# Download Helpful Hints for Students-Hawkes Certifications – Unit 4 A.8

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```Helpful Hints for Students-Hawkes Certifications – Unit 4
A.8: Introduction to complex numbers. Hawkes doesn’t state, for this section, that answers must be in
(a + b i ) form. 3 – i is the same as 3 + (-i). Students must be able to:
1) Simplify a square root that has a negative radicand.
2) Combine rational, irrational, and complex numbers.
3) Find the real and imaginary parts of a complex number.( the a and b)
4) Solve for x and y in an equation which contains complex numbers.
Ex. 2 x – 6i = 9 + 4yi
15.1: Solving quadratic equations, by the square root method. Make sure that both solutions are
reduced. Hawkes wants the solutions written as two separate answers.
15.2: Solving quadratic equations, by completing the square. Make sure that students can handle
problems with fractions. They should type in answers as two solutions with a comma separating them.
15.3:Solving quadratic equations, by the quadratic formula. Some problems have two parts. There are
three type of skills:
1) Write equations in standard form, identifying a, b, and c. (a>0)
2)Find the discriminant to determine two different real solutions, one
repeated real solution, or two non-real solutions.
3)Solve by the quadratic formula.
15.4: Applications of Quadratic equations. Make sure you cover:
1) Area of a rectangle
2)Cost per person and change in cost per person
3)Finding two numbers that have a certain product and difference.
4)Right Triangle(Pythagorean Theorem)
5) Work rates
6)Rate ,Time, Distance(headwind or tailwind; upstream or downstream)
7)Physics-height of a projectile; h = -16 t2 + v0 t + h0
A.10: Equations in quadratic form and higher degree equations(use factoring). Lots of problems have
negative exponents, whole exponents, and fractional exponents. Remember that solutions can be real
or non-real.
15.5: Quadratic Functions. There are two main topics of graphing and projectiles.
1) Graphing questions have five parts: find the vertex, line of symmetry, x-intercepts, two points
other than the vertex or x-intercepts, and dragging the mouse to sketch the graph.
2) Projectile model: h(t) = -16 t2 + v0 t + h0 . Find the maximum height of the object and the time it
takes to reach the maximum height.
A.9: Multiplication and Division of Complex Numbers. Must put all answers in a + bi form. Lots of
radicals are used in the problems for the a and b values.
```