Session 5 Homework - Math Magic & Calculations

📚 What You'll Practice

This homework focuses on advanced mathematical calculations and building practical calculators. You'll work with complex expressions and real-world math problems.

Goal: Master advanced calculations and build useful mathematical tools!

📋 Instructions

Work with complex mathematical expressions
Build practical calculators for real-world problems
Use variables to store intermediate results
Format output with appropriate decimal places
Test with different input values

📐 Program 1: Area Calculator

Calculate areas of different shapes!

What it does:

Calculates the area of a rectangle, circle, and triangle using user input dimensions.

#include <stdio.h>

int main() {
    float length, width, radius, base, height;
    float rect_area, circle_area, triangle_area;
    float pi = 3.14159;
    
    printf("=== AREA CALCULATOR ===\n");
    
    // Rectangle area
    printf("Enter rectangle length: ");
    scanf("%f", &length);
    printf("Enter rectangle width: ");
    scanf("%f", &width);
    rect_area = length * width;
    
    // Circle area
    printf("Enter circle radius: ");
    scanf("%f", &radius);
    circle_area = pi * radius * radius;
    
    // Triangle area
    printf("Enter triangle base: ");
    scanf("%f", &base);
    printf("Enter triangle height: ");
    scanf("%f", &height);
    triangle_area = 0.5 * base * height;
    
    printf("\n=== CALCULATED AREAS ===\n");
    printf("Rectangle area: %.2f square units\n", rect_area);
    printf("Circle area: %.2f square units\n", circle_area);
    printf("Triangle area: %.2f square units\n", triangle_area);
    
    return 0;
}

🧪 Test Cases

Rectangle: 5x3 → Area = 15.00
Circle: radius 4 → Area = 50.27
Triangle: base 6, height 8 → Area = 24.00

🌡️ Program 2: Temperature Converter

Convert between Celsius and Fahrenheit!

What it does:

Converts temperature between Celsius and Fahrenheit using the standard conversion formulas.

#include <stdio.h>

int main() {
    float celsius, fahrenheit;
    int choice;
    
    printf("=== TEMPERATURE CONVERTER ===\n");
    printf("1. Celsius to Fahrenheit\n");
    printf("2. Fahrenheit to Celsius\n");
    printf("Enter your choice (1 or 2): ");
    scanf("%d", &choice);
    
    if (choice == 1) {
        printf("Enter temperature in Celsius: ");
        scanf("%f", &celsius);
        fahrenheit = (celsius * 9.0 / 5.0) + 32;
        printf("%.2f°C = %.2f°F\n", celsius, fahrenheit);
    } else if (choice == 2) {
        printf("Enter temperature in Fahrenheit: ");
        scanf("%f", &fahrenheit);
        celsius = (fahrenheit - 32) * 5.0 / 9.0;
        printf("%.2f°F = %.2f°C\n", fahrenheit, celsius);
    } else {
        printf("Invalid choice!\n");
    }
    
    return 0;
}

🧪 Test Cases

Choice 1, 25°C → 77.00°F
Choice 2, 86°F → 30.00°C
Choice 1, 0°C → 32.00°F

💰 Program 3: Compound Interest Calculator

Calculate compound interest for investments!

What it does:

Calculates compound interest using the formula: A = P(1 + r/n)^(nt), where P is principal, r is rate, n is compounding frequency, and t is time.

#include <stdio.h>
#include <math.h>

int main() {
    float principal, rate, time, amount, interest;
    int n; // compounding frequency per year
    
    printf("=== COMPOUND INTEREST CALCULATOR ===\n");
    
    printf("Enter principal amount: $");
    scanf("%f", &principal);
    
    printf("Enter annual interest rate (as decimal): ");
    scanf("%f", &rate);
    
    printf("Enter time in years: ");
    scanf("%f", &time);
    
    printf("Enter compounding frequency per year: ");
    scanf("%d", &n);
    
    // Calculate compound interest
    amount = principal * pow((1 + rate / n), n * time);
    interest = amount - principal;
    
    printf("\n=== CALCULATION RESULTS ===\n");
    printf("Principal: $%.2f\n", principal);
    printf("Interest Rate: %.2f%%\n", rate * 100);
    printf("Time: %.1f years\n", time);
    printf("Compounding: %d times per year\n", n);
    printf("Final Amount: $%.2f\n", amount);
    printf("Interest Earned: $%.2f\n", interest);
    
    return 0;
}

🧪 Test Cases

Principal: $1000, Rate: 0.05, Time: 2 years, Frequency: 12 → Final: $1104.94
Principal: $5000, Rate: 0.08, Time: 5 years, Frequency: 4 → Final: $7429.74

⚖️ Program 4: BMI Calculator

Calculate Body Mass Index!

