Study sheet: SQL Queries, Dosimetry and Rational Numbers

📋 Course Outline

1. User Search Queries in SQL
2. Patient Dosimetry Calculations
3. GCD, LCM and Powers
4. Fractions and Simplification
5. Rational Number Objectives

📖 1. User Search Queries in SQL

★ Must-know

• To find users missing from the latest report, select users whose UserID is not in the report having the maximum ReportDate.

• To find currently active users, select UserID and UserName from Users where UserStatus equals 'Active'.

• To find users with a specific role, select UserID, UserName and UserRole where UserRole is in 'Administrator', 'Manager' or 'Analyst'.

Further detail

• To find users who joined in the current year, select users where YEAR(JoinDate) equals YEAR(CURDATE()).

• To find users without an assigned department, select users where DepartmentID IS NULL.

• To find users with a salary greater than 50000, select UserID, UserName and Salary where Salary > 50000.

💡 Memory Hook

Filter by report, status, role, year, department, then salary

📖 2. Patient Dosimetry Calculations

★ Must-know

• The mean dose of the whole lesion is 55.6 Gy.

📐 Formula — The dose delivered during a 4-to-7-minute session is calculated as $5.556 \times 2 = 11.11\ \text{Gy}$, so the dose per session is 11.11 Gy.

Further detail

📐 Formula — The dose of the plan by fraction is calculated as $5.556 \times 10 = 55.56\ \text{Gy}$.

• The dosimetry plan compares doses at 60% and 62% with compensation at 60% and 62%.

📖 3. GCD, LCM and Powers

🔑 Key Concepts & Definitions

• Greatest Common Divisor : obtained by taking the common prime factors with the smallest exponents
• Least Common Multiple : obtained by taking all prime factors with the largest exponents

★ Must-know

📐 Formula — The prime decompositions are $60 = 2^2 \cdot 3 \cdot 5$ and $84 = 2^2 \cdot 3 \cdot 7$.

📐 Formula — For 60 and 84, the GCD is $\operatorname{GCD}(60{,}84)=2^2\cdot3=12$.

Further detail

📐 Formula — For 60 and 84, the LCM is $\operatorname{LCM}(60{,}84)=2^2\cdot3\cdot5\cdot7=420$.

📌 For powers, $a^0=1$, $a^1=a$, and $a^{-1}=\frac{1}{a}$.

💡 Memory Hook

GCD uses common factors with the smallest exponents, whereas LCM uses all factors with the largest exponents

📖 4. Fractions and Simplification

★ Must-know

• To reduce a fraction to irreducible form, divide the numerator and denominator by their greatest common divisor.

• The fraction $20/30$ reduces to the irreducible fraction $2/3$.

Further detail

• The fraction $35/39$ is already irreducible.

• The fraction $18/24$ reduces to $3/4$.

• The fractions $33/40$ and $53/55$ are already irreducible.

📖 5. Rational Number Objectives

📝 Essential Points

• The course objectives include calculating with relative numbers using addition, subtraction, multiplication and division.

• The course objectives include solving problems involving rational numbers.

📊 Synthesis Tables

GCD and LCM comparison

Notion	Factors used	Result for 60 and 84
GCD	Common factors with smallest exponents	12
LCM	All factors with largest exponents	420