Exam Correctives
Honors Algebra II
Chapter 7
problem 1: Find all the real square, cube, or
problem 9: Write in simplest form (no negative
fourth roots.
exponents).
64
a)
3
b)
169
0.125
4
c)
!16
Use absolute value symbols if needed.
3
5
!4
b) (27b !3 )3
c) (8c !6 ) 3
problem 10: Solve. Check for extraneous solutions.
problem 2: Simplify the radical expression.
a)
!2
a) (8a !6 ) 3
125x 9
b)
4
x 8y 12
c)
4
256x 8y 14
a) 6x = 24 + 12x
b) 2x = 18 ! 6x
c) 5x = 24 + 10x
problem 11: Solve.
2
problem 3: Divide and simplify. Assume
that all the variables are positive.
3
a)
108x 7y 3
3
3
b)
2
4x y
384y 2
3
c)
3y
4
243k 13
3k
a)
c)
4
x + 2 + 9 = 14 b) 2(x + 4)3 ! 5 = 3
8x + 1 = x + 2
problem 12: Find
5
f (x)
g(x)
and their domain.
a)
f (x) = x 2 + 3x ! 10, & g(x) = x ! 2
problem 4: Multiply and simplify. Assume
b)
f (x) = 7x 3 + 21x 2 , & g(x) = x + 3
that all the variables are positive.
c)
f (x) = 2x + 1, & g(x) = 2x 2 ! 7x ! 4
a)
3
2xy 2 ! 3 4x 2y 7
problem 13: Find f (g(x)) & g(f (x)) .
b) 4 2x ! 5 6xy 2
c)
4
3a 6 ! 4 162a 2
problem 5: Simplify and then rationalize the
a)
f (x) = x + 2, & g(x) = 3x 2 ! 4
b)
f (x) = 2x ! 1, & g(x) = x 2 + 1
c)
f (x) = 3x + 1, & g(x) = 2x 2 ! 2
denominator of the expression.
a)
5x 4y
2x 2y 3
3
b)
3
18y 2
162a
c)
12y
6a
problem 6: Rationalize the denominator of
the expression.
a)
2
3+ 4
b)
2
c)
2 3!4
problem 14: Find the inverse.
3
1+ 5
1! 5
problem 7: Find the perimeter of the shape
a) y = 8x 2 + 5, b) y =
!5x + 2, c) y = 2 ! x 2
problem 15: Graph the equation and its inverse
graphically.
a) y = x 2 + 5, b) y = !2x 2 + 3, c) y = !2 ! x 2
problem 16: Find f !1 , and the domain and range of
f and f !1 . Explain whether f !1 is a function.
in simplest radical form with the given sides.
a) Rectangle: w = 3 7 and l = 8 7
a) f (x) = !2 x + 5, b) f (x) =
!6x + 7, c) f (x) = 4x 2 + 5
b) Isosocleles Triangle: 4 3 5, 4 3 5, and 9 3 5
problem 17: Graph the function.
c) Quadrilateral: 2 3, 2 27,
a) y = ! x + 2 ! 1, b) y = 2 3x ! 2 + 4,
48, and 2 50
problem 8: Write the radical expression in
exponential form.
9
12y
a)
b)
7 11
3 5 6
z
xy
c)
6
c) y = ! 2x + 4 + 2
problem 18: Graph the function.
!7
a) y = 3 x ! 5 ! 1, b) y = 2 3 2x + 4 + 3,
a 4b
c) y = ! 3 x + 4 + 4