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1 Dear Student, Please find attached your summer review packet for Academic Precalculus. The problems in this packet are taken from Algebra 1 and Algebra 2 and they should be familiar to you. However, if you need review, you can use the attached websites for additional information. Internet access is available at all public libraries. The packet is due the first day of class and will be graded. To receive full credit, you will need to show all work. This assignment will count toward your first quarter grade and your first quiz of the year will be on this material. Don't wait until the last minute!! A good overall resource for math help is: If you have any questions please do not hesitate to contact the High School at: Or you can Mrs.Bastiaanseat:bastiaansem@granby.k12.ct.us. We will be checking every few days during the month of August. Graphing calculators are required and will be used almost daily in Precalculus. Please plan to have a graphing calculator for your own use in this class. We are looking forward to seeing you on the first day of school! - The Math Team at GMHS Below is a list of topics covered in the packet with formulas and helpful websites: XI + X2 YI + Y? ) Midpoint of a line segment. 2' 2- ( /Lmidpoint.htm Distance between two points. d = ~(X2 - X I )2 + (Y2 _ YI)2 Graphing Linear Equations. linear equations.html Slope of a Line: m = Y2 - YI x 2 -XI Writing Linear Equations. form.html

2 Solving Systems of Linear Equations: Simplifying Radical Expressions: radical expressions.html Complex Numbers: a + bi, the number i = ~, complex conjugate of a-bi is a-bi col algebra/col alg tut12 comprexnum. htm Quadratic functions: parabolas, vertex, axis of symmetry Solve by factoring Solve by completing the squarehttp:// Solve using the quadratic formulahttp:// Discriminant and nature of the rootshttp:// Graphing Parabolas, find the vertex, axis of symmetryhttp:// quads/not vertex form/graph quads n ot vertex form.html of symmetry of a parabola.html

3 PreCalculus Pre-calculus Summer Review Name _ Date _ Show all work in packet. Packet is due the first day of class. Find the distance. 1. Find the length of the segment with endpoints (-8, -3) and (-3, -8). Find the midpoint. 2. A segment has endpoints (6,0) and (0, -8). What is the midpoint of the segment? Graph Y=-Jx-7 2x + 7y = 21

4 Page 2 Find the slope. 5. (4,3) (5, -2) Write the equation of the line in slope/intercept form. 6. slope = 7, contains point (-2,0) Write the equation of the line in standard form. 7. passes through (1,6) and (-2, -9) 8. Write the equation of the vertical line through (-5,9). 9. Write the equation of the horizontal line through (-8, -3). 10. What is the slope of all lines parallel to y = 5x - 2? 11. What is the slope of all lines perpendicular to y = - ~x?

5 Page 3 Solve by any method x+3y= -15 X: +y = lox - Y = 2 9x + y = An artist spends $80 on brushes and paint. For canvas and frames, she has to spend an additional $20 per painting. Write an equation and draw a graph which shows the relationship between the artist's total expenses and the number of paintings that she makes.

6 Page 4 Simplify J(121)(4) 16..J2Se J23. J J48. J J5 J O 20. J5 21. sj60 + 2JI35 Express in terms of i. 22. J-40

7 Page 5 Simplify. 23. (2+30+( ( ( ( ( (-20( (5-30( (9-20( i 4 + i 30. Find the sum of 6 + 7i and its conjugate. 31. Find the product of -3-7i and its conjugate.

8 Page 6 Solve by factoring. 32. n 2 + 3n - 28 = y2 + 34y = 0 Solve by completing the square = a a - 85 Solve using the quadratic formula. 35. d 2 + d + 5 = 0

9 Page 7 Find the discriminant and describe the roots. 36. m m + 54 = k 2-10k + 25 = 0 Graph y = x 2-3 y = -3(x - 2)2 + 1