# Lyman Memorial High School. Pre-Calculus Prerequisite Packet. Name:

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1 Lyman Memorial High School Pre-Calculus Prerequisite Packet Name:

2 Dear Pre-Calculus Students, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry. These concepts need to be reviewed and practiced throughout the summer. The completion of this review packet is very important and essential for your success in Pre-Calculus. These skills are used frequently throughout this course. Honors Pre-Calculus is a rigorous and fast-paced course. There will be extensive use of graphing calculators which is required for this course. A TI-84 Plus graphing calculator is recommended. Any other type of graphing calculator will have to be approved by the teacher. For this prerequisite packet, calculators should be used only to check work. The Pre-Calculus prerequisite packet is due the first day of school. It will be graded and it will count as a test grade. Work must be shown to support all answers. Your test grade will reflect both, your effort (50%) which is based on attempting all problems and showing work for all problems, and accuracy (50%). The packet is broken into specific concepts. Some sections have worked out examples followed by problems for you to complete. Be sure to complete each numbered exercise included in this packet. Below are a few websites you may wish to visit for additional examples and support. Algebra1online: Algebra 2 online: Algebra Help: Geometry: Results from the summer prerequisite work will help guide skill and concept reinforcement lessons that will take place the first few weeks of school. Have a nice summer, Lyman Math Department

3 Part 1 Lines and Coordinate Geometry Algebra Concepts Slope-intercept form of a line Standard form of a line Point-slope form of a line ( ) Slope of a line Geometry Concepts Midpoint formula ( ) Distance formula ( ) ( ) Perpendicular bisector a perpendicular line passing through the midpoint of a segment. Altitude of a triangle a segment from a vertex perpendicular to the opposite side. 1) Find an equation of the line in slope-intercept form that passes through ( ) ( ) 2) Write the equation of the line parallel to the line in point-slope form. 3) Write the equation of the line in slope-intercept form passing through the point ( ) and perpendicular to the line 4) Find the value of if a line containing the point ( ) has a y-intercept of 7 and a slope of 5) Find the distance between the points and then find the midpoint of the segment that joins them. a) ( ) and ( ) b) ( ) and ( )

4 Part 2 Exponents & Roots Properties of Exponents Ex: Ex: ( ) Ex: ( ) ( ) Ex: ( ) Ex: ( ) Ex: ( ) Ex: Properties of nth Roots Definition of the nth root: 1) Ex: ( ) 2) Ex: 3) Ex: 4) if n is odd Ex: ( ) 5) if n is even Ex: ( ) Simplify the expression. Eliminate any negative exponents. 6) ( ) 7) ( ) 8) 9) 10) 11) ( ) ( ) 12) 13) ( ) ( )

5 Part 3 Factoring & Solving Quadratic Equations GCF Guess and check Grouping Difference of two squares Factoring Methods Sum/difference of cubes Factor completely each expression. 14) 15) 16) 17) 18) 19) 20) 21) 22) Solve the equation. 23) 24) 25)

6 Part 4 Rational Expressions Multiplying Dividing Adding Like denominators: Multiply numerators and multiply denominators Simplifying Keep the first fraction, flip the second and multiply Unlike denominators: Factor both numerator and denominator and cancel common factors. Example: Add ( ) ( ) ( )( ) ( )( ) ( )( ) Simplify the expression. 26) ( )( ) ( ) 27) Perform the indicated operation. 28) 29) 30) 31) 32)

7 Part 5 Inequalities Solve each inequality. Graph the solution. 33) 34) 35) 36) Part 6 Functions & Graphs Determine if the graph represents a function. 37) 38) 39) 40) Sketch the graph of the each function. If you need a reminder, use your graphing calculator to help remember transformations of functions. Keep in mind, you need to be able to graph functions without a graphing calculator. 41) ( ) 42) ( ) ( ) 43) ( )

8 44) ( ) 45) ( ) ( ) 46) ( ) Combining Functions & Compositions of Functions Combining Functions ( ) ( ) Ex: ( ) ( ) ( ) Ex: ( ) Let ( ) and ( ) ( ) ( ) Ex: ( ) ( ) ( ) Ex: ( ) ( ) Given two functions f and g, the composite function,, (also called the composition of f and g) is defined by ( )( ) ( ( )) Find. Identify the domain of the new function. 47) ( ) ( ) 48) ( ) ( ) 49) Given ( ) ( ) find: 50) Given ( ) ( ) a) a) find: b) b) c) c)

9 Part 7 Polynomial Functions Polynomial Division Long Division EX: Synthetic Division Quotient: Divide the polynomials using long division 51) ( ) 52) ( ) ( ) ( ) Divide the polynomials using synthetic division. 53) ( ), ( ) 54) ( ) ( ) 55) For the graph pictured at the right: a) Describe the end behavior b) Determine whether it represents an odddegree function or an even-degree function c) State the number of real zeros

10 Part 8- Right Triangles & Trigonometry For the right triangle pictured: SOHCAHTOA Pythagorean Theorem ( ) ( ) ( ) Find the value of the trig function expressed as a fraction and as decimal to the nearest hundredth. Find the value of the angle ( ) to the nearest degree. Show all work for set up of ratios and trig equations. 56) 57) = = = = = = = = Solve for the value of x. 58) 59) 60) x x x

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