Updated: 05.04.2018 Approved: L. Byre

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Welcome to AP Calculus! You are about to embark on an exciting journey as we study God through the language of his creation.

There’s a saying that goes, “Life is hard; it’s harder if you’re stupid.” This is a cute, snarky expression that illustrates that we can sometimes make life harder on ourselves than necessary. This does not apply to you. You are the best of the best, the cream of the crop. Having said that, AP Calculus is a hard course—perhaps the hardest course at Trinity. For us, the saying goes, “AP Calculus is hard; it’s harder if you’re not ready.”

You have been getting ready for this through all the hard work you’ve put in over the past several years. Now it’s time for the final lap and the finish line. To help us get to the finish line strong, we need to keep up the good work. The summer study packet is intended to help you stay focused and not do a brain-dump over the summer that will put you behind as we start the new school year.

The packet is essentially the homework and review problems from Chapter P of the textbook. Chapter P is the preparation for calculus and essentially reviews concepts that you should have learned in Algebra and Precalculus. Completion of the packet is required if you plan to do well on your first test of the year, which will be a full period test on the Chapter P material on the second day of class. Expect this to be a hard test. However, you will not be turning in anything.

IMPORTANT: I’m going to repeat the last part of that last paragraph, in case you missed it: You will not be turning anything in. But, there will be a full period test on the Chapter P material on the second day of class. Expect this to be a hard test. This test will be your first grade of the year, and will be a measure of the effort you put into practicing the Chapter P material, along with making sure you know some key algebra techniques (see below). In education language, this is called a summative assessment.

Your strategy for getting ready: pick away at the packet through the summer. Don’t try and do it all at the last minute.

In addition to the Chapter P problems, there is a fact sheet. These are your “multiplication tables” for AP Calculus. During the year, I will be giving unannounced quizzes from time to time called Lightning Quizzes. Lightning Quizzes because they can strike at any time and because they are fast: 90 seconds to write down 10 facts. The attached fact sheet has two columns: the left column is the prompt; the right column is what you will have to produce on a quiz.

These facts are trigonometric identities and basic angles. During the year, we will be adding to these facts as we learn specific calculus formulas and theorems.

Your strategy for learning these facts: review a few at a time, morning, noon, and evening. Do this just a few minutes at a time until they become as easy as 6 x 7 = 42. These are easy grade boosters if you know your facts!

Finally, there are a few algebra/precalculus topics that some past students have struggled with in AP Calculus. These are: simplifying expressions by putting things over a common denominator, simplifying expressions by rationalizing the numerator/denominator, the absolute value function, domain and range of a function, especially logarithmic functions, completing the square, and a general fluency and ease with algebraic manipulations. In many calculus problems, using calculus to set up the problem is not hard, but to finish the problem to a final solution, you need to know your algebra well. You should expect to need to use some or all of these techniques on the Chapter P test.

2018 SUMMER ASSIGNMENT

AP CALCULUS

Updated: 05.04.2018 Approved: L. Byre

Your strategy for tackling these types of problems: Practice! Find old problems from previous years that you’ve struggled with and try similar problems until you’re comfortable with solving them. Review guides and Kahn Academy can help with this.

I look forward to seeing you on the first day of school and to the awesome year of learning we will have together studying the Creator through his creation’s language. Have a great summer!

Mr. Lubenec

AP Calculus Fact Sheet

2sec (identity)x 21 tan x

2csc (identity)x 21 cot x

sin 2 (double angle)u 2sin cosu u

cos2 (double angle)u (pick one)

