Algebra 2 Final Exam Review Mrs. Sinisko 2009

ANSWER 1. Solve for y, and then graph the solution:

Remember to flip the inequality sign when you multiply or divide by a negative number!

Graph on a number line with an open circle between -2 and -3 (closer to -3) and shaded to the right of the open circle.

ANSWER 2. Solve for y and graph the solution:

GreatOR, so your solution is a compound “or” inequality. Isolate the absolute value and then set up a compound inequality with the absolute value greater than or equal to 7 OR less than or equal to -7.

or “Classic” or graph with a closed circle halfway between -2 and -1 shaded to the left, and a closed circle at 2 shaded to the right.

ANSWER 3. Find the slope-intercept form of an equation of a line that passes through the point (-2, -5) and has a slope of.

Start with the point-slope form….

ANSWER 4. Graph: y > -2x + 4

1.Line slopes downward (down 2, right 1) 2.Y-intercept is (0, 4) 3.Line is dashed 4.Test a point to determine which side of the line to shade

ANSWER 5.Solve the system of equations by substitution: 3x + y = 7 4x + 2y = 16

Solve the 1 st equation for y and “substitute” it into the 2 nd equation for y.

(-1, 10)

ANSWER 6.Solve the following system of equations by elimination: 12x – 3y = 36 4x + 2y = 6

Eliminate the x variables by multiplying the 2 nd equation by -3 and adding the two equations together.

ANSWER 7. Simplify:

Flip flop the negative exponents and simplify the coefficients……

ANSWER 8. Divide using synthetic division:

Divide by -2 and remember to place zeros in for any missing terms.

R -35

ANSWER 9. Factor:

You need factors of that add to b, and then use grouping.

(x – 9)(4x + 1)

ANSWER 10. Simplify:

Multiply, and then substitute -1 in for

-18

ANSWER 11. Simplify:

FOIL, and then substitute -1 in for

ANSWER 12. Solve by completing the square:

1.Get rid of “old” constant 2.Complete the square with quadratic and linear term 3. Factor, and then solve for the variable

ANSWER 13. Solve by completing the square:

ANSWER 14. Solve by the quadratic formula:

1.Get equation equal to zero 2.Use the formula:

ANSWER 15. Put the quadratic equation below in the form. Find the vertex, axis of symmetry, and the direction of the opening of the parabola.

Complete the square to put the quadratic equation in vertex form.

Vertex: (6, -9) Axis of Symmetry: x = 6 Parabola opens up (a = 1)

ANSWER 16. Graph the ellipse. Find the length of the major axis.

1.Divide by Since a is “with” y, the ellipse is vertical 4. Length of major axis = 2a

Length of Major Axis: 10 units

ANSWER 17. Simplify by multiplying:

1.Factor first! 2.Then, cancel. 3.Simplify at the end.

m

ANSWER 18. Simplify by adding:

LCD = 15abc

ANSWER 19. Solve for x:

1.Multiply through by the LCD of Don’t forget to distribute the subtraction sign!

ANSWER 20. Factor:

Ask yourself: Are there two numbers that multiply to -56 and also add to -10?

(x – 14)(x + 4)

ANSWER 21. Solve:

1.Set the equation = 0 2.What is the best method for solving? Factoring? Complete the square? Quadratic Formula? 3. Are there two factors of -6 that add to +5? 4. Finish factoring by grouping 5. Set each factor to 0 and solve to get the final answer Remember, the discriminant is:

ANSWER 22. Solve:

1.Set the equation = 0 2.Calculate discriminant to determine the best method for solving the quadratic equation 3.Solve by factoring, complete the square or quadratic equation as appropriate Remember, the discriminant is:

ANSWER 23. Simplify:

1.Multiply by the conjugate of the denominator (see below) over itself 2.Distribute on top 3.FOIL on the bottom 4.Substitute -1 for 5.Simplify

ANSWER 24. Solve for x:

1.Multiply through by the LCD of 16! 2.Use the proper method (factoring or quadratic formula) to solve the remaining quadratic equation. Are you kidding me? This problem is so EASY ….. (this is just a joke …… don ’ t get so upset ………… )

x = -12 x = 4

ANSWER 25. State: a) all the possible rational roots of the given polynomial equation, and then, b) solve the equation by finding all the roots. P. S. Use Descartes’ Rule of Signs to narrow your possible rational roots

a)Factors of 60 over factors of 1 Descartes: look for # of sign changes in f(x) and f(-x)….if there are a lot of changes, the number of roots is decreased by 2 also. b)Use synthetic division to test possibilities; you MUST find two of the roots for a 4 th degree polynomial by synthetic division, and then solve the remaining quadratic by another appropriate method.

a) b) x = 3, -5, Descartes’ Rule of Signs: Two scenarios 1 positive, 1 negative, 2 imaginary (or 0) roots 3 positive, 1 negative

The End Good Luck on your Algebra 2 Final Exam!