CAMBRIDGE IGCSE™ ADDITIONAL MATHEMATICS: TEACHER’S RESOURCE

Solving simultaneous equations

After solving quadratic equations

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

Nature of roots and intersections of lines and curves

After solving quadratics and inequalities and simultaneous equations

Learning plan

Syllabus

Know the conditions for ax2 + bx + c = 0 to have: (i) two real roots, (ii) two equal roots, (iii) no real roots and the related conditions for a given line to (i) intersect a given curve, (ii) be a tangent to a given curve, (iii) not intersect a given curve.

Coursebook:

Sections 2.5 and 2.6

PowerPoints:

2.3b Roots and intersections

2.5a Worked examples 8 to 12

2.5b Connecting the nature of roots with intersections of graphs

2.6 Simultaneous equations and quadratics further practice

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 are able to complete the square for expressions of the form ax2 + bx + c where a is positive or negative and can interpret the results correctly.

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. Find the maximum or minimum value of the quadratic function f : x ↦ ax2 + bx + c by completing the square.

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.

Solve simple simultaneous equations in two unknowns, with at least one linear, by elimination or substitution.

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 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.

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.