Unit 4: Integration & Statistics

VCE Mathematical Methods Study Design 2023-2027

Units 3 & 4 (Exam-Assessed) 64 Skills • 3 Levels Each

Unit 4 Skill Map

Integral calculus, continuous random variables, normal distribution, statistical inference, pseudocode, and exam technique.

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Integral Calculus (All Function Types)

17 skills

Antidifferentiate e^(ax+b)20300 Antidifferentiate 1/(ax+b) to get logarithmic form20301 Antidifferentiate sin(ax+b) and cos(ax+b)20302 Antidifferentiate power functions (fractional and negative indices)20303 Antidifferentiate using recognition of chain rule form20304 Find the function given the derivative and a point20305 Evaluate definite integrals (all function types)20306 Calculate area under a curve (all function types)20307 Calculate area between a curve and the x-axis (signed areas)20308 Calculate area between two curves20309 Average value of a function over an interval20310 Kinematics — displacement, distance, velocity from integration20311 Kinematics — interpret area under velocity-time graph20312 Apply the trapezium rule for numerical integration20313 Trace trapezium rule pseudocode20314 Integration in modelling contexts (total quantity from rate)20315 Relationship between differentiation and integration (FTC)20316

Continuous Random Variables

10 skills

Verify a function is a valid PDF (non-negative, integral = 1)20320 Find the value of a constant to make a valid PDF20321 Calculate probabilities using a PDF (definite integral)20322 Calculate the mean E(X) of a continuous distribution20323 Calculate variance and standard deviation (continuous)20324 Find the median of a continuous distribution20325 Find percentiles and the IQR of a continuous distribution20326 Sketch and interpret PDFs20327 Relate CDF to PDF20328 Continuous probability in context20329

Normal Distribution

10 skills

Identify properties of the normal distribution curve20340 Apply the 68-95-99.7% rule20341 Standardise a value: z = (x - mu) / sigma20342 Calculate normal probabilities P(a < X < b)20343 Use the inverse normal to find x given a probability20344 Find mean or standard deviation given probability information20345 Solve problems involving the standard normal Z ~ N(0,1)20346 Normal distribution in context (heights, measurements, etc.)20347 Compare probabilities across different normal distributions20348 Normal approximation to the binomial distribution20349

Statistical Inference

11 skills

Distinguish population parameter from sample statistic20360 Define sample proportion p-hat = X/n20361 Describe the distribution of sample proportions20362 Calculate the mean and standard deviation of p-hat20363 Approximate normality of p-hat for large samples20364 Calculate an approximate confidence interval for p20365 Interpret a confidence interval correctly20366 Determine sample size for a desired margin of error20367 Test a claim using confidence intervals20368 Simulate sampling distributions20369 Understand the effect of sample size on confidence intervals20370

Pseudocode & Algorithms (Units 3 & 4)

7 skills

Trace Newton's method algorithm with tolerance20400 Write pseudocode for Newton's method20401 Trace the trapezium rule algorithm20402 Write pseudocode for the trapezium rule20403 Pseudocode for probability simulation (large samples)20404 Identify and correct errors in given pseudocode20405 Complete missing lines in pseudocode (exam style)20406

Exam Technique Skills

9 skills

Technology-free differentiation drills (Exam 1 style)20410 Technology-free integration drills (Exam 1 style)20411 Technology-free algebra drills (Exam 1 style)20412 Technology-free probability drills (Exam 1 style)20413 Extended response — functions (Exam 2 Part B style)20414 Extended response — calculus (Exam 2 Part B style)20415 Extended response — probability (Exam 2 Part B style)20416 "Show that" question technique20417 Exact value vs decimal — when to give which20418