You are currently enrolled in IB Math SL for the Fall of This course will prepare you for the IB Math SL Exam in May of 2019.

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1 Welcome to IB MATH SL! You are currently enrolled in IB Math SL for the Fall of This course will prepare you for the IB Math SL Exam in May of Prior to the Fall 2018 semester, you will need to review some basic concepts that you had learned in Pre-calculus, Geometry, and Algebra. The attached packet is representative of the level of required knowledge to be successful. Since the foundations of Calculus are on the operations of functions rather than numbers, the material in the packet is related to the concept of functions. Directions: Complete this packet of review material. You may use notes or other resources to refresh your memory. Bring the completed packet with you on the first day of school. This packet will be checked for completeness. All problems should be done or well attempted. Show work on every problem. Write neatly. You will be assessed on the topics presented in this packet during the first week of school. You will be given an opportunity to ask some questions in class in the days prior to the assessment. Try not to work together with other students nor receive extensive help from a tutor. Any student enrolled in IB Math SL should be competent with the material presented in this packet. The TI-84, TI-84 Plus or TI-84 Plus CE or latest calculator is required for the course. Please review the basics of the calculator prior to the fall semester. If you do not have a manual, visit my Wiki page friendlymath.pbworks.com and its Useful links with the uploaded manuals. Initially you should be able to graph a function, create a table of values for that function, and find zeros of a function. If you have any questions over the summer you can me at yoygenblik@ctemc.org, and I will be more than happy to help you. Have a GREAT summer and I will see you in September! Mrs. Oygenblik

2 IB Math SL2 Summer Assignment Name: 1. Given:, find the following: d) f (x + 2) f (2) e) 2. Solve the inequalities. State your answer using interval notation. a) c) d) 3. Let and,. Find the following and state the domain of each. d) e) f) 4. Let,,,,,,. Evaluate: d) e) f) g) h) 2

3 5. For each of the following functions, state if they are even, odd, or neither. d) e) 6. Simplify by factoring: a) 8x 4 6x 2 2x x 1 c) ( ) 5 2 4( x 1) 3 2 ( x +1) ( x 1) 2 ( x 1) 3 ( x +1) 2 d) x 3 7x 2 4x For the following rational functions, state the equations of the vertical, horizontal, or slant asymptotes. 8. Let,, and. Express in terms of x, y, and z. 9. Solve the equation: 10. Solve the equation:. 3

4 11. A sum of $5,000 is invested at a continuously compounded interest rate of 6.3%. a) Write down an expression for the value of the investment after n full years. What will be the value of the investment at the end of five years? c) The value of the investment will exceed $10,000 after n full years. Calculate the minimum value of n. 12. The mass m kg of a radio-active substance at time t hours is given by. If the mass is reduced to 1.5 kg., how long does it take? 13. The function f is given by. Find and its domain. 4

5 14. Use the given graph of f to sketch the graph of the transformations of f. a) c) d) e) f) 5

6 15. Sketch in standard position and find EXACT values for the 6 trig functions of. d) 16. Find the values of the other 5 trigonometric functions under the given conditions. a) and and 17. Find two degree angles 18. Find two radian angles 19. Verify the given identities. Show ALL steps. a) 20. Verify the given identities. Show all steps. Hint: Use the properties of logarithms. 21. Solve the given equations on the interval. a) c) 6

7 22. Solve the given equations. Find all solutions. a) c) 23. Solve the equation for giving your answers in terms of π. 24. ******** You must also know the unit circle like you know your name!!!! ******** 25. Evaluate each expression. Give the answer in radians. d) e) f) g) h) i) j) k) l) 27. Find the following sums: a) 7

8 28. Determine an expression to represent the given sequences below. Then use Sigma Notation to write the sum of the first n terms. a) 25, 22, 19, 16,. c) 29. Find the sum of the infinite geometric series: 30. The first three terms of an arithmetic sequence are 7, 9.5, 12. What is the sum of the first 101 terms of the sequence? 31. In an arithmetic sequence, the first term is -2, the fourth term is 16 and the n th term is 11,998. Find the common difference, d, and the value of n. 32. Find the first five terms of the recursive sequence. a) a 0 = 1 a n = a n a 0 = 0 a 1 = 2 a n = a n-1 + 2a n Find the equation of line through the points (-2,5) and (1, 4) 34. Find the equation of the line through the point (1,-3) and perpendicular to the line 3x 4 y = 7. 8

9 35. An open top box is made by cutting squares of side length 2 inches from the corners of a piece of cardboard that is 20 x 25 inches and bending up the sides. Find the volume of the resulting box. 36. The volume of a cone is V = 1 3 πr2 h, where r is the radius of the circular base and h is the height of the cone. The cone is positioned with the vertex pointing downward. a) If the volume of the cone is 350 cubic centimeters, and the radius is 5 centimeters, find the height of the cone. The same cone was filled with water. If water started leaking from the cone such that the remaining water has a height of 1 cm, find the volume of the water that is remaining. 37. Represent the function as a piecewise-defined function. 38. Find all real zeros of the polynomial analytically. It may be necessary to use the Rational Root/Zero Theorem. a) x 3 7x 6 3x 3 + 4x 2 13x + 6 c) 3x 4 + 7x 3 x 2 7x Simplify a) 2 x x 2 ( )2 ( ) + x 2 2 x ( ) 1 2 x x +1 x 2 ( x +1) Rationalize the numerator a) x x 41. Write down 3 possible topics for your Math Exploration. 9