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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.