AP Calculus Summer ReviewPacket # 1 : AP Calculus Summer ReviewPacket # 1 Monday, June 02, 2008
bleopold@manteno5.org
Instructions : Instructions We’re going to try this method out instead of using Moodle.
If you have any suggestions to make this easier, let me know.
Just enter your solution with your work on the slide following each problem
Save the Powerpoint as “Your Name, Packet #1, Answers”
Inequalities and Absolute Value : Inequalities and Absolute Value Solve 3 < | X + 2 |
Solve x > 1/x
The revenue for selling x units of a product is R = 115.95(x) and the cost of producing x units is C = 95(x) + 750. To make a positive profit, R must be greater than C. What values of x will the will product return a profit?
Solutions : Solutions 3 < | X + 2 |
Really 2 problems:
Solutions : Solutions
Solutions : Solutions R = 115.95(x)
C = 95(x) + 750
For a profit, R > C
115.95(x) > 95(x) + 750
20.95(x) > 750
X >35.79 ~ 36 units
More Review Stuff… : More Review Stuff… 4.) Write the equation of the circle.
Center: (-4,3)
Radius: 5/8
5.) Find x so that the distance between the points is 5. (2,-1), (x,2)
Solutions for #4 and #5 : Solutions for #4 and #5 Equation for a circle: (x-h)^2 + (y-k)^2 = R^2 where (h,k) is the center and R is the radius
(x+4)^2 + (y-3)^2 = 25/64
d^2 = (x2-x1)^2 + (y2-Y1)^2
25 = (2-x)^2 + (-1-2)^2
16 = (2-x)^2
4 = 2-x or 2-x = -4
X = -2 or X = 6
More…. : More…. 6. Find the x and y intercepts of y = x^3 – 4x
7. Find the points of intersection of the following equations:
x^2 y^2 = 25 and 2x + y = 1
8. Find an equation of a line that passes through (-3,-4) and (1,4). Put answer in slope-intercept form
Solutions for #6 : Solutions for #6 y = x^3 – 4x
For x-intercepts, set y = 0 and solve for x.
0= x^3 – 4x
Factor: x(x^2-4)= 0
X = 0,2,-2
For y intercepts, set x=0 and solve for y
y=0
Solutions for #7 : Solutions for #7 x^2 + y^2 = 25 and 2x + y = 1
Points of intersection will be x and y values found when solving these two equations simultaneously
Y=1-2x
X^2+(1-2x)^2=25
Point of Intersection: (2.627,-4.254)
Solution for #8 : Solution for #8 Find an equation of a line that passes through (-3,-4) and (1,4). Put answer in slope-intercept form
M=(4--4)/(1--3)=2
2=(y-4)/(x-1)
Y=2x+2
More again…. : More again…. 9. Write an equation that relates Fahrenheit to Celsius. Explain how knowing water boils at 212 F or 100 C and freezes at 32 F or 0 C. helps you derive the relationship.
10. Write equations of the lines through the point parallel to the given line and perpendicular to the given line.
(-3,2) Given Line: x + y = 7
Solution for #9 : Solution for #9 If this is a straight line relationship, the two variables are Celsius and Fahrenheit, therefore the slope would be (212-32)/(100-0) if F is the dependent variable and C is the independent variable. The y- intercept or F intercept would be (0,32).
F=1.8C + 32
Solution for #10 : Solution for #10 (-3,2) Given Line: x + y = 7 or y=-x + 7
Parallel lines have same slope
M=-1 so -1=(y-2)/(x--3)
Y=-x-1
Perpendicular lines have slopes that are negative reciprocals
M=1 so 1=(y-2)/(x--3)
y=x+5