Algebra II – Level 1



Algebra II – Level 1 Name _______________________

Unit 1: Algebra Review

Complete without a calculator

Using the complex number system, classify the following numbers. List all classifications that apply.

1. [pic] 2. [pic] 3. [pic]

4. The length of a side of an equilateral triangle is 4. Which type of number best describes the length of the altitude of the triangle?

(a) Whole Number (b) Integer

(c) Rational (d) Irrational

5. Show the following statement is false by finding a counterexample. “The product of two irrational numbers is an irrational number.”

6. Simplify: [pic] 7. Simplify: [pic]

8. Evaluate: [pic] 9. Evaluate for x = -2 and y = 5: [pic]

10. The expression [pic] represents the value of a $1000 investment that earns 10% interest per year, compounded annually for t years. Find the value of a $1000 investment at the end 2 years.

11. Solve for w: [pic] 12. Solve for x: [pic]

13. Solve for v: [pic]

14. Solve for y, graph solution and give answer in interval notation:

[pic]

15. Solve, graph and state the solution using interval notation.

[pic]

16. Solve for z, graph the solution and state the answer in interval notation.

[pic]

17. Solve for x, graph the solution and state the answer in interval notation.

[pic]

18. Give an example of a compound inequality whose solution set is [pic].

19. An isosceles trapezoid has three congruent sides. Each of these sides is 5 cm shorter than the fourth side. If the trapezoid has a perimeter of 33 cm, find the length of the longest side. Set up an algebraic equation and clearly show your work.

20. Graph: [pic] 21. Graph: [pic]

m = ______ x-int: ________

y-int: _______ y-int: ________

22. Graph x = 3. 23. Write the equations for both

lines.

f(x) = _______________

g(x) = _______________

24. Find the slope of the linear equation [pic].

25. Find the slope of the line containing the points [pic] and [pic].

26. Suppose you have $24.00 to buy napkins and plates for a class picnic. Napkins cost $3.00 per package and plates cost $4.00 per package.

(a) If x is the number of packages of napkins purchased and y is the number of packages of plates purchased, write an equation to model this situation.

(b) Find your x- and y-intercepts. Explain their meaning in the context of the application.

(c) Graph the line using your intercepts.

(d) Does every point on the line have meaning in the context of this application? Explain.

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