Exam Preparation Time Allocator

Exam Preparation Time Allocator distributes study hours across subjects based on number, difficulty, topic volume, and exam proximity for efficient planning.

Number of Subjects:

Available Study Time (hours/week):

Weeks Until Exam:

Formulas Used in Exam Preparation Time Allocator

The calculator uses the following formulas to allocate study time:

Subject Weight:

\\[ W_i = D_i \cdot V_i \cdot P \\]

Total Weight:

\\[ W_{\text{total}} = \sum W_i \\]

Allocated Time per Subject:

\\[ T_i = A \cdot \frac{W_i}{W_{\text{total}}} \\]

Efficiency Score:

\\[ S = \min\left(100 \cdot \frac{A}{A_{\text{max}}}, 100\right) \\]

Where:

\\( W_i \\): Weight for subject \\( i \\)
\\( D_i \\): Difficulty of subject \\( i \\) (Easy: 1, Medium: 1.5, Hard: 2)
\\( V_i \\): Topic volume of subject \\( i \\) (%)
\\( P \\): Proximity factor (>8 weeks: 0.8, 4–8 weeks: 1.0, <4 weeks: 1.2)
\\( W_{\text{total}} \\): Sum of weights
\\( T_i \\): Study time for subject \\( i \\) (hours/week)
\\( A \\): Total available study time (hours/week)
\\( S \\): Efficiency score (%)
\\( A_{\text{max}} \\): Maximum study time (40 hours/week)

Example Calculations

Example 1: Simple Case

Input: Subjects = 2 (Math: Medium, 50%; English: Easy, 50%), Available Time = 10 h/week, Weeks = 10

\\[ W_{\text{Math}} = 1.5 \cdot 0.5 \cdot 0.8 = 0.6, \quad W_{\text{English}} = 1 \cdot 0.5 \cdot 0.8 = 0.4 \\] \\[ W_{\text{total}} = 0.6 + 0.4 = 1 \\] \\[ T_{\text{Math}} = 10 \cdot \frac{0.6}{1} = 6 \ \text{h/week}, \quad T_{\text{English}} = 10 \cdot \frac{0.4}{1} = 4 \ \text{h/week} \\] \\[ S = 100 \cdot \frac{10}{40} = 25 \ \% \\]

Result: Math: 6 h/week, English: 4 h/week, Efficiency = 25%

Example 2: Moderate Case

Input: Subjects = 3 (Math: Hard, 40%; Physics: Medium, 30%; History: Easy, 30%), Available Time = 20 h/week, Weeks = 6

\\[ W_{\text{Math}} = 2 \cdot 0.4 \cdot 1.0 = 0.8, \quad W_{\text{Physics}} = 1.5 \cdot 0.3 \cdot 1.0 = 0.45, \quad W_{\text{History}} = 1 \cdot 0.3 \cdot 1.0 = 0.3 \\] \\[ W_{\text{total}} = 0.8 + 0.45 + 0.3 = 1.55 \\] \\[ T_{\text{Math}} = 20 \cdot \frac{0.8}{1.55} \approx 10.32 \ \text{h/week}, \quad T_{\text{Physics}} = 20 \cdot \frac{0.45}{1.55} \approx 5.81 \ \text{h/week}, \quad T_{\text{History}} = 20 \cdot \frac{0.3}{1.55} \approx 3.87 \ \text{h/week} \\] \\[ S = 100 \cdot \frac{20}{40} = 50 \ \% \\]

Result: Math: 10.32 h/week, Physics: 5.81 h/week, History: 3.87 h/week, Efficiency = 50%

Example 3: Intensive Case

Input: Subjects = 5 (Math: Hard, 25%; Physics: Hard, 25%; Chemistry: Medium, 20%; Biology: Medium, 20%; English: Easy, 10%), Available Time = 30 h/week, Weeks = 2

\\[ W_{\text{Math}} = 2 \cdot 0.25 \cdot 1.2 = 0.6, \quad W_{\text{Physics}} = 2 \cdot 0.25 \cdot 1.2 = 0.6, \quad W_{\text{Chemistry}} = 1.5 \cdot 0.2 \cdot 1.2 = 0.36 \\] \\[ W_{\text{Biology}} = 1.5 \cdot 0.2 \cdot 1.2 = 0.36, \quad W_{\text{English}} = 1 \cdot 0.1 \cdot 1.2 = 0.12 \\] \\[ W_{\text{total}} = 0.6 + 0.6 + 0.36 + 0.36 + 0.12 = 2.04 \\] \\[ T_{\text{Math}} = 30 \cdot \frac{0.6}{2.04} \approx 8.82 \ \text{h/week}, \quad T_{\text{Physics}} = 8.82 \ \text{h/week}, \quad T_{\text{Chemistry}} = 30 \cdot \frac{0.36}{2.04} \approx 5.29 \ \text{h/week} \\] \\[ T_{\text{Biology}} = 5.29 \ \text{h/week}, \quad T_{\text{English}} = 30 \cdot \frac{0.12}{2.04} \approx 1.76 \ \text{h/week} \\] \\[ S = 100 \cdot \frac{30}{40} = 75 \ \% \\]

Result: Math: 8.82 h/week, Physics: 8.82 h/week, Chemistry: 5.29 h/week, Biology: 5.29 h/week, English: 1.76 h/week, Efficiency = 75%