Free Practice Questions for PNG Grade 12 Mathematics

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Sample PNG Grade 12 Mathematics Practice Questions

Try these sample questions to review concepts for the PNG Grade 12 Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 97+ question experience with AI tutoring.

1When the polynomial P(x) = 2x³ - 5x² + 4x - 7 is divided by (x - 2), what is the remainder?

A.3

B.-3

C.7

D.-11

Explanation: According to the Remainder Theorem, dividing P(x) by (x - c) yields a remainder equal to P(c). Evaluating at x = 2 gives P(2) = 2(2)³ - 5(2)² + 4(2) - 7 = 2(8) - 5(4) + 8 - 7 = 16 - 20 + 8 - 7 = -3. Hence, the remainder is -3.

2The binomial (x - 2) is a factor of P(x) = 2x³ + kx² - 13x + 6. What is the value of the constant k?

A.-1

B.2

C.1

D.-4

Explanation: By the Factor Theorem, (x - 2) is a factor of P(x) if and only if P(2) = 0. Substituting x = 2 yields P(2) = 2(2)³ + k(2)² - 13(2) + 6 = 16 + 4k - 26 + 6 = 4k - 4. Setting 4k - 4 = 0 gives 4k = 4, so k = 1.

3The polynomial P(x) = x³ - 3x² - 10x + 24 has (x - 2) as one of its factors. What is the complete factorization of P(x) into linear factors?

A.(x - 2)(x + 4)(x - 3)

B.(x + 2)(x - 4)(x + 3)

C.(x - 2)(x - 6)(x + 2)

D.(x - 2)(x - 4)(x + 3)

Explanation: Dividing P(x) by (x - 2) via polynomial long division or synthetic division yields the quadratic quotient x² - x - 12. Factoring this quadratic gives (x - 4)(x + 3) since (-4)(3) = -12 and -4 + 3 = -1. Therefore, the complete factorization is (x - 2)(x - 4)(x + 3).

4What are the equations of the vertical and horizontal asymptotes of the rational function f(x) = (3x - 5)/(x + 2)?

A.x = -2 and y = 3

B.x = 2 and y = 3

C.x = -2 and y = -5/2

D.x = 3 and y = -2

Explanation: The vertical asymptote occurs where the denominator is zero and the numerator is non-zero: x + 2 = 0 implies x = -2. The horizontal asymptote is found by taking the limit as x approaches ±∞: lim_{x→±∞} (3x - 5)/(x + 2) = 3/1 = 3, yielding y = 3. Thus, the asymptotes are x = -2 and y = 3.

5Consider the rational function g(x) = (2x² - 5x - 3)/(x - 3). Which statement accurately describes the graph of g(x)?

A.It has a vertical asymptote at x = 3 and an oblique asymptote y = 2x + 1.

B.It is a straight line y = 2x + 1 with a hole at the point (3, 7).

C.It is a straight line y = 2x - 1 with a hole at the point (3, 5).

D.It has a vertical asymptote at x = 3 and a horizontal asymptote at y = 2.

Explanation: Factoring the numerator gives 2x² - 5x - 3 = (2x + 1)(x - 3). For all x ≠ 3, the factor (x - 3) cancels completely, simplifying the function to the linear equation g(x) = 2x + 1. At x = 3, there is a removable discontinuity (a hole) at (3, 2(3) + 1) = (3, 7), rather than an asymptote.

6Solve the exponential equation 4^(2x - 1) = 32 for x.

A.3/2

B.9/4

C.7/4

D.7/2

Explanation: Express both sides as powers of 2: 4 = 2² and 32 = 2⁵. The equation becomes (2²)^(2x - 1) = 2⁵, which simplifies to 2^(4x - 2) = 2⁵. Equating exponents gives 4x - 2 = 5, so 4x = 7 and x = 7/4.

7Find all real solutions to the equation 3^(2x) - 10 · 3^x + 9 = 0.

A.x = 1 and x = 9

B.x = 0 and x = 2

C.x = -1 and x = 2

D.x = 0 and x = 3

Explanation: Substitute u = 3^x. The equation transforms into the quadratic u² - 10u + 9 = 0. Factoring gives (u - 1)(u - 9) = 0, so u = 1 or u = 9. Substituting back gives 3^x = 1 (which gives x = 0) and 3^x = 9 (which gives x = 2). Thus, the solutions are x = 0 and x = 2.

8What is the solution set to the logarithmic equation log₂(x + 5) + log₂(x - 1) = 4?

A.x = 3 and x = -7

B.x = 7

C.x = 5

D.x = 3 only

Explanation: Using the product rule for logarithms gives log₂[(x + 5)(x - 1)] = 4. Rewriting in exponential form yields (x + 5)(x - 1) = 2⁴ = 16. Expanding gives x² + 4x - 5 = 16, so x² + 4x - 21 = 0, which factors into (x + 7)(x - 3) = 0. Since log₂(x - 1) requires x > 1, x = -7 is extraneous, leaving x = 3 as the only valid solution.

9Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, calculate the value of log₁₀ 72.

