Designed for the Rising Pre-Calculus student
Summer Practice 2014
Name ____________________________
This summer packet emphasizes the key algebra skills required to be successful in Pre-Calculus.
You should be able to complete each problem without the aid of a calculator. The calculator
is a tool to verify your solution. Use EXACT answers and reduce all fractions to lowest terms.
There are helpful websites at the end of the exercises to assist you. This is an optional
assignment designed to keep your skills fresh over the summer break. Get a group of students
together to work these out – happy computing 
Solve the equation.
1.  52x  1  3x  4
2.
Solve the equation for y.
3. 3y  5x  13
4. 3xy  y  15
1
x  6   2 x  14
3
5
15
Solve the inequality. Then graph your solution on a number line.
5. 3 x  7  28
6. 6 x  4  22 or 5 x  8  32
7.  6  2  3 x  11
9.
8. 4a  7  13
4  8x  100
Determine whether the lines are parallel, perpendicular, or neither.
10. Line 1: 1,5 and  4,5
11. Line 1:  6,7  and  3,6
Line 2:  1,9 and 2,3
Line 2:  1,9 and 1,3
12. Write the equation of the line with the slope of
4
and the y-intercept of -5.
5
13. Write the equation of the line that passes through the points  5,3 and 5,3 .
Graph the equation using the most appropriate method. Be sure to include key points. Use the
separate graph grids on the last page of this packet for your final answer.
14. 5x  3y  12
15. 5y  3x  10
16. f x    x  2
17. f x   x  2  3
18. f x   1  x  3
19. f x  
20. f x    x 2  2
21. f x   2x  1   4
1
x  32
2
2
Solve each system of equations, and determine the number of solutions for each.
2 x  y  11
 4 x  3y  19
22. 
23. 
 6 x  3y  33
5 x  7 y  27
21 x  7 y  7
24. 
 3 x  y  2
1
 xy9
25.  3
 2 x  2 y  6

3x 2  2, if x  1
#26 – 28 Evaluate the function for the given value of x. f x   
 x  4, if x  1
26. f  2 =
27. f  1 =
28. f 0 =
1
 x  5, if x  2
29. Graph the function. f x    2
5 x  4, if x  2
Factor the trinomial. (Be sure to factor completely!)
30. 3x 2  11x  4
31. 9a 2  56a  12
32. 4 x 2  2 x  20
Use square roots or factoring to solve each equation.
33. x 2  10x  21
x2
38.
1  5
9
34. 8y 2  5y  2y 2  4
1
3
2
39. x  2 
35. 2x 2  13x  7  0
3
4


36. 2 n 2  20  17n  10n 2
37.  4x  2   20
2
40. 
1
x  12  5
4
Solve the equation by completing the square. (Must use ‘completing the square’ method!)
41. x 2  4 x  8  0
42. x 2  10x  1
43. 2x 2  5 x  7
Use the quadratic formula to solve the equation. (Must use quadratic formula!)
44. 2 x 2  3x  8  0
45. 4 x 2  2 x  3
Write the equation of the quadratic function in standard form y  ax  h   k .
2
46. Given the vertex is 2,1 and passes through the point 5,2 .
47. Given the vertex is  1,4 and passes through the point  2,6 .
Find the product of the polynomials.
2
49. x  12 2x 2  3x  5
48. 4 x  1 


50. 2 x  3 
3
Factor the polynomials completely.
51. 256x 5  81 x 3

53. x 3  27

52. x 3  5 x 2  8x  40
54. 2x 3  18x 2  5 x  45
55. 3x 5  6x 3  45 x
Solve the equation. Check for extraneous solutions.
56.
5x  1  x  4
57. x 2 / 3  16
58.
x  3  2x  7
59.
3
x 42
Perform the indicated operation. Simplify the result completely.
60.
20 x 5 x 2 y 2

y 2 10 x 3
61.
2x  1
5

2
x 4 x 2
62.
7 x 2  14x 5 x  10

x3
x5
63.
8x  1
4

x  x 6 x 2
2
4
4
x
64.
1
2
x
2x  1
5

2
x 4 x 2
66.
65.
x 2  x  20
x 3
 2
x4
x  2 x  15
67.
4
2

3x 5x
Solve each equation.
68.
70.
2
1

x 3 x 1
69.
3
2
x


x 4 x 2 x 2
3
6

x 9 x 3
2
2
Find the value of each variable. Write your answers in simplest radical form.
71
72.
73.
74.
75.
76.
3
a)
b)
c)
77. Perimeter The altitude of an
equilateral triangle is 12 centimeters.
Find the perimeter of the triangle.
Round to the nearest tenth.
78. Area The diagonal of a square is 12
inches. Find the area. Round to the
nearest tenth.
79. Bleachers A fan at a sporting event
is sitting at point A in the bleachers.
The bleacher seating has an angle of
elevation of 30° and abase length of
90 feet. Round to the nearest tenth.
80. Canyon A symmetrical canyon is
4850 feet deep. A river runs through
the canyon at its deepest point. The
angle of depression from each side
of the canyon to the river is 60°.
Round to the nearest tenth.
Find the height CD of the bleachers.
Find the height of the fan sitting at point
A from the ground.
Find the distance AB that the fan is
sitting from the base, point B.
Here are several websites that may help you:
www.algebra.com
www.algebrahelp.com
www.mathforum.org
http://www.khanacademy.org/math/algebra
http://www.khanacademy.org/math/trigonometry
a) Find the distance across the canyon.
b) Find the length of the canyon wall
from the edge to the river.
c) Is it more or less than a mile across
the canyon? (5280 feet = 1 mile)