LCHL10 - Solving Equations and the Factor Theorem

These lessons will involve the students in investigating and understanding:

– 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

Khan

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) = 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

Alison

Equations with linear functions in the denominator

Khan

KA4.2.1a KA4.2.1b

• f(x) = k with f(x) = ax2 + bx + c (and not necessarily factorisable) where a, b, c ∈ Q and interpret the results

Alison

Quadratic equations using the formula

Quadratic equations non unitary x squared

Quadratic equations both brackets the same sign

Quadratic equations brackets with different signs

Quadratic equations that have to be rearranged

Hidden quadratics

Khan

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

Alison

Solving simultaneous equations graphically

Simultaneous equations both negative signs

Simultaneous equations negative and positive signs

Simultaneous equations both positive

Non-linear simultaneous equations

Khan

KA4.2.2a

• one linear equation and one equation of order 2 with two unknowns and interpret the results

Khan

KA4.2.3.b

– form quadratic equations given whole number roots

Alison

From roots to functions

– use the Factor Theorem for polynomials

Alison

Factor Theorem - Part 1

Factor Theorem - Part 2