Name: ________________________ Class: ___________________ Date: __________
Algebra II Honors--Test Review 5-6 to 5-8
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Identify the graph of the complex number 4 + 5i.
a.
c.
b.
d.
Short Answer
2. Simplify
−48 using the imaginary number i.
Write the number in the form a + bi.
3.
−4 + 7
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ID: A
4. Find | − 3 + 3i | .
5. Find the additive inverse of −7 − 3i.
Simplify the expression.
6. (−2 − 3i) + (6 + 6i)
7. (3 + 5i)(−5 − 6i)
Solve the equation.
8. 36x 2 + 36 = 0
9. x 2 + 12x + 36 = 100
10. Find the first three output values of the fractal-generating function f(z) = z 2 − 3 + 4i. Use z = 0 as the first
input value.
11. Find the missing value to complete the square.
x 2 + 8x + ____
2
Solve the quadratic equation by completing the square.
12. x 2 + 10x + 15 = 0
13. 3x 2 − 3x = 5
Rewrite the equation in vertex form.
14. y = x 2 − 4x − 3
15. The function P = −h 2 + 60h − 400 models the daily profit a barbershop makes from haircuts that include a
shampoo. Here P is the profit in dollars, and h is the price of a haircut with a shampoo. Write the function in
vertex form. Use the vertex form to find the price that yields the maximum daily profit and the amount of the
daily profit.
Use the Quadratic Formula to solve the equation.
16. −2x 2 + 7x + 9 = 0
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17. x 2 + 5x − 7 = 0
18. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards
greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155
square yards. The situation is modeled by the equation h 2 + 5h = 155. Use the Quadratic Formula to find the
height that will give the desired area. Round to the nearest hundredth of a yard.
19. Determine the type and number of solutions of 6x 2 − 8x − 2 = 0.
4
20. During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The
manufacturer of the machine recommends that the temperature of the machine part remain below 135°F. The
temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by
T = −0.005x 2 + 0.45x + 125.
a. Tell whether the temperature of the part will ever reach or exceed 135°F. Use the
discriminant of a quadratic equation to decide.
b.
If the machine is in operation for 90 minutes before being turned off, how many times
will the temperature of the part be 134°F?
Other
21. A data processing consultant charges clients by the hour. His weekly earnings E are modeled by the function
E = −0.2x 2 + 40x, where x is his hourly rate in dollars. Can he earn $2500 in a single week? Explain.
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ID: A
Algebra II Honors--Test Review 5-6 to 5-8
Answer Section
MULTIPLE CHOICE
1. A
SHORT ANSWER
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
4i 3
7 + 2i
3 2
7 + 3i
4 + 3i
15 − 43i
−1i, 1i
4, –16
−3 + 4i, − 10 − 20i, − 303 + 404i
16
10
−5 ±
69
6
1
±
2
14. y = (x − 2) 2 − 7
15. P = −(h − 30) 2 + 500; $30; $500
16. −1,
9
2
53
5
2
2
18. 10.2 yards
19. two real solutions
17. − ±
20.
a.
b.
yes
two times
OTHER
21. No; the discriminant of –0.2x2 + 40x – 2500 = 0 is less than 0, so there are no real solutions.
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