Download Algebra Review 2

Accelerated Precalculus
Algebra Review #2
Name___________________
Period___Date____________
I. Solve each of the following equations for x.
1. y =
7x
3x  2
2. Y =
3  6
x4
2
3. (2x + 1)3  (x  2)3 = 0
4.  4   4  12
1x
1  x 
5.
6.
2x  6  3  x  4
3
4
1


x  x  2 x  x  6 3x  3
2
2
7. x3 + bx2  2b2x = 0
8. (2x + 1)3/2 = 5(2x + 1)1/2
9. 2(2x  3) + 5 = 7 2 x  3
10. 24  5  1
x
x
2
II. Solve each of the following inequalities for x.
1. x4  34x2 + 225  0
3.
1  2x 1

1  2x 2
5. |x + 4| > |3x|
2.
x  3x  4
0
x 9
2
2
4. x2 +
6.
4
>5
x
2
2x  15
3
x5
III. Write an absolute value inequality for each of the following:
1.
1 2 3 4 5 6 7 8 9 10
2. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
IV. Factor each of the following:
1. a3 + b3 + 3ab(a + b)
2. x6  y6
3. ax2 + (a + b)x + b
4. 64(x  a)3  x + a
5. (ax + b)1/2 
ax  b
b
7. x4 + 64 (Hint: Add and subtract 16x2)
6. (x + y)2 + (x + z)2  (z + t)2  (y + t)2
8. x4  15x2 + 9 (add and subtract a term)
3  2 x for x  1 


V. If f(x) =  x for  1  x  1  , sketch f(x), and evaluate f(3) + f(2) + f(0).
 3  2 x for x  1 


2
VI. Given that the coordinates of A = (4, 3), B = (8, 7) and C = (2, 5),
1. Write the equation of AB in standard form.
2. Find BC.
3. Write the equation of the perpendicular bisector of AC in slope-intercept form.
4. Find the area of ∆ABC.
5. Write the equation of the line that contains the median to BC.
6. Write the equation of the line that contains the altitude to BC.
7. Locate the coordinates of D if ABCD is a parallelogram.
8. If h is the length of any vertical segment that joins points on AB to points on BC,
write an expression for h in terms of x.
VII. If f(x) = 3x2 – 4x and g(x) = 4 – x:
1. Write f(g(x)).
2. Write
f(x  h)  f(x)
h
Answers:
I. 1. x =
2y  7
3y  1
3. x = −3 or x =
2. x =
3  5 3i
14
4y  21
6y
4. x = 0 or x =
7
3
5. x = 29 or x = 5
6. x = 3 or x = −7
7. x = −2b or x = b or x = 0
8. x = 2 or x = −1/2
9. x = 2 or x = 37/8
10. x = 8 or x = −3
II. 1. [−5, −3] U [3, 5]
2. (−∞, −3) U (−1, 3) (4, ∞)
3. (−∞, -½) U [ 1/6 , ∞)
4. (−∞, −2) U (−1, 0) U (0, 1) U (2, ∞)
5. (-1, 2)
6. (−∞, −6] U [0, ∞)
III. 1. |x – 6.5| > 1.5
2. |x + 1| < 4
IV. 1. (a + b)3
2. (x – y)(x2 + xy + y2)(x + y)(x2 – xy + y2)
3. (ax + b)(x + 1)
4. (x – a)(8x – 8a – 1)(8x – 8a + 1)
5.
( ax) ax  b
b(ax  b)
6. 2(x – t)(x + y + z + t)
7. (x2 + 8 + 4x)(x2 + 8 − 4x)
= (x2 + 4x + 8)(x2 – 4x + 8)
8. (x2 − 3 + 3x)(x2 − 3 − 3x)
= (x2 + 3x – 3)(x2 – 3x – 3)
V. 3 – 2(−3) + 3 + 2∙2 + 02 = 16
VI. 1. 5x – 2y = 26
2.
102  22  2 26
5. 9x + y = 33
6. y = − 5x + 17
7. (14, −1) or (−6, −5) or (2, 15)
VII. 1. 3x2 – 20x + 32
9. h(x) = |2.3x – 7.6|
3. y = (3/4)x + (1/4)
8. 2x + 5y = 22
2. 6x + 3h - 4