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100+ Free QCE Maths Methods Practice Questions

QCE Mathematical Methods (Units 3 & 4) External Assessment practice questions are available now; exam metadata is being verified.

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Key Facts: QCE Maths Methods Exam

2 papers

External assessment is Paper 1 (technology-free) and Paper 2 (technology-active)

QCAA — Mathematical Methods syllabus

55 marks each

Paper 1 and Paper 2 are each worth 55 marks, for 110 marks total

QCAA — External assessment

50%

External assessment contributes 50% of the final subject result

QCAA — External assessment (myQCE)

Units 3 & 4

The Year 12 units assessed externally: Further calculus and Further functions and statistics

QCAA — Mathematical Methods syllabus

A–E grade

Final subject result is reported as a mark out of 100 and an A–E grade

QCAA — External assessment

Technology-free

Paper 1 prohibits calculators; Paper 2 permits an approved graphics or CAS calculator

QCAA — Mathematical Methods syllabus

Year 12

Sat by Year 12 students in Queensland within their QCE program

QCAA — Senior subjects

100

Free original practice questions provided here

OpenExamPrep

QCE Mathematical Methods (Units 3 & 4) is the Year 12 General senior subject assessed externally by QCAA. The external assessment has two papers: Paper 1 is technology-free (55 marks) and Paper 2 is technology-active (55 marks), each combining multiple-choice and short-response questions, for 110 marks total. There is no single pass mark; the external assessment contributes 50% of the final subject result, which is reported as a mark out of 100 and an A–E grade. Unit 3 (Further calculus) covers exponential, logarithmic and trigonometric calculus, applications and integration; Unit 4 (Further functions and statistics) covers the second derivative, continuous random variables, the normal distribution and interval estimates for proportions. This 100-question bank provides original concept practice modelled on the syllabus skills.

Sample QCE Maths Methods Practice Questions

Try these sample questions to test your QCE Maths Methods exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate log_2(32).
A.4
B.5
C.6
D.16
Explanation: log_2(32) asks for the power of 2 that gives 32. Since 2^5 = 32, log_2(32) = 5.
2Using the logarithm laws, log(a) + log(b) is equal to:
A.log(a + b)
B.log(ab)
C.log(a) · log(b)
D.log(a/b)
Explanation: The product law of logarithms states log(a) + log(b) = log(ab). Adding logs corresponds to multiplying the arguments.
3Solve for x: 3^x = 81.
A.3
B.4
C.9
D.27
Explanation: Write 81 as a power of 3: 81 = 3^4. So 3^x = 3^4 gives x = 4.
4Simplify ln(e^5).
A.e^5
B.5
C.ln(5)
D.5e
Explanation: Since ln is the natural logarithm (base e), ln(e^5) = 5 by the inverse relationship ln(e^x) = x.
5Solve for x: log_5(x) = 3.
A.8
B.15
C.125
D.243
Explanation: log_5(x) = 3 means x = 5^3 = 125. Convert from logarithmic to exponential form to solve.
6The expression log(a) − log(b) can be rewritten as:
A.log(a − b)
B.log(a/b)
C.log(ab)
D.log(a) / log(b)
Explanation: The quotient law of logarithms gives log(a) − log(b) = log(a/b). Subtracting logs corresponds to dividing the arguments.
7Solve for x, correct to two decimal places: 2^x = 20. (Use ln 20 ≈ 2.9957, ln 2 ≈ 0.6931.)
A.4.32
B.5.00
C.3.32
D.10.00
Explanation: Take logs: x = ln(20)/ln(2) ≈ 2.9957/0.6931 ≈ 4.32. This is the standard method for solving exponential equations with non-integer answers.
8A population grows according to P(t) = 500 e^(0.04t), where t is in years. What is the initial population (t = 0)?
A.0
B.500
C.520
D.40
Explanation: At t = 0, e^(0.04 × 0) = e^0 = 1, so P(0) = 500 × 1 = 500. The coefficient in front of the exponential is the initial value.
9The graph of y = ln(x) has which of the following features?
A.A horizontal asymptote at y = 0
B.A vertical asymptote at x = 0
C.A maximum turning point
D.A y-intercept at (0, 1)
Explanation: The natural log function y = ln(x) is defined only for x > 0 and decreases without bound as x approaches 0 from the right, giving a vertical asymptote at x = 0.
10Solve for x: e^(2x) = 7. Give the exact answer.
A.ln(7)
B.(1/2) ln(7)
C.ln(7)/2 + 1
D.2 ln(7)
Explanation: Take the natural log of both sides: 2x = ln(7), so x = (1/2) ln(7). This isolates x using the inverse property of ln and e.

About the QCE Maths Methods Practice Questions

Verified exam format metadata for QCE Mathematical Methods (Units 3 & 4) External Assessment is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.