Sample problems

These 16 problems — two from each NSW Mathematics course — are a preview of the full bank. Open a problem to see its statement, hints, worked solution and takeaways. The rest of the question bank still requires a login.

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Section 1: Year 12 Extension 2

Problem 1: Integration via Partial Fractions: Simple Proper Fraction

Problem 2: Integration by Parts - Definite Integrals

Section 2: Year 12 Extension 1

Problem 1: Reverse Chain Rule with Exponential Functions

Problem 2: Evaluating Indefinite Integrals

Section 3: Year 12 Advanced

Problem 1: Arithmetic Sequence Analysis

Problem 2: Normal Distribution of Rainfall Levels

Section 4: Year 12 Standard 1

Problem 1: Election Votes Ratio

Problem 2: Writing Simplified Rates

Section 5: Year 12 Standard 2

Problem 1: Die Roll Outcomes

Problem 2: Simplifying Fraction Ratios

Section 6: Year 11 Extension 1

Problem 1: Algebraic Simplification of Factorials

Problem 2: Solving Polynomial Inequations via Factorisation

Section 7: Year 11 Advanced

Problem 1: Adding and Subtracting Algebraic Fractions

Problem 2: Express as a Single Logarithm

Section 8: Year 11 Standard

Problem 1: Converting 12-hour Time to 24-hour Time

Problem 2: Percentage Decrease Calculations