Algebra 2 Intensified
Quarter 1 Exam Review
Name__________________________
Date_________________ Pd_______
12 x 6 y 5
1. Simplify
16 x 2 y 2
3y 7
a)
4
3x 4
b)
4 y3
3x 8 y 7
c)
4
3x 4
d)
4 y5
2. Simplify (5x  4) 2
a) 25x 2  40x  16
c) 25x 2  20x  16
b) 25x 2  40x  16
d) 25x 2  16
3. Simplify (3y 4 )(2 y) 3
a) 18 y 2
b) 24 y12
c) 18 y 7
d) 24 y 7
4. Simplify ( x  3)( x 2  4 x  1)
a) x 3  x 2  11x  3
c) x 3  12 x  3
b) x 3  4 x 2  11x  3
d) x 3  x 2  x  3
5. Find y in the following problem: x16  x 4 y  x 7
a) 9
b)
6. Simplify p3  4 yp2  4 y 2 p
a) p3  4 yp( y  p)
c) p( p 2  4 yp  4 y 2 p)
9
4
c) 4
b) p( p  2 y) 2
d) ( p  2 y)( p2  2 yp)
d)
9
2
7. Use long division to find (6x 3  16x 2  11x  5)  (3x  2) .
8. Use long division to find (6t 3  5t 2  2t  1)(3t  1)1
9. Use synthetic division to find (3x 4  7 x 3  2 x 2  x  1)  ( x  2) .
10. Use synthetic division to simplify
2 x3  4 x  6
x3
11. Factor completely. 12 x 2  x  6
12. Factor completely. 4ax  14ay  10bx  35by
13. Multiply (3x 2 - x +1)(2x 2 + 3x - 4)
14. Simplify (3x  2) 2
15. Name all the sets of numbers to which the following numbers belong.
a)
5
3
b) 0.651
d) -4
c) 2 17
16. Evaluate  2a  b  4b , if a = 2 and b = -6
2
0 3 1
17. Simplify (2 x y ) 
(4 x 3 y 3 )  x 5 z 7 
  5 
18. Simplify
x 1 y
 2y 
19. Simplify (2  6i )  (3  5i)
20. Simplify
 2x 
5 
 4y 
2
(5  i )  2(3  i )
3
21. Solve by completing the square.
a)
x2  2x  5  0
22. Find exact solutions to
b) 4 x  x  6
2
x 2  3x  2
23. Write y  2 x  6 x  5 in vertex form. Then, find the vertex and axis of symmetry and compare the
shape of the graph to the graph of y = x2
2
24. Write y  4 x  8 x  16 in vertex form. Then, find the vertex and axis of symmetry and compare the
shape of the graph to the graph of y = x2
2
25. Find f(-2) if f ( x)  4 x 4  3x  1
26. Find c(-2a-2) if c( x)  2 x 2  x  10
27. State the domain and range of the function f ( x)  x  5
28. State the domain and range of the function f ( x)   2 x  4  3
29. Name the property illustrated by a  (b  c)  a  (c  b)
30. Name the property illustrated by 5 x  ( x  2)  (5 x  x)  2
31. Find the value of c that makes x 2  2 x  c a perfect square.
32. Identify the number of real zeros for the function below and determine if the function has an even degree or
odd degree.
33. Identify the equation of the quadratic to the right:
34. Write the equation of the quadratic that has a vertex of (-3, -1) and goes through the point (-4, 2).
35. Write the equation of the quadratic with vertex (0, -4) and goes through the point (1, 4).
36. Simplify
2i
4i
37. Simplify
1  6i
1  3i
38. Graph the solutions for the inequality -1.2 > 1 - 0.1x on a number line.
39. Graph the solutions for the equation 1  2 x  2  5 on a number line.
40. State the domain and range of the relation. Then determine whether it’s a function.
{(2, 4),(3, 7),(5,-2)(6,-2)}
1
41. Find the x-intercept and y-intercept of y = - x - 9 .
4
42. Find the slopes of the lines parallel and perpendicular to 2x - 3y = -5 .
43. Graph the function. State the domain and range.
Find the following if it exists:
ì2x - 6, x > 3
ï 1
ï1- x, x < -5
g(x) = í 3
ï 4,
- 5 < x £ -1
ï
0£x£3
î x,
g(-5)
g(-7)
g(5)
Domain:
Range:
44. Simplify.
æ 3-12 -2 xy 4 ö
a) ç 2 2 -7 ÷
è 3 x y ø
-2
4
-6
æ 1ö æ 1ö æ 1ö
b) ç ÷ ç ÷ ç ÷
è 3ø è 3ø è 3ø
2
45. Perform the indicated operation.
a)
( 2b
3
- b 2 - 7 ) - ( -b 3 + 8b -1)
b)
( 3x - 2y )( x 2 + 3xy - 4y2 )
46. The area of a triangle is 15x 4 + 3x 3 + 4x 2 - x - 3 square meters. The length of the base of the triangle is
6x 2 - 2 meters. What is the height of the triangle?
47. If h(x) = 2x 3 - 3x + 4 find 2h(3x -1) - h(x) .
48. Write equations for the piecewise functions whose graphs are shown below. Assume that the units are 1 for
every tic marc.
a.
b.
c.
d.
49. Factor Completely. f (x) = 4x 4 - 2x 3 - 2x +1
50. Expand. (4x - 5)3
51. Solve.
a) -2 3x -1 = 6
b) 2 4x -1 = 10x + 74
c) 3- 2 x - 5 < -3
d) 4 3x -1 - 2 £ 18
52. Write the equation of the line perpendicular to x + 3y = -12 and passing through (3,-1) .
53. Graph the following. State the vertex, axis of symmetry and the domain and range.
b) y = 3 -
a) y = 2 x - 3 +1
1
x+2
2
Vertex:
Domain:
Vertex:
Domain:
Axis of symmetry:
Range:
Axis of symmetry:
Range:
d) y = - ( x - 2 ) +1
c) y = 2x 2 - 4x +1
Vertex:
Axis of symmetry:
2
Domain:
Vertex:
Domain:
Range:
Axis of symmetry:
Range: