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CAMBRIDGE IGCSE™ ADDITIONAL MATHEMATICS: TEACHER’S RESOURCE
Nature of roots and intersections of lines and curves
After solving quadratic equations
After solving quadratics and inequalities and simultaneous equations
Learning plan
Solve simple simultaneous equations in two unknowns, with one linear, by elimination or substitution.
Coursebook: Section 2.1 PowerPoints: 2 recap a Solving two linear simultaneous equations 2.1a Solving two simultaneous equations with one linear including Worked example 1 2.1b Solving two simultaneous equations both non linear
PL E
Solving simultaneous equations
Know the conditions for Coursebook: ax2 + bx + c = 0 to have: (i) two real Sections 2.5 and 2.6 roots, (ii) two equal roots, (iii) no real roots PowerPoints: 2.3b Roots and intersections and the related conditions for a 2.5a Worked examples 8 to 12 given line to (i) intersect a given 2.5b Connecting the nature of roots curve, (ii) be a tangent to a with intersections of graphs given curve, (iii) not intersect 2.6 Simultaneous equations and a given curve. quadratics further practice
Success criteria
SA M
Syllabus learning objectives / learning intentions Solve quadratic equations for real roots and find the solution set for quadratic inequalities. Make a simple sketch of the graph of a quadratic function using any roots and the y-intercept.
Students can solve quadratic equations using an appropriate method for the problem being considered. They can use this information to make a sketch of the graph of the quadratic function. They understand how to use this skill to find the critical values needed to solve quadratic inequalities. They are also able to write the solution set for quadratic inequalities in the correct form.
Students are able to complete the square for expressions of Find the maximum or minimum value of the quadratic function f : x ↦ ax2 + bx + c the form ax2 + bx + c where a is positive or negative and can by completing the square. interpret the results correctly. Students can apply the methods of finding roots and completing the square to sketching graphs and to finding domains and ranges of quadratic functions.
Students can apply the methods of finding roots and completing the square to sketching graphs and to finding domains and ranges of quadratic functions.
Understand the relationship between y = f (x) and y = | f (x) |, where f (x) is quadratic.
Students can successfully apply the method of finding roots and sketch or draw accurately the graph of y = | ax2 + bx + c |. They can also use this to solve simple problems.
Solve simple simultaneous equations in two unknowns, with at least one linear, by elimination or substitution.
Students choose an appropriate method of solution and show the method of solution in full. They are able to understand that two lines can only intersect once and how the number of points of intersection changes when one of the equations is not linear. (Continued)
2
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