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Exam Review

Key Facts: TASC Mathematics Methods – Foundation Level 3 Exam

Course Code: MTM315117 (Level 3 course accredited by TASC).

Earns 15 TCE (Tasmanian Certificate of Education) credit points upon successful completion.

External exam length is 3 hours (180 minutes).

Covers 5 major mathematical modules equally weighted at 20% each.

Essential prerequisite for university entry into tertiary science, engineering, and commerce programs.

Prepare for the TASC Mathematics Methods – Foundation Level 3 (MTM315117) exam with this targeted 100-question practice assessment. Featuring step-by-step worked algebraic calculations across all 5 core modules, this question bank builds fluency in linear and quadratic algebra, index and logarithm laws, introductory differential calculus, and probability. These practice questions are an English-language multiple-choice study aid for revising course knowledge and are not an official TASC paper or a simulation of the written external examination format.

Sample TASC Mathematics Methods – Foundation Level 3 Practice Questions

Try these sample questions to review concepts for the TASC Mathematics Methods – Foundation Level 3 exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Solve the linear equation: 3(2x - 5) + 4 = 19.
A.x = 3
B.x = 4
C.x = 5
D.x = 6
Explanation: Expanding the brackets gives 6x - 15 + 4 = 19, which simplifies to 6x - 11 = 19. Adding 11 to both sides yields 6x = 30, and dividing by 6 gives x = 5.
2Expand and simplify the algebraic expression: (4x - 3)(x + 2) - 2x(x - 1).
A.2x^2 + 7x - 6
B.2x^2 + 3x - 6
C.6x^2 + 7x - 6
D.2x^2 + 7x + 6
Explanation: Expanding the first double brackets yields (4x^2 + 8x - 3x - 6) = 4x^2 + 5x - 6. Expanding the second term yields -(2x^2 - 2x) = -2x^2 + 2x. Combining like terms: (4x^2 - 2x^2) + (5x + 2x) - 6 = 2x^2 + 7x - 6.
3Solve the linear inequality: 5 - 2x > 13.
A.x > -4
B.x < -4
C.x > 4
D.x < 4
Explanation: Subtracting 5 from both sides gives -2x > 8. Dividing both sides by -2 requires reversing the inequality sign, yielding x < -4.
4Rearrange the formula A = 1/2 * h * (a + b) to make b the subject.
A.b = (2A - ah) / h
B.b = (A - ah) / h
C.b = (2A + ah) / h
D.b = 2A / (h - a)
Explanation: Multiply both sides by 2 to clear the fraction: 2A = h(a + b). Divide by h: 2A / h = a + b. Subtract a from both sides: b = (2A / h) - a = (2A - ah) / h.
5Solve the system of simultaneous equations: 2x + 3y = 12 and 5x - 2y = 11.
A.x = 3, y = 2
B.x = 2, y = 3
C.x = 3, y = -2
D.x = 4, y = 1
Explanation: Multiply the first equation by 2: 4x + 6y = 24. Multiply the second equation by 3: 15x - 6y = 33. Adding the two equations eliminates y: 19x = 57, so x = 3. Substituting x = 3 into 2(3) + 3y = 12 gives 6 + 3y = 12, so 3y = 6 and y = 2.
6Simplify the algebraic fraction expression: 3 / (x + 2) + 2 / (x - 1).
A.(5x + 1) / ((x + 2)(x - 1))
B.(5x - 1) / ((x + 2)(x - 1))
C.5 / ((x + 2)(x - 1))
D.(5x + 5) / ((x + 2)(x - 1))
Explanation: Find a common denominator (x + 2)(x - 1): 3(x - 1) / ((x + 2)(x - 1)) + 2(x + 2) / ((x + 2)(x - 1)) = (3x - 3 + 2x + 4) / ((x + 2)(x - 1)) = (5x + 1) / ((x + 2)(x - 1)).
7Solve the fractional linear equation: (2x + 1)/3 - (x - 2)/4 = 3.
A.x = 4.8
B.x = 5.0
C.x = 5.2
D.x = 5.6
Explanation: Multiply every term by the least common denominator 12: 4(2x + 1) - 3(x - 2) = 36. Expanding gives 8x + 4 - 3x + 6 = 36, which simplifies to 5x + 10 = 36. Subtracting 10 gives 5x = 26, so x = 26/5 = 5.2.
8Solve the double inequality: -3 <= 4x - 7 < 9.
A.1 <= x < 4
B.-1 <= x < 4
C.1 <= x <= 4
D.0 < x < 4
Explanation: Add 7 across all three parts of the inequality: -3 + 7 <= 4x < 9 + 7, yielding 4 <= 4x < 16. Divide all parts by 4: 1 <= x < 4.
9An event venue sells adult tickets for $8 and child tickets for $5. A total of 150 tickets were sold for $960. How many adult tickets were sold?
A.60
B.65
C.70
D.80
Explanation: Let a be the number of adult tickets and c be child tickets. We have a + c = 150 (so c = 150 - a) and 8a + 5c = 960. Substituting c gives 8a + 5(150 - a) = 960 => 8a + 750 - 5a = 960 => 3a = 210 => a = 70 adult tickets.
10Evaluate the function f(x) = (3x - 7) / (2x + 1) at x = -2.
A.-13/3
B.13/3
C.1/3
D.-1/3
Explanation: Substitute x = -2 into numerator and denominator: f(-2) = (3(-2) - 7) / (2(-2) + 1) = (-6 - 7) / (-4 + 1) = (-13) / (-3) = 13/3.

