Additional Maths Module 1 Lesson 1

Yo students! I hope Lesson 1 had not been too boring! Ok, let us do a quick recap of the topics we had covered in Lesson 1:

1.)Quadratic Equations and Inequalities
2.)Surds and Indices
3.)Polynomials (Remainder and Factor Theorem)


Quadratic Equations and Inequalities
I am sure everyone remembers the "Discriminant" right?
Always remember that for an expression/curve/quadratic equation that is always positive, the parabola faces upwards (smiling curve) and will never cross/touch the x-axis, which means no roots (imaginary roots) Therefore...

For an expression/curve/quadratic equation that is never negative the parabola faces downwards (frowning curve) and it may either cut the x-axis at two distinct points or just touch the x-axis at one point. This means that it may have 2 distinct roots or repeated roots. Therefore ...

As for the Alpha/Beta section, things to note when solving such questions:

• Find the coefficients of the quadratic equation (a,b,c)
• Find the sum of roots.
• Find the product of roots.
  

You will be asked to find the new roots,which you will need to manipulate the equation to the original sum and product of roots. By substituiting them, you will get the new sum and product of roots. Following that always remember that you must an additional minus sign (-) for the new sum of roots for the new equation. That should solve the question. =)

Surds and Indices
Remember the law of indices on page 19 of the course book....
For surds, rationalising the denominator will be common and always remember the following:

Polynomials (Remainder and Factor Theorem)

For solving of cubic equations, do you remember how to use the equation mode in the calculator? Under Mode, choose Eqn. Choose 3. Plug in the values of a,b,c,d. Press “=” and you will get all the 3 roots. Use the first root as the factor and perform long division. From there, you will be able to factorise the quadratic equation.

Thats all for now! See you in Lesson 2!!!