Download SUMMER REVIEW PACKET (for those coming into Pre

6
Pre-Calculus Review Assignment (Summer 201 )
Name: ____________________________
This assignment is made up of several types of problems from the Prerequisite chapter in Pre-Calculus. This is
not a required assignment but is recommended for you to be sure you are ready for Pre-Calculus next year.
Reviewing this material ahead of time will help us move on to NEW content earlier and will help you to be
more successful in this class.
We will use the textbook: Demana: Pre-Calculus: Graphical, Numerical, Algebraic, 7th edition
Visit www.phschool.com/home.html to access the book online.
In the web codes box, enter aze-0640 (NOTE: this is the 8th edition, but the same book we use).
Materials for this class:
3 ring binder/folder
Notebook/Looseleaf paper
1 subject Notebook
TI-83 plus or TI-84 plus graphing calculator recommended – watch for sales this summer!
Section P.1
1.) Use the distributive property to write the expanded for 2  x 2  x  .
_____________________
2.) Use the distributive property to write the factored form of 2 x3  4 x 2 .
______________________
3.) Convert from inequality to interval notation:
x  4 .
______________________
4.) Convert from interval to inequality notation:
[ -5, 8 )
______________________
In exercises 5 & 6, simplify the expression. Assume that denominators are not zero.
 uv 
2 3
5.)
2 3
vu
___________
6.)  3x 2 y 3 
2
_____________
Section P.2
7.) Given the points (-4, 3) and (5, -1).
a.) Find the distance between the points.
______________________
b.) Find the midpoint of the line segment determined by the points.
______________________
8.) Let (3, 5) be the midpoint of the line segment with endpoints (-1,1) and (a, b).
Determine a and b.
______________________
9.) Write the standard form of the equation of a circle with radius 5 and center at (-2, 7).
______________________
Section P.3
10.) Find the slope of the line through the points (-1, -2) and (4, -5).
______________________
11.) Find an equation in point-slope form for the line through the point (2, -1) and
slope m = -2/3.
______________________
In exercises 12 - 14, solve each equation algebraically.
12.) 3x – 4 = 6x + 5
______________________
13.) (5 - 2y) – 3(1 - y) = y + 1
14.)
x2 x5 1


3
2
3
______________________
______________________
In exercises 15 - 16, solve the inequality and draw a number line to graph the solution and write the
solution in interval notation.
15.) 5x + 1  2x - 4
______________________
16.)
3x  5
 -1
4
______________________
Section P.4
In exercises #17 - 22, find an equation for the line. Use the indicated form of the line.
17.) The line through (3, -2) with slope m = 4/5. (general form)
______________________
18.) The line through the points (-1, -4) and (3, 2). (slope-intercept form)
______________________
19.) The line through (-2, 4) with slope m = 0.
______________________
20.) The line 3x – 4y = 7 (slope-intercept form)
______________________
21.) The line through (2, -3) and parallel to the line 2x + 5y = 3. (general form)
______________________
22.) The line through (2, -3) and perpendicular to the line 2x + 5y = 3. (slope-intercept form)
______________________
In exercises 23 - 24, solve each equation algebraically.
23.) x(2x + 5) = 4(x + 7)
______________________
24.) 4 x  1  3
______________________
Section P.5
In exercises 25-31, solve each equation algebraically. (Quadratics that can be solved by factoring should
be solved by factoring).
25.) 16 x 2  24 x  7  0
______________________
26.) 6 x 2  7 x  3
______________________
27.) 4 x 2  20 x  25  0
______________________
28.) 9 x 2  12 x  4  0
______________________
29.) 3(3x  1)  21
2
______________________
30.) x 2  4 x  3  0
______________________
31.) Use the quadratic formula to solve the equation 3x 2  4 x  1  0
______________________
In exercises 32 & 33, use factoring to solve the equation.
32.) 3x3  19 x 2  14 x  0
______________________
33.) x3  2 x 2  4 x  8  0
______________________
Section P.6
Perform the indicated operation, and write your answer in standard form a + bi.
34.)
 2  5i   3  2i 
35.)
 4  i  3  5i 
______________________
______________________
36.) Multiply  4  7i  by its conjugate
37.)
2  6i
3i
______________________
______________________
38.) Solve the equation 4 x 2  6 x  5  x  1
_____________________
Section P.7
Solve the inequalities algebraically. Write your solutions using interval notation.
39.) 5x  2  0
______________________
40.)
x 5
6
4
______________________
Solve the inequalities graphically. Sketch the graph in the space provided. Write your solutions using
interval notation.
41.) 2 x3  2 x  5
______________________
FORMULAS
(These will not be given to you on the test – you need to know them!)
1.) Distance Formula:
2.) Midpoint Formula:
d
 x2  x1    y2  y1 
2
 x  x y  y2 
M  1 2 , 1

2 
 2
y2  y1
x2  x1
3.) Slope Formula:
m
4.) Point-Slope Form:
y  y1  m( x  x1 )
5.) Slope-intercept Form:
y  mx  b
6.) General Form:
Ax  By  C  0
7.) Quadratic Formula:
x
b  b2  4ac
2a
2