Algebra II Semester 2 Practice Final _18 Pages

ID: A
41. Use the Pascal’s Triangle to expand the bionomial 42. Multiply or divide. State any restrictions on the
(d + 2b) 3 .
variables.
a. d 3 − 6d 2 b + 12db 2 − 8b 3
t 2
b. d 3 + 3d 2 b + 3db 2 + b 3
c. d 3 − 3d 2 b + 3db 2 − b
t + 2 ⋅ t2 + t − 2
t 2 − 3t
3
d. d 3 + 6d 2 b + 12db 2 + 8b 3 t 2 − t
a.
t − 3 , t ≠ −2, 3
b.
c.
d.
t 2 − t
, t ≠ −2, 0, 3
t − 3
t − 1
, t ≠ −2, 0, 3
t − 3
t − 1
t − 3 , t ≠ −2, 3
43. Factor the expression.
x 4 − 25x 2 + 144
a. (x − 4)(x + 4)(x − 3)(x + 3) c. (x − 4)(x − 4)(x + 3)(x + 3)
b. (x − 4)(x − 3)(x 2 ) d. no solution
44. Divide and simplify.
3
120x 27
3
3x
3
a. 24x 26
b. 2x 8 24x 2
c. 5x 2 3
2x 8
d. 2x 8 3
5x 2
45. Solve ln(4x − 4) = 8. Round to the nearest
thousandth.
a. 2,981.958
b. 746.239
c. 2,976.958
d. 744.239
46. Simplify.
1
3
3
⋅ 9
a. 9
1
3
b.
3
3
c. 3
d. 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.
a. y = 6z
wx ; 12
b. y = 8wx
z ; 64
c. y = 6wx
z ; 48
d. y = 8z
wx ; 1
48. Multiply.
2
Ê ˆ
−5 − 3
Ë
Á
¯
˜
a. 28 + 10 3
b. 28 − 10 3
c. −13 + 5 3
d. 25 − 10 3
6