A.1.8572

B.1.7582

C.2.1582

D.1.5361

Explanation: Prime factorize 72 as 8 × 9 = 2³ × 3². Applying logarithm laws yields log₁₀ 72 = log₁₀(2³ × 3²) = 3 log₁₀ 2 + 2 log₁₀ 3. Substituting the given approximations gives 3(0.3010) + 2(0.4771) = 0.9030 + 0.9542 = 1.8572.

10Solve for x in the equation ln(x² - 3) - ln(x) = ln(2).

A.x = 3 and x = -1

B.x = 3 only

C.x = 1 and x = -3

D.x = √5

Explanation: Combine the left side using the quotient rule: ln((x² - 3)/x) = ln(2). Equating arguments gives (x² - 3)/x = 2, so x² - 3 = 2x, which rearranges to x² - 2x - 3 = 0. Factoring yields (x - 3)(x + 1) = 0. For real logarithms, ln(x) requires x > 0 and ln(x² - 3) requires x > √3. Thus x = -1 is inadmissible and x = 3 is the unique solution.

About the PNG Grade 12 Mathematics Exam

Independent English-language MCQ practice for PNG Grade 12 Mathematics. An umbrella study bank with an Advanced Mathematics emphasis: algebra and functions, calculus, trigonometry and vectors, sequences and finance, probability and statistics. General Mathematics and Advanced Mathematics are distinct official senior-secondary courses; calculus, vectors, and complex-number items are not advertised as General Mathematics requirements. This is independent English-language MCQ study practice. It is not an official translation, format simulation, or substitute for writing, speaking, practical, or performance assessment. Passages, resource-booklet extracts, datasets, and policy scenarios written for these exercises are illustrative unless a named primary source is identified. They are not the actual 2026 paper or resource booklet.

Exam sponsor: Department of Education, Measurement Services Division (MSD). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written examinations in the candidate’s registered General Mathematics or Advanced Mathematics course. This shared practice URL is not a simulation of either paper. Current per-course item counts, durations, and calculator rules were not verified. Confirm the registered Mathematics course and all school/external requirements. No separate compulsory 2026 national oral, practical, or case-study paper was verified. Work full solutions as well as selecting MCQ answers.

Time Limit

2026 per-paper duration not verified; confirm current instructions

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Exam / Certification Fees

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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.

22 study questions; official weight not verified

Functions And Algebra

Selected independent practice in functions and algebra. These are editorial study groupings, not official blueprint allocations.

18 study questions; official weight not verified

Calculus

Selected independent practice in calculus. These are editorial study groupings, not official blueprint allocations.

19 study questions; official weight not verified

Trigonometry And Vectors

Selected independent practice in trigonometry and vectors. These are editorial study groupings, not official blueprint allocations.

20 study questions; official weight not verified

Sequences And Finance

Selected independent practice in sequences and finance. These are editorial study groupings, not official blueprint allocations.

18 study questions; official weight not verified

Probability And Statistics

Selected independent practice in probability and statistics. These are editorial study groupings, not official blueprint allocations.

Preparing for the PNG Grade 12 Mathematics Exam

What You Need to Know

Passing score: No universal 2026 pass mark verified; confirm current certification and selection requirements
Assessment: Written examinations in the candidate’s registered General Mathematics or Advanced Mathematics course. This shared practice URL is not a simulation of either paper. Current per-course item counts, durations, and calculator rules were not verified. Confirm the registered Mathematics course and all school/external requirements. No separate compulsory 2026 national oral, practical, or case-study paper was verified. Work full solutions as well as selecting MCQ answers.
Time limit: 2026 per-paper duration not verified; confirm current instructions
Exam / certification fees: Official fee not verified; confirm with your school or MSD Official sources

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PNG Grade 12 Mathematics: Suggested Study Strategy

1Use the syllabus for your registered General or Advanced course to choose relevant practice.

2Show complete working and check domains, units, and rounding assumptions.

3Advanced candidates should practise calculus and complex numbers beyond recognition questions.

Frequently Asked Questions

When is the 2026 assessment scheduled?

The Department’s 2026 calendar lists 12–16 October 2026 for this assessment or its grade-level examination window. Follow your school’s subject timetable.

What is the official assessment format?

What language and eligibility information was verified?

Official curriculum resources are published in English, but a current examination-specific response-language policy was not verified. Confirm permitted response languages with your school or MSD. This practice bank uses English. This is a Grade 12 school assessment administered through nominated candidates and registered subject choices, rather than an unrestricted public certification test. Confirm nomination, schoolwork, and any FODE pathway requirements with the school or provider.

What other assessment work is required?

Confirm the registered Mathematics course and all school/external requirements. No separate compulsory 2026 national oral, practical, or case-study paper was verified. Work full solutions as well as selecting MCQ answers.

What are the fee, duration, question count, and pass mark?

A current official per-paper fee, duration, item count, and universal pass mark were not verified as of 7 October 2026. Confirm them with your school or MSD; tuition-subsidy policy alone does not establish a zero examination fee.

How should this English-language MCQ bank be used?

This is independent English-language MCQ study practice. It is not an official translation, format simulation, or substitute for writing, speaking, practical, or performance assessment. Passages, resource-booklet extracts, datasets, and policy scenarios written for these exercises are illustrative unless a named primary source is identified. They are not the actual 2026 paper or resource booklet.