Preliminary Mark: Where to Invest the Last Two Weeks
Aisha is an s7 student taking Economics. Her school calculates the Economics preliminary mark as 40% A marks and 60% Pre-Baccalaureate exam. Her current A marks average is 72/100, and her Pre-Baccalaureate score is 68/100. She wants a preliminary mark of at least 74/100 to reduce pressure on the final written exam. She has two weeks left. She can either complete an optional extra assignment that would raise her A marks average by 5 points (to 77), or spend the time preparing for the Pre-Baccalaureate exam, which she estimates could raise her Pre-Bac score by 8 points (to 76). She can only do one due to time constraints. The extra assignment is marked by her teacher and the 5-point increase is guaranteed if completed. The Pre-Baccalaureate improvement is her own estimate and carries uncertainty; she might improve by as little as 3 points or as much as 10. She also has other subjects to revise. She needs to decide which option to pursue.
1. Calculate Aisha's current preliminary mark. Then calculate the preliminary mark under each option (extra assignment vs. Pre-Bac preparation). Which option should she choose to reach her target of 74?
Read the worked answer
Current preliminary mark: 0.4 × 72 + 0.6 × 68 = 28.8 + 40.8 = 69.6.
Option 1 – extra assignment: New A marks = 77. Preliminary = 0.4 × 77 + 0.6 × 68 = 30.8 + 40.8 = 71.6.
Option 2 – Pre-Bac preparation: New Pre-Bac = 76. Preliminary = 0.4 × 72 + 0.6 × 76 = 28.8 + 45.6 = 74.4.
Only Option 2 reaches the target of 74. Therefore she should choose to prepare for the Pre-Baccalaureate exam. The extra assignment, while guaranteed, leaves her below target at 71.6, so it cannot meet her goal.
2. How does the uncertainty in the Pre-Bac estimate affect your recommendation? Show the range of possible preliminary marks for the Pre-Bac option and discuss the risk.
Read the worked answer
The Pre-Bac improvement is estimated at 8 points but could range from 3 to 10. Calculate the range:
- Low end (+3): Pre-Bac = 71. Preliminary = 0.4 × 72 + 0.6 × 71 = 28.8 + 42.6 = 71.4.
- High end (+10): Pre-Bac = 78. Preliminary = 0.4 × 72 + 0.6 × 78 = 28.8 + 46.8 = 75.6.
To reach 74, she needs a Pre-Bac score of at least 75.33, i.e. an improvement of at least 7.33 points. Her estimate of 8 is just above this threshold, so the target is plausible but not guaranteed. The extra assignment gives a certain 71.6, which is below target but risk-free. Since neither option guarantees 74, she must decide based on risk tolerance. If she is risk-averse, she might take the guaranteed 71.6 and accept a lower preliminary mark. If she is willing to accept risk for a chance at 74 or higher, she should choose the Pre-Bac preparation, but she should have a fallback plan (e.g., strong performance in the final written exam) in case the improvement is only 3–6 points. Given her target, the Pre-Bac option is the only one with any chance of reaching 74, so it is the rational choice if she can manage the uncertainty.