Student: Instructor: Vicky Kauffman Assignment: Final problems Date: Course: Kauffman's Math 12 1 1. A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window shown to the right. How much wood m The area of the window is A =n ft2. (f<o~~~icl to two dcci~~i;-~l ~~l:~ces. 1, : ~ 3. I,:! ibr.~.) The amount of wood frame needed to enclose the window is 1 ft (120111111 Iil det~rr~~~l IJI~ICC> I,i 3 ;l lot n ) 2. Multiply the given polynomial using the perfect cube formula. (x- 3)3 (x- 3)3 =U 3. Factor completely the given polynomial. 4. Perform the indicated operation and simplify the result. Leave your answer in factored form. Page 1 of 35
1 Student: Instructor: Vicky Kauffman Assignment: Final probl I Date: Course: Kauffman's Math 12 1 1 ~ ime: I 1.- -- - - - --.. -- -.- - -_.. _-_ 5. Simplify the given expression. 6. Solve the equation. 7. A total of $39,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment? The amount invested in CDs is $1. The amount invested in bonds is $n. 8. Solve the equation by factoring. What is the solution set?, 'ye {[I) 21 COIIIIII:~ :>L;\>:~T;I:L ;~II\\,\. L,., ;I\ ~i~x,t.ic(i j Page 2 of 35
~ Student: Instructor: Vicky Kauffman Assignment: Final probl~ Date: Course: Kauffman's Math 12 1. -. - -. -.. - - - - - -. - - - -- - - 7 - - An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. (See the figure on the right.) If the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?......-.-...,... ~ -........ -..... - -. What is the length of a side of the square piece of sheet metal? 0 feet 10. Find the real solutions of the equation.... -........ What is the solution set? (I lsc ;I co1111na to \epal.arc ;llls\\cr\ as I I C C ~ ~ C I. I PC \ I l'tlicrc i\ no solr~~ ion. ) 11. Solve the inequality.. -----. -.... What is the solution? (1-ype your answer ill inter\fal notation. Type real entlpoint-s as integers 01. simplified fractions.)......... - -. -. -~... ~- -...... Page 3 of 35
Student: Instructor: Vicky Kauffman Assignment: Final problems Date: Course: Kauffman's Math 12 1 A motorboat maintained a constant speed of 1 1 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 5.5 hours. Use this information to find the speed of the current. The speed of the current is miles per hour............ 13. Find the distance d(p,, P2) between the points P1 and P2. (Simplil) your answl.. '17ype all exact answer, using raclicals ah nceded.)......... -. - - --. 14. Find the midpoint of the line segment joining the points P1 and P2. The midpoint is 0. (Type an ordered pair.) Page 4 of 35
- - --- ---- Student: --- -- - Instructor: Vicky Kauffman - Assignment: Final proble Date: Course: Kauffman's Math 121 15. For the given equation, list the intercepts and test for symmetry. What are the x-intercept(s)? What are the y-intercept(s)? Y = 0 (I cc ~o~ll~iiii-, IO 5C!?:lri113 irl:~rr~'pi, 11 il~crc arc' no Irrictccpr5 crrlcr \ lor \r)lic i Is the graph of the equation symmetric with respect to the x-axis? " Yes i-) 2 No Is the graph of the equation symmetric with respect to the y-axis? rl Yes (:I No Is the graph of the equation symmetric with respect to the origin? Page 5 of 3 5
Student: Instructor: Vicky Kauffman Assignment: Final proble Date: Course: Kauffman's Math 12 1 I 16. Write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). Then graph the circle. Write the standard form of the equation ofthe circle, (x- h12 + (y- k12 =r2. Write the general form of the equation of 2 2 the circle, x + y + ax + by + c = 0. Graph the circle. Page 6 of 35
Student: Instructor: Vicky Kauffman Assignment: Final p~ Date: Course: Kaufhan's Math 12 1 1 17. A circle has the equation 2 2 x +y +2x-2y-14=0. (a) Graph the circle using the center (h,k) and radius r. (b) Find the intercepts, if any, of the I " " " ' graph. -8 (a) Graph the circle using the center (h,k) and radius r. " " " ' 1 ~ E Click to @ c ;e (b) What are the x-intercept(s) and y-intercept(s), if any, of the graph? 8. Find an equation for the line with the given properties. Express the equation in slope-intercept form. Containing the points P = (- 2, - 1) and Q = (- 1,l) What is the equation of the line? Page 7 of 35
Student: Instructor: Vicky Kauffrnan Assignment: Final prc Date: Course: Kauffrnan's Math 12 1 19. A truck rental company rents a moving truck for one day by charging $23 plus $0 09 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 153 miles? 428 miles? Type the linear equation that relates the cost C, in dollars, of renting the truck to the number of x miles driven. What is the cost of renting the truck if the truck is driven 153 miles? What is the cost of renting the truck if the truck is driven 428 miles? 20. Find the equation of a line that is parallel to the line y = 3x and contains the point 21. 1 Find the equation of a line that is perpendicular to the line y = -x+ 9 and contains the 7 point ( - 5,0). Page 8 of 35
1 Student: Instructor: Vicky Kauffman Assignment: Final problems Date: Course: Kaufian's Math 12 1 filer 1. 50 I ut O ~ I 8,- 8 64 the second choice the first choice the second choice