has 32 machine-scored questions (24 multiple-choice and 8 numerical-response) worth 75% of the mark and 2 written-response questions worth 25%, written over 3 hours with up to 3 additional hours allowed.

What percentage of my final mark is the diploma exam?

The diploma exam mark counts for 30% of your final blended course mark, and your school-awarded mark counts for the other 70%.

What is the difference between Math 30-2 and Math 30-1?

Math 30-2 is the applied/conceptual pathway accepted by many non-STEM university programs, while Math 30-1 is the pre-calculus pathway required for STEM programs. Math 30-2 emphasizes logical reasoning, probability, and applied functions over heavy calculus preparation.

What does 'acceptable standard' and 'standard of excellence' mean?

The acceptable standard is a final course mark of 50% or higher; the standard of excellence is a final course mark of 80% or higher, as defined by Alberta Education.

Can I use a calculator and formula sheet?

Yes. An approved graphing calculator is permitted and a formula sheet is provided (viewable digitally or available on paper), covering permutation/combination and probability formulas plus set-theory symbols.

When is the Math 30-2 Diploma Exam offered?

Mathematics 30-2 diploma exams are administered in January, April, June, and August sessions during the school year.

Free Practice Questions for Math 30-2 Diploma

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