4. Equations, inequalities and graphs
- Syllabus
- 0606–2028–2029
- Topic
- 4
- Level
- —
4.1. Solve modulus equations
- Solve equations of the type |ax + b| = c, |ax + b| = cx + d, |ax + b| = |cx + d| and |ax^2 + bx + c| = d using algebraic or graphical methods.
- For graphical solutions, draw an accurate graph.
- For algebraic methods, any valid method is acceptable.
4.2. Solve modulus inequalities
- Solve graphically or algebraically inequalities involving k|ax + b| and |ax^2 + bx + c|, including comparisons with constants, linear expressions and other modulus expressions.
- Use k > 0 and c >= 0 or c > 0 where specified.
- For graphical solutions, draw an accurate graph; for algebraic methods, any valid method is acceptable.
4.3. Use substitution for related equations
- Use substitution to form and solve a quadratic equation in order to solve a related equation.
- Identify the appropriate substitution in equations involving powers, logarithms or exponentials.
4.4. Sketch cubic polynomials and moduli
- Sketch graphs of cubic polynomials and their moduli when given as a product of three linear factors.
- Clearly label points of intersection with the coordinate axes.
4.5. Solve cubic inequalities graphically
- Solve graphically cubic inequalities of the form f(x) >= d, f(x) > d, f(x) <= d and f(x) < d where f(x) is a product of three linear factors and d is a constant.
Objective notes
5 learning objectivesConceptIGCSE Additional Math