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Exam-style practice (harder): Maths Methods multiple choice

QCEMath MethodsStudy guide6 min read

14 harder, exam-style QCE Mathematical Methods multiple-choice questions on the quotient and chain rules, tangents, concavity, optimisation, integrals and areas, the fundamental theorem, random variables, the binomial and continuous distributions, z-scores, sample proportions and confidence intervals. Each is tagged with its question type and every distractor explained.

Jump to a section
  1. Why this set is harder than a recall quiz
  2. The question types
  3. Question map
  4. Five rules the distractors test
  5. What to do next

Why this set is harder than a recall quiz

A recall quiz asks for a rule. The QCAA Mathematical Methods external assessment asks you to apply the right rule to an unfamiliar function, interpret a probability model or choose the correct meaning of a statistical result. Each wrong option in these questions is the answer produced by a specific, common slip.

These 14 questions are original practice questions written by ExamExplained, not from any QCAA paper. Each explanation begins with a Type tag and names the slip behind every wrong option.

Exam tip

For every calculus question, write the rule you are using (product, quotient, chain, fundamental theorem) before you start. Most distractors come from using a nearly right rule: adding instead of subtracting in the quotient rule, or forgetting one link of the chain.

The question types

Type What it looks like Typical trap
Calculation Derivatives, tangents, optimisation, areas, expected values, binomial probabilities, standard deviation of P^\hat{P} Missing chain factors, wrong antiderivative, variance scaled by a instead of a2a^2, variance reported as standard deviation
Concept application Concavity, fundamental theorem, confidence intervals First derivative used for concavity; integral given instead of its derivative; the 95% attached to the wrong thing
Data interpretation Density functions, z-scores Density height treated as probability; raw scores compared across different distributions

Question map

Q Type Topic
1 Calculation Quotient rule
2 Calculation Chain rule with trigonometric functions
3 Calculation Tangents to exponential curves
4 Concept application Second derivative and concavity
5 Calculation Optimisation
6 Calculation Integration and logarithms
7 Calculation Area between curves
8 Concept application Fundamental theorem of calculus
9 Calculation Discrete random variables: linear transformations
10 Calculation Binomial distribution
11 Data interpretation Continuous random variables
12 Data interpretation Standardised scores
13 Calculation Sampling distribution of P^\hat{P}
14 Concept application Interpreting confidence intervals

Five rules the distractors test

  1. Quotient rule: (uv)′=vu′−uv′v2\left(\frac{u}{v}\right)' = \frac{vu' - uv'}{v^2}, with a MINUS sign.
  2. Concavity uses f′′f'', not f′f'.
  3. ddx∫axf(t) dt=f(x)\frac{d}{dx}\int_a^x f(t)\,dt = f(x). Differentiate the integral and you get the integrand back.
  4. Var(aX+b)=a2Var(X)\text{Var}(aX + b) = a^2\text{Var}(X). Constants shift but do not spread.
  5. A 95% confidence interval describes the method: about 95% of intervals made this way contain p.
Common trap

Reading a probability density function's height as a probability. For a continuous random variable, probabilities are areas under the curve.

What to do next

Sources & how we know this

  • math-methods
  • qce-maths-methods
  • multiple-choice
  • external-assessment
  • exam-technique
  • practice-questions
  • units-3-4

Based on the official QCAA syllabus and published QCAA past papers and marking guidelines. Not yet individually reviewed by a person; always check QCAA and your school's materials for current rules.

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