SUMMER WORK FOR RISING PRECALCULUS STUDENTS

Transcription

1 SUMMER WORK FOR RISING PRECALCULUS STUDENTS Solve part I in June, part II in July, part III in August. The Barrie School 2014

2 The idea of the review is to do little work (each of these 3 packets should take about 3 4 hours of work), but spread in time so it refreshes your memory every now and then and keeps alive the knowledge you acquired during the year. Of course, you can do everything in August, but by then your memory will be stale beyond the rejuvenating power of this packet. Or you can do it all now, but by late August, when classes begin, you will have trouble to retrieve this knowledge from the dungeons of your memory. If you want to invest your time poorly, go ahead. If you solved a problem and the solution can be checked using your calculator, by all means do it. Moreover, consider the checking-with-your-calculator thing part of the problem. Work hard at resolving discrepancies. Not so hard that it mars your vacation (intelligence includes having a sense of proportion). If a problem or group thereof is still driving you crazy, you will find help at rvilarrubi@barrie.org. USE IT! Be explicit about what you did, what you got, and/or what you find puzzling. A couple of sentences. You may include a scan in your . Help may delay a day or two. Turn in the packet with your solutions the first day of classes. It will be a conversation piece the first week of class. Starred questions deal with material not covered by all the students Enjoy your vacation!

3 PART I - June Question 1 the graph below The height h(t) of a rocket launched for the physics project last year is shown in 1a. Find the rule of h(t) 1b. What equation would you set up to find when exactly the rocket s height was 50 meters? 1c. Solve it

4 Question 2 2a. Draw (if possible with compass and to the best of your ability) the circle of 2 2 equation ( x + 12) + y = 625. Explain your choices. 2b. You may have noticed that the points (-5, 24) and (12,6) seem to be on the circle or very close to it. Determine if they are on the circumference, inside the circle, or outside it. 2c. Find the points where the line x = 9 intersects the circle

5 Question 3 A helicopter approaching its target heliport is running out of fuel. At a certain moment, the height of the helicopter is 900 ft and the angle of depression of the heliport in the distance is 12. What is the (oblique) distance between the helicopter and the heliport? Use the information in the figure below and answer the question Question 4 A power walker walking on a track at constant speed crosses the 400 meter sign 40 seconds after she started walking, and the 560 meter sign 104 minutes after the start. 4a. What is her speed? 4b. Find a rule that gives her position (in meters) as a function of time (in seconds) after she started. 4c. What is her position 3 minutes (180 seconds) after she started walking?

6 Question 5 shown below The variation in value of shares of a well known company starting in Jan 2010 is Set V(t) = value of a share t months after January a. What would someone who set up the inequatlity V(t) > 500 be interested in finding? 5b. Eyeball the solution of the inequality V(t) > 500

7 2 Question 6 Graph the function f ( x) = x 8x + 7 without the aid of a calculator. Your graph should include vertex and x-intercepts. Show your work.

8 Question 7 Expand and collect like terms 2 (2x 1) + (3x + 2)(2x x 1) = 2

9 PART II July Question 1 The Tower of Pisa is 56 meters tall. Set h(t) = height in meters of a small, heavy object t seconds after it was dropped from the top of the tower. 1a. Find the rule of h(t) 1b. What equation would you set up to find when the object hit the ground? 1c. Solve it Question 2 2a. Find the equation of the circle with center (-3, 2) and radius 13. 2b. Find the points where the line x = 9 intersects the circle

10 Question 3 If you could stand 200 meters from the Statue of Liberty (your feet may get wet), the angle of elevation of its top would be meters 25 How tall is the statue? Question 4 A runner is running on a 1000 meter long track. The position of the runner (in meters) as a function of time (in seconds) is Pos( t) = t 4a. What is the meaning of the numbers 200 and 3.2? 4b. You would like to know how long it will take the runner to get to the end of the track (the 1000 meters milestone). Set up an equation whose solution will answer the question. 4c. Solve it

11 Question 5 Find a suitable rule for the each of the lines below

12 Question 6 Graph the function f ( x) = 0.4( x 3) 2. 5 without the aid of a calculator. Your graph should include vertex and x-intercepts. Use transformations of the rule to find the vertex and concavity. 2 +

13 Question 7 7a. Solve the equation x ( x 2) = ( x 3)( x + 5) 13 7b. Solve the equation ( x + 2) = 8x + 1 2

14 Question 8 Find the shaded area between the regular octagon in the figure and the circle inside it (Note: 5 is not the radius of the circle!)

15 PART III August Question 1 Find the lengths of the missing sides in the triangle below Question 2 Find the measure of the acute angles and the missing side in this triangle

16 Question 3 The graph of a function f(x) is shown below In each of the following cases, use the supplied grid to graph the indicated function tidily 3a. g(x) = f(x 4) 3b. h(x) = 2f(x) 1

17 Question 4 The circle below has center at A and passes thru the point B. 4a. Find its equation 4b. Find the rule of the tangent to the circle at B Question 5 5a. Solve the equation 3x 2 + 5x + 11= 0 5b. What does your finding in 5a say about the graph of the function 2 f ( x) = 3x + 5x + 11

18 Question 6* The pentagon is regular. The center of the circle is A. Find the shaded area.