2 2

2

2

cos sin

2cos 1

1 2sin

u u

u

u

tan 2 (double angle)u 2

2 tan

1 tan

u

u

2sin u (power reducing) 1 cos 2

2

u

2cos u (power reducing) 1 cos 2

2

u

2tan u (power reducing) 1 cos 2

1 cos 2

u

u

sin u v sin cos cos sinu v u v

cos u v cos cos sin sinu v u v

tan u v tan tan

1 tan tan

u v

u v

sin 0 0

sin30 or sin𝜋

6

1

2

sin45 or sin𝜋

4 √2

2

sin60 or sin𝜋

3 √3

2

sin90 or sin𝜋

2 1

sin120 or sin2𝜋

3

√3

2

sin135 or sin3𝜋

4

√2

2

sin150 or sin5𝜋

6

1

2

sin180 or sin𝜋 0

sin210 or sin7𝜋

6 −

1

2

sin225 or sin5𝜋

4 −

√2

2

sin240 or sin4𝜋

3 −

√3

2

sin270 or sin3𝜋

2 −1

sin300 or sin5𝜋

3 −

√3

2

sin315 or sin7𝜋

4 −

√2

2

sin330 or sin11𝜋

6 −

1

2

sin360 or sin2𝜋 0

cos 0 1

cos 30 or cos𝜋

6 √3

2

cos 45 or cos𝜋

4 √2

2

cos 60 or cos𝜋

3

1

2

cos 90 or cos𝜋

2 0

cos 120 or cos2𝜋

3 −

1

2

cos 135 or cos3𝜋

4 −

√2

2

cos 150 or cos5𝜋

6 −

√3

2

cos 180 or cos 𝜋 −1

cos 210 or cos7𝜋

6 −

√3

2

cos 225 or cos5𝜋

4 −

√2

2

cos 240 or cos4𝜋

3 −

1

2

cos 270 or cos3𝜋

2 0

cos 300 or cos5𝜋

3

1

2

cos 315 or cos7𝜋

4

√2

2

cos 330 or cos11𝜋

6

√3

2

cos 360 or cos 2𝜋 1

tan 0 0

tan 30 or tan𝜋

6 √3

3

tan 45 or tan𝜋

4 1

tan 60 or tan𝜋

3 √3

tan 90 or tan𝜋

2 undefined, approaches ∞

tan 120 or tan2𝜋

3 −√3

tan 135 or tan3𝜋

4 −1

tan 150 or tan5𝜋

6 −

√3

3

tan 180 or tan𝜋 0

tan 210 or tan7𝜋

6

√3

3

tan 225 or tan5𝜋

4 1

tan 240 or tan4𝜋

3 √3

tan 270 or tan3𝜋

2 undefined, approaches ∞

tan 300 or tan5𝜋

3 −√3

tan 315 or tan7𝜋

4 −1

tan 330 or tan11𝜋

6 −

√3

3

tan 360 or tan 2𝜋 0

csc 0 undefined

csc 30 or csc𝜋

6 2

csc 45 or csc𝜋

4 √2

csc 60 or csc𝜋

3

2√3

3

csc 90 or csc𝜋

2 1

csc 120 or csc2𝜋

3

2√3

3

csc 135 or csc3𝜋

4 √2

csc 150 or csc5𝜋

6 2

csc 180 or csc𝜋 undefined

csc 210 or csc7𝜋

6 −2

csc 225 or csc5𝜋

4 −√2

csc 240 or csc4𝜋

3 −

2√3

3

csc 270 or csc3𝜋

2 −1

csc 300 or csc5𝜋

3 −

2√3

3

csc 315 or csc7𝜋

4 −√2

csc 330 or csc11𝜋

6 −2

csc 360 or csc2𝜋 undefined

sec 0 1

sec 30 or sec𝜋

6

2√3

3

sec 45 or sec𝜋

4 √2

sec 60 or sec𝜋

3 2

sec 90 or sec𝜋

2 undefined

sec 120 or sec2𝜋

3 −2

sec 135 or sec3𝜋

4 −√2

sec 150 or sec5𝜋

6 −

2√3

3

sec 180 or sec 𝜋 −1

sec 210 or sec7𝜋

6 −

2√3

3

sec 225 or sec5𝜋

4 −√2

sec 240 or sec4𝜋

3 −2

sec 270 or sec3𝜋

2 undefined

sec 300 or sec5𝜋

3 2

sec 315 or sec7𝜋

4 √2

sec 330 or sec11𝜋

6

2√3

3

sec 360 or sec 2𝜋 1

cot 0 undefined

cot 30 or cot𝜋

6 √3

cot 45 or cot𝜋

4 1

cot 60 or cot𝜋

3 √3

3

cot 90 or cot𝜋

2 0

cot 120 or cot2𝜋

3 −

√3

3

cot 135 or cot3𝜋

4 −1

cot 150 or cot5𝜋

6 −√3

cot 180 or cot 𝜋 undefined

cot 210 or cot7𝜋

6 √3

cot 225 or cot5𝜋

4 1

cot 240 or cot4𝜋

3

√3

3

cot 270 or cot3𝜋

2 0

cot 300 or cot5𝜋

3 −

√3

3

cot 315 or cot7𝜋

4 −1

cot 330 or cot11𝜋

6 −√3

cot 360 or cot 2𝜋 undefined