Interactive Coursebook (Online) of C03 Equations
C03 Equations
What’s on the Specification
| M4.15 | Set up and solve, both algebraically and graphically, simple equations including simultaneous equations involving two unknowns; this may include one linear and one quadratic equation.
Solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically. Find approximate solutions using a graph. Translate simple situations or procedures into algebraic expressions or formulae; for example, derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution. |
| MM1.4 | Simultaneous equations: analytical solution by substitution, e.g. of one linear and one quadratic equation. |
Learning Objectives
- Analyse simultaneous linear systems: Determine parameter conditions for unique, infinite, or no solutions, and link them to their geometric equivalents (intersecting, coincident, or parallel lines/planes).
- Solve linear-quadratic systems: Solve mixed systems via substitution and map algebraic results to geometric intersections (secants, tangents, or disjoint curves).
- Deconstruct absolute value equations: Solve nested equations (e.g., $||f(x)|-a|=b$ ) using critical boundary points, piecewise case analysis, and graphical sketching.
- Solve irrational equations: Resolve radical terms by isolating and squaring, or by applying polynomial substitutions like $u=\sqrt{f(x)}$.
- Enforce domain restrictions: Identify and reject extraneous solutions, ensuring derived roots satisfy the original domains for square roots $(x \geq 0)$ and absolute values $(|x| \geq 0)$.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 17 | 140 min |
| Quiz | 7 | 15 min |
| Practice A | 20 | 50 min |
| Practice B | 20 | 75 min |
| Total | 64 | approx. 5-6 hrs |
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