WACE Mathematics Methods Practice Questions
The 64 practice questions inside the WACE Mathematics Methods Mastery Pack, grouped by area of study. Every question comes with a full worked solution.
- Topic 3.1: Further differentiation and applications
- Multiple choice × 8
- Determine × 1
- Show that × 1
- Sketch × 1
- Topic 3.2: Integrals
- Multiple choice × 8
- Calculate × 1
- Determine × 1
- Estimate × 1
- Topic 3.3: Discrete random variables
- Multiple choice × 8
- Calculate × 1
- Interpret × 1
- Topic 4.1: The logarithmic function
- Multiple choice × 8
- Solve × 1
- Determine × 1
- Sketch × 1
- Topic 4.2: Continuous random variables and the normal distribution
- Multiple choice × 8
- Show that × 1
- Calculate × 1
- Topic 4.3: Interval estimates for proportions
- Multiple choice × 8
- Explain × 1
- Justify × 1
- Determine × 1
Show the worked answer
Answer: Worked solution
Let height be h. The volume constraint gives h=32/x² (1 mark). Surface area is A=x²+4xh=x²+128/x (1 mark). Differentiating gives A′=2x−128/x² (1 mark). A′=0 implies 2x³=128, so x=4 m (1 mark). Since A″=2+256/x³>0 for every x>0, A is strictly convex and this stationary point is the unique global minimum on its domain (1 mark). The height is 32/16=2 m, so the required dimensions are a 4 m by 4 m base and height 2 m (1 mark).
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
Unlock Mathematics Methods — $20
Preview a sample note and question free on the WACE Mathematics Methods hub →