Calculus Summer Packet 2021-2022 - Floridachristian

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Florida Christian School High School Mathematics Department 2021-2022Name:Date:Honors Calculus and AP Calculus AB Readiness Summer ReviewThis package is intended to help you prepare you for Honors Calculus and/or AP Calculus AB coursethis next fall by reviewing prerequisite algebra and pre-calculus skills. You can use online resources toreview the learned concepts as well as your class notes from previous years. Complete each problemand include the work that led you to the answer. Unsupported answers will result in no credit. Whilemany of the exercises cover basic skills, you might encounter a few tough problems. Your work is veryimportant, as it will help you identify the concepts you need to review the most. You should be able towork on this review during the summertime, plan accordingly.This assignment is due the first day of school and it will count and your first grade of the year.Have a wonderful summer! We are looking forward to a year full of learning experiences and funinteraction that will continue to build your knowledge on mathematics. Calculus is a fascinatingcourse! Blessings.

Florida Christian School High School Mathematics Department 2021-2022The following formulas and identities will help you complete this packet. Additionally, all students are expectedto know these formulas for memory as they will be referenced throughout the course.

Florida Christian School High School Mathematics Department 2021-2022Write an equation for each line in point-slope form.11. Containing (4, –1) with a slope of 2.2. Containing the points (–6, –1) and (3, 2).53. Write an equation of a line passing through (2, 8) that is parallel to 𝑦 6 π‘₯ 1.4. Write an equation of a line passing through (6, –7) that is perpendicular to 𝑦 2π‘₯ 5.Solve each equation for x.5. π‘₯ 2 3π‘₯ 8π‘₯ 66. 𝐴 π‘Žπ‘₯ 𝑏π‘₯7.8.2π‘₯ 5π‘₯ 𝑦34 3 𝑦5π‘₯ 6 5π‘₯ 1253

Florida Christian School High School Mathematics Department 2021-20229. π‘₯ 1 3π‘₯ 110. 2 sin π‘₯ 1 011. π‘₯ 3 6π‘₯ 2 27π‘₯ 0Solve each quadratic equation by factoring.12. π‘₯ 2 4π‘₯ 12 013. 9π‘₯ 2 1 014. 4π‘₯ 2 4π‘₯ 1 0Determine whether each function is odd, even, or neither.15. 𝑓(π‘₯) π‘₯ 616. 𝑓(π‘₯) sin π‘₯

Florida Christian School High School Mathematics Department 2021-2022Find the inverse if possible. Note: remember that only functions that are one-to-one have an inverse.17. 𝑓(π‘₯) 5π‘₯ 718. 𝑓(π‘₯) 6 5π‘₯7519. 𝑔(π‘₯) π‘₯ 1Use 𝑓(π‘₯) π‘₯ 2 1, 𝑔(π‘₯) 3π‘₯, π‘Žπ‘›π‘‘ β„Ž(π‘₯) 5 π‘₯ to find each composite function.20. (𝑓 𝑔)(π‘₯) 21. (𝑔 𝑓)(π‘₯) 22. (𝑓 𝑓)(4) 23. (𝑔 β„Ž)( 4) 24. 𝑔(𝑓(π‘₯ 3 )) 25.𝑓(π‘₯ β„Ž) 𝑓(π‘₯)β„Ž

Florida Christian School High School Mathematics Department 2021-2022Solve each exponential equation, rounding answers to the nearest thousandth. Note that some equations can besolved by writing each side as the same base instead of using a logarithm.126. 5π‘₯ 527. 10π‘₯ 5 125Simplify each expression without the use of a calculator28. 𝑒 ln 429. 5 ln 𝑒 3Solve each equation using natural logarithm. Round to the nearest thousandth.30. ln(3π‘₯ 2) 2.831. 𝑒 π‘₯ 8 51Find the exact value of the expression using the Unit Circle. NO CALCULATOR.32. sin 120 33. cos34. tan11πœ‹67πœ‹4

Florida Christian School High School Mathematics Department 2021-2022Prove algebraically that the given equation is an identity.35. csc π‘₯ tan π‘₯ sec π‘₯36. sin2 𝐡 sec 𝐡 csc 𝐡 tan 𝐡37.1 cos2 π‘₯tan π‘₯ sin π‘₯ cos π‘₯Convert each inequality to interval notation (ex. x 3 becomes (3, ).38. 1 π‘₯ 1039. π‘₯ 4 π‘Žπ‘›π‘‘ π‘₯ 10Find the domain and range of each function. Write the answer in interval notation. Confirm your answer bygraphing the function in your graphing calculator.40. 𝑓(π‘₯) π‘₯ 5141. 𝑓(π‘₯) π‘₯ 742. 𝑓(π‘₯) π‘₯ 2 543. 𝑓(π‘₯) π‘₯ 3 2π‘₯ 7

Florida Christian School High School Mathematics Department 2021-2022Simplify the following expressions.π‘₯ 144.12 π‘₯ 19 π‘₯ 245. 3 π‘₯ 1Determine the vertical asymptotes for the function.146. 𝑓(π‘₯) π‘₯ 22 π‘₯47. 𝑓(π‘₯) π‘₯ 2 (1 π‘₯)Solve the following equations and inequalities.48. 4𝑑 3 12𝑑 2 8𝑑 0π‘₯ 549. 3 π‘₯ 031150. 4 6π‘₯ π‘₯

Florida Christian School High School Mathematics Department 2021-202251. 4𝑒 2π‘₯ 552. log 5 (π‘₯ 3) log 5 π‘₯ 253. Sketch the graph without the calculator.54. Use polynomial division to state the quotient and remainder of2π‘₯ 3 5π‘₯ 2 5π‘₯ 9π‘₯ 255. Review all perimeter, area, volume, surface area, and temperature formulas.

Honors Calculus and AP Calculus AB Readiness Summer Review This package is intended to help you prepare you for Honors Calculus and/or AP Calculus AB course this next fall by reviewing prerequisite algebra and pre-calculus skills. You can use online resources to review the learned concepts as well as your class notes from previous years.

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