Section 1.1
1. Determine whether the given ordered pair is a solution of the given equation
(2, -1);x2+y2-6x+8y= -15
2. Determine whether the given ordered pair is a solution of the given equation
(1, -1); x2/2 + y2/3 = -4
3. From 2000 to 2007 the total net assests of US equity mutual funds (in billions of dollars) could be approximated by
Y=331.35x3 - 1099.6x2 + 224.15x + 3962.3, where x = 0 corresponds to the year 2000. What was the lowest amount of total assets and when did this occur?
Section 1.2
1. Find the slope of the given line, if it is defined
The line through (-5, -2) and (-4,11)
2. Find the slope of the given line, if it is defined
The line through the origin and (8, -2)
3. Find an equation of the line with the given y-intercept and slope m
-3, m = 4/3
4. Find the slope m and the the y-intercept b of the line whose equation is given
4x + 2y = 0
5. On one graph sketch six straight lines that meet a single point and satisfy this condition: one line has slope 0, two lines have positive slope, two lines have negative slope, and one line has undefined slope. (PLEASE USE GRAPH PAPER)
6. Determine whether each pair of lines is parallel, perpendicular or neither
2x - 5y = 7 and 15y - 5 = 6x
7. Determine whether each pair of lines is parallel, perpendicular or neither
X - 3y = 4 and y = 1 - 3x
8. Find an equation of the line with slope m that passes through the given point. Put the answer in slope-intercept form
(-5, -2),m = 4/5
9. Find an equation of the line with slope m that passes through the given point. Put the answer in slope-intercept form
(-3, -9),m = 0
10. Find an equation of the line satisifying the given conditions
Through the origin and horizontal
11. Find an equation of the line satisfying the given conditions
Through (6,8) and perpendicular to y = 2x - 3
Section 1.3
1. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then answer the question.
Finance. The approximate number of tax returns examined by the IRS in 1996 was 1.9 million. IN 2006 it was 1.2 million. (let x = 0 correspond to 1996, and estimate the number of examined returns in 2008)
2. Business. The accompanying table shows the daily newspaper circulation (in millions)*:
YEAR CIRCULATION
1990 62.3
1995 58.2
2000 55.8
2001 55.6
2002 55.2
2003 55.2
2004 54.5
2005 53.3
a-Find a linear model for the data, with x = 0, corresponding to 1991
b- Assuming the trend continues indefinitely, estimate the circulation in 2010 and 2012
3. Finance. The accompanying table gives the median household income (in thousand of dollars) for women living without a spouse (this means that 50% of females earn more than the median and 50% earn less than that amount) for various years*:
YEAR 1980 1990 1995 1997 1998 1999
INCOME 10.4 16.9 19.7 21.0 22.1 23.8
YEAR 2000 2001 2002 2003 2004 2005
INCOME 25.7 25.7 26.4 26.6 27.0 27.2
(a) Find a linear model for these data with x = 0 corresponding to 1980
(b) Intercept the meaning of the slope
Section 1.4
1. Solve each inequality and graph each solution
-8k ≤ 32
2. Solve each inequality and graph each solution -2b>0
3. Solve each inequality and graph each solution
M - (4 + 2m) + 3 < 2m + 2
4. Solve each inequality and graph each solution 8 ≤ 3r + 1 ≤ 16
5. Solve each inequality and graph each solution
-4≤ 2k - 1 / 3 ≤ 2 Please note 2K -1 is actually over the number 3
6. Solve each inequality. Graph each solution using graph paper
|p| > 7
7. Solve each inequality. Graph each solution using graph paper
|b| > -5
8. The cost of a taxi in NYC (as of 2008) is $2.50, plus 40 cents for each 1/5 mile. How far could you travel for at least $8.50, but not more than $12.50?
9. Find all the values of x for which the given products will at least break even
The cost to produce x units of squash is C = 100x+6000, while the revenue if R=500x
10. Find all the values of x for which the given products will at least break even
C = 25,000x + 21,700,000; R = 102,500x