What it does:

Calculates BMI using the formula: BMI = weight(kg) / height(m)² and categorizes the result.

#include <stdio.h>

int main() {
    float weight, height, bmi;
    char name[50];
    
    printf("=== BMI CALCULATOR ===\n");
    
    printf("Enter your name: ");
    scanf("%s", name);
    
    printf("Enter your weight in kg: ");
    scanf("%f", &weight);
    
    printf("Enter your height in meters: ");
    scanf("%f", &height);
    
    // Calculate BMI
    bmi = weight / (height * height);
    
    printf("\n=== BMI RESULTS ===\n");
    printf("Name: %s\n", name);
    printf("Weight: %.1f kg\n", weight);
    printf("Height: %.2f m\n", height);
    printf("BMI: %.2f\n", bmi);
    
    // BMI Categories
    printf("\n=== BMI CATEGORY ===\n");
    if (bmi < 18.5) {
        printf("Underweight (BMI < 18.5)\n");
    } else if (bmi >= 18.5 && bmi < 25) {
        printf("Normal weight (BMI 18.5-24.9)\n");
    } else if (bmi >= 25 && bmi < 30) {
        printf("Overweight (BMI 25-29.9)\n");
    } else {
        printf("Obese (BMI >= 30)\n");
    }
    
    return 0;
}

🧪 Test Cases

Weight: 70kg, Height: 1.75m → BMI: 22.86 (Normal weight)
Weight: 60kg, Height: 1.60m → BMI: 23.44 (Normal weight)
Weight: 90kg, Height: 1.80m → BMI: 27.78 (Overweight)

🔬 Program 5: Mathematical Constants and Functions

Work with mathematical constants and basic functions!

What it does:

Demonstrates mathematical constants and basic mathematical operations using predefined values.

#include <stdio.h>
#include <math.h>

int main() {
    float radius = 5.0;
    float pi = 3.14159;
    float area, circumference;
    float base = 4.0;
    float height = 3.0;
    float triangle_area;
    
    printf("=== MATHEMATICAL CALCULATIONS ===\n");
    
    // Circle calculations
    area = pi * radius * radius;
    circumference = 2 * pi * radius;
    
    printf("Circle with radius %.1f:\n", radius);
    printf("Area: %.2f square units\n", area);
    printf("Circumference: %.2f units\n", circumference);
    
    // Triangle calculations
    triangle_area = 0.5 * base * height;
    
    printf("\nTriangle with base %.1f and height %.1f:\n", base, height);
    printf("Area: %.2f square units\n", triangle_area);
    
    // Square calculations
    float side = 6.0;
    float square_area = side * side;
    float square_perimeter = 4 * side;
    
    printf("\nSquare with side %.1f:\n", side);
    printf("Area: %.2f square units\n", square_area);
    printf("Perimeter: %.2f units\n", square_perimeter);
    
    return 0;
}

🧪 Expected Output

Circle: radius 5.0 → Area: 78.54, Circumference: 31.42
Triangle: base 4.0, height 3.0 → Area: 6.00
Square: side 6.0 → Area: 36.00, Perimeter: 24.00

🏠 Session 5 Homework

Math Magic & Calculations

📚 What You'll Practice

📋 Instructions

📐 Program 1: Area Calculator

What it does:

🧪 Test Cases

🌡️ Program 2: Temperature Converter

What it does:

🧪 Test Cases

💰 Program 3: Compound Interest Calculator

What it does:

🧪 Test Cases

⚖️ Program 4: BMI Calculator

What it does:

🧪 Test Cases

🔬 Program 5: Mathematical Constants and Functions

What it does:

🧪 Expected Output

🎯 Remember