| Equation Type | What You Must Be Able To Do |
|---|---|
| Systems of Linear Equations | Solve up to 3 variables using technology |
| Polynomial Equations | Find accurate roots (zeros) using GDC |
📌 Systems of Linear Equations (Using Technology)
A system of linear equations is a group of two or more equations that must be satisfied at the same time.
Each solution gives values that work in every equation simultaneously.
- Equations can have 2 or 3 variables.
- The solution is where all equations intersect.
- In exams, there will always be a unique solution.
Example idea:
- 2x + y = 7
- x − y = 1
- Technology quickly finds x = 2 and y = 3
🌍 Real-World Connection
Electrical circuit problems (Kirchhoff’s Laws in physics) rely on solving systems of equations to determine currents and voltages.
Electrical circuit problems (Kirchhoff’s Laws in physics) rely on solving systems of equations to determine currents and voltages.
📌 Polynomial Equations & Roots
A polynomial equation is an equation of the form:
axⁿ + bxⁿ⁻¹ + … + c = 0
The solutions are called the roots or zeros of the function. These are the x-values where the graph crosses the x-axis.
- Quadratic → up to 2 roots
- Cubic → up to 3 roots
- Higher powers → more roots
Manual solving is not required — technology is always used.
📗 GDC Tip
Use Graph → Zero or Poly-Root to find solutions directly.
Always verify roots by substituting them back into the equation.
Use Graph → Zero or Poly-Root to find solutions directly.
Always verify roots by substituting them back into the equation.
📌 Interpretation of Solutions
Solutions must always be interpreted in the context of the problem:
- Time cannot be negative
- Distance cannot be imaginary
- Population cannot be fractional in certain models
🔍 TOK Perspective
Mathematics uses words like real and imaginary differently from everyday language — how does language shape how we interpret knowledge?
Mathematics uses words like real and imaginary differently from everyday language — how does language shape how we interpret knowledge?
📌 Exam Expectations
- No specific algebraic solving method is required
- You must correctly interpret the technology output
- Answers should always be checked for context validity
🧠 Examiner Tip
Most errors occur when students accept a root without checking if it makes real-life sense.
Most errors occur when students accept a root without checking if it makes real-life sense.
📐 IA Spotlight
You can model real systems using polynomial or simultaneous equations:
You can model real systems using polynomial or simultaneous equations:
- Motion problems
- Break-even analysis
- Population models
📝 Paper 1 Strategy
Always:
Always:
- Write down what the variables represent
- Confirm the number of expected solutions
- Round only at the final stage
📌 Why This Topic Matters
- Used in physics, economics, engineering, AI models
- Allows prediction and optimization
- Forms the basis of most modelling methods