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100+ Free WACE Maths Methods Practice Questions

WACE Mathematics Methods ATAR (Units 3 & 4) practice questions are available now; exam metadata is being verified.

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2026 Statistics

Key Facts: WACE Maths Methods Exam

Units 3 & 4

The ATAR examination is set only on Unit 3 and Unit 4 content

SCSA Mathematics Methods ATAR Year 12 Syllabus

2 sections

Section One Calculator-free and Section Two Calculator-assumed

SCSA Mathematics Methods examination design brief

50 minutes

Working time for Section One Calculator-free

SCSA Mathematics Methods examination design brief

100 minutes

Working time for Section Two Calculator-assumed

SCSA Mathematics Methods examination design brief

About 65%

Share of exam marks in the Calculator-assumed section

SCSA Mathematics Methods examination design brief

50%

The ATAR examination's contribution to the final course mark

SCSA WACE assessment policy

No calculator allowed

Section One must be completed without a calculator or a penalty applies

SCSA Mathematics Methods examination design brief

100

Free original multiple-choice practice questions here

OpenExamPrep

WACE Mathematics Methods is the Year 12 calculus and statistics ATAR course run by the SCSA in Western Australia, examined only on Unit 3 and Unit 4. The written exam has two sections: Section One Calculator-free (50 minutes working time, about 35% of the marks) and Section Two Calculator-assumed (100 minutes working time, about 65%), both short-answer and extended-response rather than multiple choice. There is no single pass mark; the exam contributes 50% of the final course mark and is standardised and scaled statewide for ATAR. Core content spans differentiation and its applications, integration and the fundamental theorem, exponential and logarithmic functions, the binomial and normal distributions and confidence intervals for proportions. This 100-question bank is an original multiple-choice study tool covering that syllabus.

Sample WACE Maths Methods Practice Questions

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

1Differentiate y = (3x + 1)^5 with respect to x.
A.15(3x + 1)^4
B.5(3x + 1)^4
C.3(3x + 1)^4
D.15(3x + 1)^5
Explanation: Using the chain rule, bring down the power 5 and reduce it by one to get 5(3x + 1)^4, then multiply by the derivative of the inside, which is 3. This gives 15(3x + 1)^4.
2What is the derivative of f(x) = e^(2x)?
A.e^(2x)
B.2e^(2x)
C.2x e^(2x-1)
D.e^(2x)/2
Explanation: The derivative of e^(g(x)) is g'(x) e^(g(x)). Here g(x) = 2x so g'(x) = 2, giving 2e^(2x).
3Differentiate y = ln(x) with respect to x.
A.x
B.1/x
C.ln(x)/x
D.x ln(x)
Explanation: The derivative of the natural logarithm ln(x) is 1/x for x > 0. This is a standard result in Mathematics Methods.
4Differentiate f(x) = sin(3x).
A.cos(3x)
B.3cos(3x)
C.-3cos(3x)
D.3sin(3x)
Explanation: The derivative of sin(g(x)) is g'(x)cos(g(x)). With g(x) = 3x, g'(x) = 3, so the derivative is 3cos(3x).
5Differentiate f(x) = cos(x).
A.sin(x)
B.-sin(x)
C.cos(x)
D.-cos(x)
Explanation: The derivative of cos(x) is -sin(x). This is a standard derivative students must know for the calculator-free section.
6Use the product rule to differentiate y = x^2 e^x.
A.2x e^x
B.e^x(x^2 + 2x)
C.2x e^x + x^2
D.x^2 e^x
Explanation: The product rule gives (u v)' = u'v + uv'. With u = x^2 (u' = 2x) and v = e^x (v' = e^x), the derivative is 2x e^x + x^2 e^x = e^x(x^2 + 2x).
7Use the quotient rule to find the derivative of y = x / (x + 1).
A.1 / (x + 1)^2
B.1 / (x + 1)
C.-1 / (x + 1)^2
D.x / (x + 1)^2
Explanation: The quotient rule gives (u'v - uv')/v^2. With u = x (u' = 1) and v = x + 1 (v' = 1): ((1)(x+1) - x(1)) / (x+1)^2 = (x + 1 - x)/(x+1)^2 = 1/(x+1)^2.
8Differentiate y = ln(5x).
A.5/x
B.1/x
C.1/(5x)
D.5/(5x)
Explanation: Using the chain rule, the derivative of ln(5x) is (1/(5x)) times 5 = 5/(5x) = 1/x. Equivalently, ln(5x) = ln 5 + ln x, whose derivative is 1/x.
9Differentiate f(x) = e^(x^2).
A.2x e^(x^2)
B.e^(x^2)
C.x^2 e^(x^2-1)
D.2x e^(2x)
Explanation: By the chain rule, the derivative of e^(g(x)) is g'(x) e^(g(x)). Here g(x) = x^2 so g'(x) = 2x, giving 2x e^(x^2).
10Differentiate y = tan-like composite cos(2x + 1).
A.-2sin(2x + 1)
B.2sin(2x + 1)
C.-sin(2x + 1)
D.2cos(2x + 1)
Explanation: The derivative of cos(g(x)) is -g'(x)sin(g(x)). With g(x) = 2x + 1, g'(x) = 2, so the derivative is -2sin(2x + 1).

About the WACE Maths Methods Practice Questions

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