VCE Methods Unit 4 Skills () « back to units
The skills below are aligned with the VCE Mathematical Methods Study Design 2023-2027. Skills are organised into key areas: Integral Calculus, Continuous Random Variables, Normal Distribution, Statistical Inference, and Exam Technique. To master a skill, you will have to gain 10 stars.
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Integral Calculus (All Function Types)
- Antidifferentiate e^(ax+b)
- Antidifferentiate 1/(ax+b) to get logarithmic form
- Antidifferentiate sin(ax+b) and cos(ax+b)
- Antidifferentiate power functions (fractional and negative indices)
- Antidifferentiate using recognition of chain rule form
- Find the function given the derivative and a point
- Evaluate definite integrals (all function types)
- Calculate area under a curve (all function types)
- Calculate area between a curve and the x-axis (signed areas)
- Calculate area between two curves
- Average value of a function over an interval
- Kinematics — displacement, distance, velocity from integration
- Kinematics — interpret area under velocity-time graph
- Apply the trapezium rule for numerical integration
- Trace trapezium rule pseudocode
- Integration in modelling contexts (total quantity from rate)
- Relationship between differentiation and integration (FTC)
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Continuous Random Variables
- Verify a function is a valid PDF (non-negative, integral = 1)
- Find the value of a constant to make a valid PDF
- Calculate probabilities using a PDF (definite integral)
- Calculate the mean E(X) of a continuous distribution
- Calculate variance and standard deviation (continuous)
- Find the median of a continuous distribution
- Find percentiles and the IQR of a continuous distribution
- Sketch and interpret PDFs
- Relate CDF to PDF
- Continuous probability in context
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Normal Distribution
- Identify properties of the normal distribution curve
- Apply the 68-95-99.7% rule
- Standardise a value: z = (x - mu) / sigma
- Calculate normal probabilities P(a < X < b)
- Use the inverse normal to find x given a probability
- Find mean or standard deviation given probability information
- Solve problems involving the standard normal Z ~ N(0,1)
- Normal distribution in context (heights, measurements, etc.)
- Compare probabilities across different normal distributions
- Normal approximation to the binomial distribution
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Statistical Inference
- Distinguish population parameter from sample statistic
- Define sample proportion p-hat = X/n
- Describe the distribution of sample proportions
- Calculate the mean and standard deviation of p-hat
- Approximate normality of p-hat for large samples
- Calculate an approximate confidence interval for p
- Interpret a confidence interval correctly
- Determine sample size for a desired margin of error
- Test a claim using confidence intervals
- Simulate sampling distributions
- Understand the effect of sample size on confidence intervals
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Pseudocode & Algorithms (Units 3 & 4)
- Trace Newton's method algorithm with tolerance
- Write pseudocode for Newton's method
- Trace the trapezium rule algorithm
- Write pseudocode for the trapezium rule
- Pseudocode for probability simulation (large samples)
- Identify and correct errors in given pseudocode
- Complete missing lines in pseudocode (exam style)
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Exam Technique Skills
- Technology-free differentiation drills (Exam 1 style)
- Technology-free integration drills (Exam 1 style)
- Technology-free algebra drills (Exam 1 style)
- Technology-free probability drills (Exam 1 style)
- Extended response — functions (Exam 2 Part B style)
- Extended response — calculus (Exam 2 Part B style)
- Extended response — probability (Exam 2 Part B style)
- "Show that" question technique
- Exact value vs decimal — when to give which