LCHL - Solving equations and the Factor Theorem
I should be able to:
Ordinary Level
– select and use suitable strategies (graphic, numeric, algebraic, mental) for finding solutions to equations of the form:
• f(x) = g(x) with f(x) = ax+b, g(x) = cx+d where a, b, c, d ∈ Q KA4.2.1a
• f(x) = g(x) with f(x)= a/(bx+c) ± q/(px+r); g(x)=e/f where a, b, c, d, e, f, p, q, r ∈ Z
• f(x) = k with f(x) = ax2 + bx + c (and not necessarily factorisable) where a, b, c ∈ Q and interpret the results KA4.2.1b
– select and use suitable strategies (graphic, numeric, algebraic, mental) for finding solutions to
• simultaneous linear equations with two unknowns and interpret the results KA4.2.2a
• one linear equation and one equation of order 2 with two unknowns (restricted to the case where either the coefficient of x or the coefficient of y is ± 1 in the linear equation) and interpret the results KA4.2.3.b
– form quadratic equations given whole number roots
Higher Level
– select and use suitable strategies (graphic, numeric, algebraic, mental) for finding solutions to equations of the form:
• f(x) = g(x) with f(x)= (ax+b)/(ex+f) ± (cx+b)/(px+q); g(x)=k where a, b, c, d, e, f, p, q ∈ Z KA4.2.1a KA4.2.1b
– use the Factor Theorem for polynomials hl.ka.4.2.2
– select and use suitable strategies (graphic, numeric, algebraic, mental) for finding solutions to
• cubic equations with at least one integer root hl.ka.4.2.2
• simultaneous linear equations with three unknowns hl.ka.4.3.3
• one linear equation and one equation of order 2 with two unknowns and interpret the results KA4.2.3.b