IB HL Math Year 2

Summer 2011 Math Packet for students enteringIB HL Math Year 2The problems in this packet are meant to help you review materialthat you have learned in previous math courses. The questions on theHL math exam may require the use of any math that you have everlearned, so it is important to keep your skills sharp! Show all of yourwork on a separate sheet of paper. ALL work should be completed tothe best of your ability.This packet will be due on the second day of class.You will be tested on the material during the first two weeks ofschool.Have a great summer. Make sure to get some rest! I am lookingforward to seeing you this fall.- Miss MullerStudent Name _________________________________________Previous Course Taken __________________________________* = No Calculator

Part I: Precalculus Review1. a) Ten boys are to be grouped into five tennis doubles pairs. Inhow many ways can this be done?b) The same ten boys are going to the seaside, two each toBethany, Rehoboth, Ocean City, Wildwood, and Cape May. Inhow many ways can this be done?2. Using the binomial theorem, expand5(2p 3) .3. * Find the sum of the series: k14k 1 3 .4. * Express the series using sigma notation: 3 2 7 ... 77 2 p 35. * If A = and det A = 14, find the possible values of p.4 p p6. * (a) Find a vector perpendicular to the two vectors:OP = i – 3 j + 2 k OQ = –2 i + j – k (b) Find the measure of the angle between OP and OQ to thenearest degree.7. Triangle ABC has AB = 8 cm, BC = 6 cm, and BAC ˆ 20possible area of ABC .. Find the smallest8. * 3 is a zero ofzeros of Pz. ()3 2 2P( z) z z [ k 5] z [ k 7] . Find k and hence find allPart II: Calculus Review9. * Evaluate.a.limx4x 2x 4b.limx012sin x cos x10. * Find the equation of the tangent to the curveperpendicular to the line 2yx 1.2y x 2xwhich is

2x 2x411. Without using a calculator, sketch the graph of f( x)x 2.(Find the relative extrema, concavity, x- and y-intercepts, and anyasymptotes before sketching.)12. A balloon rises at a rate of 3 m/s from a point on the ground 30 metersfrom an observer. Find the rate of change of the angle of elevation of theballoon from the observer when the balloon is 30 meters above theground.13. * Given that xcosy ycosx 1, find dydx .14. * Find the area enclosed by the curvesy2 x 7 and 2y x2 3.15. * The area between the graph of y = e x and the x-axis from x = 0to x = k (k > 0) is rotated through 360° about the x-axis. Find, interms of k and e, the volume of the solid generated.16. * Evaluate.a.dy xln( 3t ) dtdx b.0x14x2dx317. * The velocity of a car is given as vt () t 1m/s for t 0 . Given thatthe initial position of the car is 10 m, find the position of the car after 3seconds.