Algebra 2 Chap 10 Review Problems

Front 1

R1. If f(x) = -x^3 + 5x^2 + 4x -11, find f(3) by direct substitution and evaluation of the function.

Back 1

a.) Plug and chug

Front 2

R2. a.) Evaluate i^59
b.) Evaluate i^(-15)
c.) Evaluate i^(500)
d.) Write in terms of i and simplify: Sqrt (-63)
e.) Plot -5+3i on the complex plane.
f.) Write the complex conjugate of -17+3i
g.) Subtract: (8-2i) - (3-11i)
h.) Multiply: (5-7i)(2+8i)
i.) Multiply: (12+i)(12-i)
j.) Do the squaring: (12+i)^2
k.) Divide: (12+9i)/(3-4i)
l.) Find the absolute value of 11 + 4i

Back 2

R2. a.) Evaluate i^59. This is easy if you remember that i^4 is 1.
b.) Evaluate i^(-15). Same thing, but on the denominator.
c.) Evaluate i^(500). Again easy.
d.) Write in terms of i and simplify: Sqrt (-63). Take the i out from under the radical sign.
e.) Plot -5+3i on the complex plane. Real number -5 on the abscissa and imaginary number on the ordinate.
f.) Write the complex conjugate of -17+3i. Simple
g.) Subtract: (8-2i) - (3-11i). Just keep the signs straight and do it.
h.) Multiply: (5-7i)(2+8i). Use the foil method.
i.) Multiply: (12+i)(12-i). Again use foil.
j.) Do the squaring: (12+i)^2. Again.
k.) Divide: (12+9i)/(3-4i). Multiply by a clever form of 1 which is the complex conjugate of the denominator.
l.) Find the absolute value of 11 + 4i

Front 3

R3.
a.) Solve: 3x^2 + 4x + 10 = 0
b.) Write a quadratic equation with real-number coefficients if one of the solutions is 3+4i.
c) Factor over the set of complex numbers: x^2 - 4x + 5.
d.) Factor over the set of complex numbers: 25x^2+1
e.) Without actually solving the equation, find the sum of the solutions and the product of the solutions: 5x^2 + 13x + 79 = 0

Back 3

R3.
a.) Solve: 3x^2 + 4x + 10 = 0; Figure it out directly or use the quadratic equation.
b.) Write a quadratic equation with real-number coefficients if one of the solutions is 3+4i. Use the complex conj and the solution relationships.
c) Factor over the set of complex numbers: x^2 - 4x + 5. Use the quadratic equation.
d.) Factor over the set of complex numbers: 25x^2+1. Recognize the two squares.
e.) Without actually solving the equation, find the sum of the solutions and the product of the solutions: 5x^2 + 13x + 79 = 0; Use the solution relationships.

Front 4

R4.
a.) If P(x) = 5x^3 - 11x^2 + 8x + 9, find P(2) by synthetic substitution.
b.) Plot the graph of P(x) = -2x^3 -x^2 _+ 6x + 8 in the domain -3 <_ x <_ 3.
c.) Find all zeros of the function in part (b)
d.) Find the remainder if P(x) = x^3 + 17 is divided by (x+2)
e.) Sketch the graph of the quartic function with two distinct positive zeros, two distinct negative zeros, and a negative y intercept.

Back 4

R4.
a.) If P(x) = 5x^3 - 11x^2 + 8x + 9, find P(2) by synthetic substitution. Use the synthetic method to solve
b.) Plot the graph of P(x) = -2x^3 -x^2 _+ 6x + 8 in the domain -3 <_ x <_ 3. First use the method.
c.) Find all zeros of the function in part (b). Use the synthetic method to locate the zeros
d.) Find the remainder if P(x) = x^3 + 17 is divided by (x+2). Use the formula.
e.) Sketch the graph of the quartic function with two distinct positive zeros, two distinct negative zeros, and a negative y intercept. Sketch.

Front 5

R5 Look at the word problems

Back 5

R5. Look at the word problems.