Download Honors Algebra II

Honors Algebra II
Mid-Term Review
Name________________
Graphing- Graph the following on graph paper
1.
2.
3.
4.
5.
y=│x+2│ -3
y = ( x – 2)2 + 4
y = ( x + 1) ( x – 1)
y= x2 + 2x + 3
The system of Inequalities:
6.
7.
y2 = 16x, identify focus and directrix
x2 = -6y, identify focus and directrix
8. f(x) =
y<x–3
x + 3y > 2
3x + 1 if x<1
-x-3 if x≥ 1
Solve each of the following over the set of complex numbers ( means you can have real and imaginary
solutions)
9.
2x2 + 5 = 11
10. 1(x – 3) 2 = 2
11. x 2 + 2 = -14
3
12. 4x2 + 12x + 9
13. x 2– 9 = 0
14. 3x2 – 13x – 10= 0
15. 2x 2+ x – 5 = 0
16. x3 – 64= 0
17. 10x4 – 9x2 - 1 = 0
18.
-2x > 6
1
19. │ 6 – x │= 5
20. │3x – 2 │ ≥ 14
Simplify
21. The lengths of a side of a triangle are consecutive integers. The longest side is x. Write an expression
to show the perimeter of the triangle.
Solve the system. You can use graphing, substitution or elimination.
22. 3x – 4y = 17
2x – y = 8
23. 3x + 8y = 3
2x – 5y = 2
24. x-9y+4z=1
-2x+9y-4z=-3
2x+y-4z=-3
25. Evaluate the function when x = 2
F(x) = 3x , if x ≤ 2
x – 1 , if x > 2
Factor the Polynomial
26. x3 – 27=0
27. 256x5 – 81x3=0
28. 9x 4– 56x2 + 12=0
29. 3x2 + 15x =42
Find the product
30. ( x2 – 2x + 1) ( x3 -3)
31.( 3x – 1) (3x + 1)
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Operations with Complex Numbers- remember i2= -1
32. ( 9 + 4i) + ( 9 – i)
33. (-5 + 3i) – ( -2 –i)
34. – i(7 + 2i)
35. i5
36. (3 + i)(3 – i)
37.
(
-3
)
2
38. Find the discriminant of 5x2 – 3x + 10. What does this value tell you about the type of solution this
quadratic has?
Simplify
39
8
40.
125
41.
9
42.
5
7
43. 3
( 2 – i)
44. (6 + i)
2i
Simplify using properties of exponents
45. (3x2 y) 5 =
9x10 y6
46. (2/3) 2 (6xy-1) 3 =
47. x4 (x-5 x3) 2 =
48. -63xy9
18x-2y3
3
49. In the function f(x) = x2 + 6x + c , what values of c would give the equation
a. Two real number solutions
b. Two imaginary solutions
c. One real number solution
Use synthetic division to find each quotient.
50. (x4 + x2 – 5x + 11) ÷ (x + 1)
51. (2x3 + x2 – 2x + 1) ÷ (x – 2)
Determine whether each function is a polynomial. If it is a polynomial, state the degree, type, leading
coefficient, and constant term.
52. f(x) = 13 – 6x
53. f(x) =
1 3
x  2x  8
3
54. f(x) = 6x  x 
2
2
x
Find all the real zeros of the polynomial function
55. f(x) = x3 -2x2 – 11x + 12
56. x4 + 5x3 + 10x2 + 20x + 24
57. Write the equation of the parabola that have a vertex of (-3, 4) and a focus of (-3, 7).
58. A polynomial function has the following characteristics:
1. The function has exactly 3 zeros at -2, 0, 1
2. The lead coefficient is positive.
Sketch a function that meets these two characteristics.
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