Algebra 2 Semester 2 Practice Final Summer 13

ID: A
26. Write an equation for the translation of y = −7
x
that has the asymptotes x = –2 and y = –7.
27. The values (5.1, 10) and (x, 3) are from an inverse
variation. Find the missing value and round to the
nearest hundredth.
28. Solve 27x 3 + 343 = 0. Find all complex roots.
29. Zach wrote the formula w(w – 1)(2w + 3) for the
volume of a rectangular prism he is designing, with
width w, which is always has a positive value
greater than 1. Find the product and then classify
this polynomial by degree and by number of terms.
30. Use synthetic division to find P(–4) for
P(x) = x 4 + 8x 3 + 2x 2 + 5x − 9.
31. Expand the logarithmic expression.
log 4
8k 4
32. Divide using synthetic division.
(x 4 − 12x 3 + 20x 2 + 36x − 45) ÷ (x − 3)
33. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
2e 4x + 11 = 22
34. Solve the equation.
x + 9 − 8 =−4
35. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
8e 4x + 11 = 30
36. Multiply or divide. State any restrictions on the
variables.
x 2
x − 4 ⋅ x 2 + x − 20
x 2 + 4x
37. Write the equation in logarithmic form.
4 2 = 16
38. Find the foci of the ellipse with the equation x 2
9 + y 2
49
= 1. Graph the ellipse.
39. Write an equation in standard form of an ellipse
that has a vertex at (–3, 0), a co-vertex at (0, –5),
and is centered at the origin.
40. Write an equation for the translation of
x 2 + y 2 = 49, 4 units right and 2 units down.
41. Use the Pascal’s Triangle to expand the bionomial
(d + 2b) 3 .
42. Multiply or divide. State any restrictions on the
variables.
t 2
t + 2 ⋅ t2 + t − 2
t 2 − 3t
43. Factor the expression.
x 4 − 25x 2 + 144
44. Divide and simplify.
3
120x 27
3
3x
45. Solve ln(4x − 4) = 8. Round to the nearest
thousandth.
46. Simplify.
1
3
3
⋅ 9
1
3
47. Suppose that y varies jointly with w and x and
inversely with z and y = 160 when w = 5, x = 24
and z = 6. Write the equation that models the
relationship. Then find y when w = 4, x = 10 and z
= 5.
2