Lakeshore High School



PreCalculus HonorsName___________________________Mrs. MecomSummer Assignment 2013Period: ______Date_______________931793349725SHOW EVIDENCE OF YOUR UNDERSTANDING for each problem in this packet on loose-leaf. This packet will be turned in on the first day of school and then graded. Every problem in this packet is to be completed WITHOUT A CALCULATOR unless indicated with this symbol. Do NOT purchase a graphing calculator if you do not already have one. There are online calculators to use for this assignment. We will use a TI 30 XIIS in PreCalculus(H). 1. Graph the equation 3x – 2y = 6. Label the origin and the x- and 1. ______________y-intercepts as O, P and Q, respectively. Find the area of ΔOPQ. 2. Plot A(5, 1), B(7, -1), C(1, -3), and D(-1,-1). Use the midpoint formula to show that the diagonals of quadrilateral ABCD have the same midpoint. What kind of quadrilateral is ABCD? ________________________________82550355603. Find the slope and y-intercept of the line 4x – 2y = 8.Slope: __________y-int: ___________4. Tell which of the given equations have parallel line graphs and which have perpendicular line graphs. Show evidence.A. y= 52x-8 B. -15x+6y-10=0 C. 4x+10y=15Find the value of k if the line joining (4, k) and (6,8) and the line joining (-1,4) and (0,8) are5a. parallel5a. _____________5b. perpendicular5b. ____________6. Write an equation of the perpendicular 6. ______________________bisector of the segment joining (0, 3) and (-4, 5).7. The vertices of ΔABC are A(8, 5), B(0, 1) and C(9, -2). Draw a picture to help you solve the following.4551045-19057a. Find the length and an equation of BC. 7a. Length: _______________ Equation:_____________________7b. Find an equation of the altitude from A to BC. 7b. _____________________7c. Find the point where the altitude from A intersects BC. 7c. _____________________7d. Find the length of the altitude from A to BC. 7d. _____________________7e. Find the area of ΔABC. 7e. ______________________46621701187458. Let f be a linear function such that f(1) = 5 and f(3) = 9.8a. Sketch the graph of f. 8a. 8b. Find an equation for f(x).8b. ____________________________9. Maria Correia’s new car costs $280 per month for car payments and insurance. She estimates that gas and maintenance cost $0.15 per mile.9a. Express her total monthly cost as a function of the miles driven 9a. ____________________________during the month.9b. What is the slope of the graph of the cost function?9b. ____________________________10. The last test that Mr. Clements gave was so hard that he decided to scale the 10. ____________________________grades upward. He decided to raise the lowest score of 47 to a 65 and highest score of 78 to a 90. Find a linear function that would give a fair way to convert the other test scores.11. Solve by completing the square. Give both real and imaginary roots if applicable.11. ____________________________2z2- 16z-1768=012. Solve by using the quadratic formula. Give your answers in simplest radical form.12. ____________________________Give both real and imaginary roots.4v= v-6v-413. Solve by factoring. Be sure not to lose or gain roots.13. ____________________________4x+7x-1=2x-114. Solve by whichever method seems easiest. Be sure not to lose or gain roots.14. ____________________________x+3x-3+ x-3x+3= 18-6xx2- 9For #15 a – e, provide an equation/inequality for each.15a. What is the discriminant of the equation 4x2+ 8x+k=0? 15a. ___________________________15b. For what value of k will the equation have a double root?15b. ___________________________15c. For what values of k will the equation have two real roots?15c. ___________________________15d. For what values of k will the equation have imaginary roots?15d. ___________________________15e. Name three values of k for which the given equation has rational roots.15e. ___________________________Find an equation of the quadratic function described.16. Its graph is a parabola with x-intercepts 2 and -1 and y-intercept 6.16. ____________________________17. Its graph is a parabola with vertex (4, 8) and passing through the origin.17. ____________________________-102235119380 18. A baseball player tries to hit a ball over an outfield fence that is 4 m high and 110 m from home plate. The ball is hit 1m above home plate and reaches its highest point 30 m above a point on the ground that is 60 m from home plate.18a. Make a sketch showing the path of the baseball. If home plate 18a. ___________________________is at the origin of the coordinate system, find an equation of the parabolic path of the baseball.18b. Will the ball go over the outfield fence? Explain.18b. ___________________________19. State whether the function mx= x2- 3x-4x2+ 1 is a function. 19. ____________________________Give the zeros of the function if they exist.Zeros: _________________________20. Find the values of the function fx= x3- 9x. Provide each answer in simplest exact form.20a. f-23 20a. ___________________________20b. fx320b. ___________________________20c. fx-3 20c. ___________________________21. If 4 is a zero of fx=3k3+ kx-2, find the value of k.21. ___________________________22. If a ball is thrown vertically upward at 30 m/s, then its approximate height in meters t seconds later is given by ht=30t-5t2.22a. After how many seconds does the ball hit the ground?22a. ___________________________22b. What is the domain of h?22b. ___________________________22c. How high does the ball go?22c. ___________________________3112107386523. In a rectangular piece of cardboard with perimeter 20 ft, three parallel and equally spaced creases are made, as shown. The cardboard is then folded to make a rectangular box with open square ends. 23a. Show that the volume of the box is Vx= x210-4x.23a. ___________________________23b. What is the domain of V?23b. ___________________________28656175461024. A rectangular piece of sheet metal with perimeter 50 cm is rolled into a cylinder with open ends, as shown. 24a. Express the volume of the cylinder as a function of x.24. Volume: ___________________Then give the domain of this function.Domain: _______________________Solve the given equation or inequality and graph its solution on the number line. If there is no solution, say so.25. x+24- 2-x3+ 4x-56<425. ___________________________26. 2x-4≤526. ___________________________27. Solve the given inequality 1≤x-4≤3 and 27. ___________________________graph its solution on the number line.Simplify each expression.28. a-1- b-1-1 28. ___________________________ 29. a-1b-1-129. ___________________________30. 6a-2+9a23a-230. ___________________________31. 2-12-2 + 2-3 31. ___________________________ 32. 4-54-2 + 4-332. ___________________________Simplify by using powers of the same base.33. 359427433. ___________________________Simplify.34. 16-355434. ___________________________Solve.35. 8x-3=6435. ___________________________36. 8x-3=6436. ___________________________37. 8+x-3=6437. ___________________________-12573076200 Use a calculator to check your graphs for #38-42.38a. Sketch y= 4x and its asymptotes. 38a. Graph:38b. Give equations for the asymptotes.38b. Asymptotes: ________________39. Give the domain and the range of the function. Then graph the function.39. Domain: ___________________y= x2- 4Range: ________________________Graph:Sketch each graph and label the vertex as well as two other points.40a. y= 18x2 40b. x= 18y2Sketch each graph and label two important points.41a. y= x 41b. y= -x42a. y= -x-3 42b. y= x+2- 1 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download