ATARMAxxing · General Mathematics
TCE General Mathematics Practice Questions
64 exam-style questions · full worked solutions
The 64 practice questions inside the TCE General Mathematics Mastery Pack, grouped by area of study. Every question comes with a full worked solution.
- Module 2 Topic 1: Statistical analysis
- Multiple choice × 12
- Calculate × 1
- Explain × 1
- Describe × 1
- Interpret × 1
- Module 2 Topic 2: Growth and decay in sequences
- Multiple choice × 10
- Find × 1
- Show that × 1
- Explain × 1
- Module 3 Topic 1: Investment, loans and annuities
- Multiple choice × 10
- Calculate × 1
- Determine × 1
- Explain × 1
- Module 3 Topic 2b: Graphs, networks and decision mathematics
- Multiple choice × 8
- Determine × 1
- State × 1
- Module 3 Topic 2a: Trigonometry and Earth geometry
- Multiple choice × 8
- Calculate × 1
- Find × 1
- Module 1: Mathematical modelling, problem solving and the statistical investigation process
- Explain × 1
- Comment on × 1
Sample question
For x = 1,2,3,4 and y = 3,5,8,10, calculate the least-squares line y-hat = ax+b and the residual at x=3. Show the summary substitutions and interpret the residual.
Show the worked answer
Answer: Worked solution
Σx=10, Σy=26, Σx²=30 and Σxy=77 (1). a=[4(77)−10(26)]/[4(30)−10²]=48/20=2.4 and b=[26−2.4(10)]/4=0.5, so y-hat=2.4x+0.5 (1). At x=3, predicted y=7.7 and residual=actual−predicted=8−7.7=+0.3 (1). The observed response at x=3 is 0.3 response units above the modelled value (1).
Included in the TCE General Mathematics Mastery Pack
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
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