About the TASC Mathematics Methods – Foundation Level 3 Exam

TASC Mathematics Methods – Foundation Level 3 (Course Code: MTM315117) is a senior secondary course accredited by the Tasmanian Assessment, Standards and Certification (TASC) body for senior secondary students undertaking the Tasmanian Certificate of Education (TCE). The course serves as an essential foundation for students intending to pursue tertiary programs requiring competence in functions, calculus, exponential and logarithmic relationships, linear and quadratic modeling, and statistical probability. The syllabus is structured across five major topic areas: Algebraic Manipulation, Linear Equations & Inequalities; Quadratic Functions, Equations & Graphs; Exponents, Indices & Logarithms; Introduction to Differential Calculus & Rates of Change; and Probability Concepts, Combinatorics & Data Analysis. Candidates develop fluency in performing worked algebraic operations, solving algebraic equations and inequalities, completing the square, analyzing function features, evaluating derivatives via differentiation rules, identifying turning points, and computing discrete probabilities and sample statistics.

Exam sponsor: Tasmanian Assessment, Standards and Certification (TASC). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The TASC Mathematics Methods – Foundation Level 3 assessment evaluates mathematical reasoning, algebraic computation, function analysis, introductory differential calculus, and probability analysis across 5 core topic areas.

Time Limit

Recommended 180 minutes for full 100-question practice assessment.

Passing Score

Satisfactory Achievement (SA) or higher (award scale EA–LA)

Exam / Certification Fees

Included in standard Tasmanian secondary school enrolment / TASC course delivery.

Exam sponsor website

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

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.

20%

Syllabus Topic Module 1

Comprehensive coverage of core concepts, theories, and analytical skills for Module 1 in the official TASC curriculum.

20%

Syllabus Topic Module 2

Comprehensive coverage of core concepts, theories, and analytical skills for Module 2 in the official TASC curriculum.

20%

Syllabus Topic Module 3

Comprehensive coverage of core concepts, theories, and analytical skills for Module 3 in the official TASC curriculum.

20%

Syllabus Topic Module 4

Comprehensive coverage of core concepts, theories, and analytical skills for Module 4 in the official TASC curriculum.

20%

Syllabus Topic Module 5

Comprehensive coverage of core concepts, theories, and analytical skills for Module 5 in the official TASC curriculum.

Preparing for the TASC Mathematics Methods – Foundation Level 3 Exam

What You Need to Know

  • Passing score: Satisfactory Achievement (SA) or higher (award scale EA–LA)
  • Assessment: The TASC Mathematics Methods – Foundation Level 3 assessment evaluates mathematical reasoning, algebraic computation, function analysis, introductory differential calculus, and probability analysis across 5 core topic areas.
  • Time limit: Recommended 180 minutes for full 100-question practice assessment.
  • Exam / certification fees: Included in standard Tasmanian secondary school enrolment / TASC course delivery. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

TASC Mathematics Methods – Foundation Level 3: Suggested Study Strategy

1Practice full algebraic derivations step-by-step, including expanding brackets and collecting like terms before attempting numerical substitutions.
2Master the discriminant b^2 - 4ac to rapidly determine the number and nature of real roots in quadratic problems.
3Remember that when differentiating polynomials using f'(x), lower each exponent by 1 and multiply by the original coefficient.
4Check logarithmic solutions against original equation domains to ensure log arguments remain strictly positive.

Frequently Asked Questions

What is TASC Mathematics Methods – Foundation Level 3 (MTM315117)?

MTM315117 is a Level 3 senior secondary course under TASC in Tasmania that provides foundational mathematical methods coverage in algebra, quadratic functions, logarithms, introductory calculus, and probability.

How is the TASC MTM315117 assessment structured?

Assessment includes school-based internal assessments and a final 3-hour TASC external written examination featuring short answer, structured working, and multi-part problem solving.

Why are step-by-step worked algebraic calculations included in this practice bank?

TASC assessment standards mandate showing full working steps for mathematical credit. All 100 practice questions provide explicit algebraic operations in their explanations to reinforce exact working methods.

What award scale is used by TASC for Level 3 courses?

TASC awards range from Exceptional Achievement (EA), High Achievement (HA), Commendable Achievement (CA), Satisfactory Achievement (SA), to Preliminary Achievement (PA) and Ungraded.

Can I use graphics and scientific calculators during the TASC examination?

Yes, standard TASC approved scientific and CAS/graphics calculators are permitted in the calculator-assumed sections of the external exam.