Algebra II Honors
Midterm Exam Review
Chapter 1 – Tools of Algebra
Evaluate:
1. when x = -1 2.
3. 4.
Solve:
5. 6.
7. 8.
9. 10.
11. 12.
Solve and graph on a number line.
13. 14.
15. 16.
17. 18.
19. 20.
Solve for the indicated variable and state restrictions when necessary:
21. for h 22.
23. 24.
25. 26.
Proof Unit
Name the property used in each stop of simplification.
1.
2.
3. Prove:
Chapter 2 – Functions, Equations, and Graphs
Determine whether each relation is a function.
1. 2.
Find the indicated value of f(x).
3. f(x) = 3x – 7 f(-2) 4. f(x) = x2 – 2x – 4 f(4)
5. f(x) = 3x2 – x – 1 f(-8)
Sketch the graph of the following equations:
6. and 7. and
8. Find the intercepts of x-intercept:
y-intercept:
9. Rewrite in slope-intercept form: slope:
y-intercept:
10. Write an equation of the line containing (-2, -3) and (5, 8).
11. Write an equation of the line passing through (6, 2) and having a slope of 0.
12. Write an equation of the line having an undefined slope (no slope) and passing through
the point (-3, 5).
13. Write an equation of the line passing through (1, 4) and parallel to the line .
14. Write an equation of the line passing through (-2, 3) and perpendicular to
15. If x and y vary directly, find an equation that relates x and y given that .
Sketch the graph of the following absolute value equations.
16. 17.
Chapter 3 – Systems of Equations and Inequalities
1. Is (-9, 2) a solution of: 2. Solve by graphing:
Why or why not?
Solve the following system of linear equations.
3. 4. 5.
6. A total of $4,500 was invested in two funds paying 4% and 5% annual interest. The combined annual interest is $210. How much of the $4,500 is invested in each fund?
7. The measure of one of two complementary angles is 2 degrees less than three times that of each other. How large are the angles?
8. Tickets for a pre-Broadway showing of a play sold at $32 for the main floor and $22 for the balcony. If the receipts from the sale of 1600 tickets were $44,200, how many tickets were sold at each price?
9. There are 37 students in an algebra class. If there are 9 more boys than girls in the class, how many boys and girls are in the class?
Chapter 5 – Quadratic Equations and Parabolas
1. Write a system of equations that could be used to find the quadratic equation through the points
(5, -2), (1, 3), and (-2, 4).
2. Change the following from standard to vertex form by finding the vertex and using the same a value.
a) b)
3. Change each of the following from vertex form to standard form by using the FOIL method and simplifying.
a) b)
4. Write the equation of the parabola in vertex form given the following information.
a) vertex: (1, 2) point: (2, -5) b) vertex: (-2, 6) y-intercept at 12
5. Determine the vertex, axis of symmetry, and whether it opens up or down for each parabola.
a. 5a. Vertex
Axis of Symmetry
Up or down?
b. 5b. Vertex
Axis of Symmetry
Up or down?
c. 5c. Vertex
Axis of Symmetry
Up or down?
6. Graph the following parabolas.
a) b)
7. Solve the following by factoring.
a) b) c)
8. Solve each equation by finding square roots.
a) b) c)
Simplify the following.
9. 10. 11. 12.
13. 14. 15. (3i)2 16. -(2i)2
17. 3i2 18. 19. 20. -i
Perform the indicated operation.
21. (9 + 3i) + ( 7 – i) 22. (1 – 6i) – (8 + i)
23. 4i(1 + i) + 3i(6 – 7i) 24. (5 + 4i)(2 + i)
25. (1 – 10i)(3 – 2i) 26. (3 + i)2
27. Solve the following.
a) b) c)
28. Solve by completing the square.
a) b) c)
29. Re-write the following in vertex form using completing the square methods.
a) b)
30. Solve the following using the quadratic formula.
a) b)
31. What is the discriminant of the equation? 5x2 – 12x + 10 = 0
32. Find the number of solutions of the equation. 3x2 + 6x + 3 = 0
Complete the following problem by showing all work and explaining your steps.
33. The path of a baseball after it has been hit is modeled by the function , where h is the height in feet of the baseball and t is the time in seconds that the ball has traveled.
A) How many seconds does it take for the ball to reach its maximum height?
B) What is the maximum height reached by the baseball?
C) At what time does the baseball hit the ground?
Algebra II Honors Midterm Review (11/07) Page 5 of 13