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NAME:______________________ For: Students entering PreCalculus Summer Review Packet The problems in this packet are designed to help you review topics that are important to your success in your next level of math. Show all your work for each problem. You may want to work with one or more people on this, but each student must submit his/her own packet. All work should be completed and ready to turn in on the first day of school. You will be held accountable for this material. HAVE FUN! 1. Simplify: a. 3 63 b. 10 ( 2 + 2) 2. The lengths of the legs of a right triangle are 3 cm and 6 cm. Find the length of the hypotenuse. 3. Multiply: a. (2x – 5)2 b. ( 3 + 2) ( 3 – 2) b. x2 - 25 c. 5x3 – 20x 6. Solve for x: a. (x – 2)2 = 9 b. 4 + 3(x – 1) = 511 c. x(5 + 3x) = 175 2 7. Simplify: a. x3 x2 (4x3)2 b. (3x)3y4 (6xy2)2 c. 2x -2 6y -3 4. Factor: a. x2 – 5x + 6 5. Complete the square: x2 – 4x = 8 8. Solve the system of equations: 2x + 5y = -11 3x – 7y = 27 9. Triangle ABC has vertices A(0, 0), B(4, 8) and C(10, 0). a. Find the coordinates of the midpoint, M of line segment AB. b. Find the slope of BC. c. Find the equation of the line that contains M and is parallel to BC. 10. Simplify the complex numbers: a. (1 – 3i) + (1 + 3i) b. (1 – 3i)(1 + 3i) c. 2 1 – 2i 11. Sketch each function and identify the domain and range. a. y = x2 b. y = x3 c. y = x Domain____________ Range _____________ Domain____________ Range _____________ Domain____________ Range _____________ Sketch: Sketch: Sketch: Use the definition of the three trigonometric ratios to complete each statement. Simplify answers. 13. sin <R = _____ cos <R = _____ 14. cos <B = ______ tan <B = ______ 15. sin<C = ________ tan<C = ________ T Y r sS S s R 30 R O t B C A 3 2 34 Set calculator to degree mode. Use a 4 place decimal. 16. sin 57° = __________ 17. cos 9° = ___________ Give answer to the nearest degree. 18. sin <A = 0.5447 <A = ___________ 19. cos<B = .0696 <B = ____________ Write a trigonometric equation and solve. Find the answer to the nearest whole number. 20. 21. 68° 42° x 12 28 22° 48° Equation: _______________________ x Equation: _________________________ x = ______________ x = _____________ 22. 23. 15 14 x° 25 x° 30 Equation: _______________________ Equation: _________________________ x = _____________ x = _____________ Draw a figure and show your work. 24. The angle of elevation from a ship to the top of a 40 meter lighthouse on the shore is 18 degrees. How far is the ship from the shore to the nearest meter? 25. Jim is flying a kite with 300 meters of kite string out. His kite string makes an angle of 64 degrees with the level ground. To the nearest meter, how high is his kite? 26. Juliet on her balcony 15 feet off the ground spots Romeo approaching on the ground level. She uses her angle measuring device and finds his position to be 3 degrees from the horizontal ( angle of depression is 3 degrees) How far away is Romeo from the base of her balcony?