AP-PRECALCULUS EXAM REVIEW

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When you plug -x into a polynomial and it ends up identical to the original polynomial, is it even or odd?

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1

When you plug -x into a polynomial and it ends up identical to the original polynomial, is it even or odd?

even

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2

When you plug -x into a polynomial and it ends up exactly opposite to the original polynomial, is it even or odd?

odd

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3

When you plug -x into a polynomial and it ends up neither identical to the original polynomial or exactly opposite to the original polynomial, is it even or odd?

neither

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4

What does the tangent function look like? (draw it out) What is the period?

The period is pi

<p>The period is pi</p>
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5

What's the domain and range for sin inverse (arcsin)?

Domain: [-1,1] Range: [-pi/2, pi/2]

<p>Domain: [-1,1] Range: [-pi/2, pi/2]</p>
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6

What's the domain and range for cos inverse (arccos)?

Domain: [-1,1] Range: [0,pi]

<p>Domain: [-1,1] Range: [0,pi]</p>
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7

What's the domain and range for tan inverse (arctan)?

Domain: (-infinity, infinity) Range: [-pi/2, pi/2]

<p>Domain: (-infinity, infinity) Range: [-pi/2, pi/2]</p>
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8

What's the range for csc?

(-infinity, -1] U [1, infinity)

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9

What does csc look like? (draw it out) Name a few asymptotes.

Asymptotes: 0, pi, 2pi, etc.

<p>Asymptotes: 0, pi, 2pi, etc.</p>
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10

What is the range of sec?

(-infinity, -1] U [1, infinity)

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11

What does sec look like? (draw it out) Name a few asymptotes.

Asymptotes: pi/2, 3pi/2, 5pi/2, etc.

<p>Asymptotes: pi/2, 3pi/2, 5pi/2, etc.</p>
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12

What is the range if cot?

(-infinity, infinity)

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13

What does cot look like? (draw it out) Name a few asymptotes.

Asymptotes: -pi, pi, 2pi, etc.

<p>Asymptotes: -pi, pi, 2pi, etc.</p>
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14

What are the three trig identities?

sin²θ+cos²θ=1

tan²θ+1=sec²θ

cot²θ+1=csc²θ

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15

Angle Sum Identity: sin(α±β) = ?

sinαcosβ±sinβcosα

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16

Angle Sum Identity: cos(α±β) = ?

cosαcosβ∓sinαsinβ

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17

sin2θ = ?

2sinθcosθ

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18

cos2θ = ?

cos²θ-sin²θ

2cos²θ-1

1-2sin²θ

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19
<p>Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?</p>

Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?

Concave up, outputs are decreasing, ROC is neg. & incr.

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20
<p>Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?</p>

Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?

Concave up, outputs are increasing, ROC is pos. & incr.

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21
<p>Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?</p>

Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?

Concave down, outputs are increasing, ROC is pos. & decr.

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22
<p>Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?</p>

Is this concave up or down? What is happening to the outputs? Is the ROC neg. or pos., increasing or decreasing?

Concave down, outputs decr., ROC neg. & decr.

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23

cartesian to polar

r²= √x^2+y^2 tan^-1(y/x)

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24

polar to cartesian

x= r*cosθ

y=r*sinθ

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25

rectangular to complex

(a,b) => z= a+b*i

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26

polar (r, θ) to complex

z= r*cosθ + r*sinθ*i

or

z= r(cosθ+i*sinθ)

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27

Formulas for circles

r= acosθ

r=asinθ

(a= diameter)

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28

What kind of symmetry does r=acosθ have?

Polar axis sym

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29

What kind of symmetry does r=asinθ have?

Y-axis sym

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30

Formulas for roses

r = acos(nθ)

r=asin(nθ)

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31

What kind of symmetry does r = acos(nθ) have?

polar axis (x-axis) sym.

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32

What kind of symmetry does r = asin(nθ)

θ = pi/2 sym.

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33

Where is r = acos(nθ) 1st petal?

θ = 0

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34

Where is r = asin(nθ) 1st petal?

θ = pi/2n

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35

If n is odd=? petals

n petals

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36

If n is even=? petals

2n petals

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37

Limacon formulas?

r= a+bcosθ

r= a+bsinθ

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38

If |a|<|b|, what kind of limacon?

loop

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39

If |a| = |b|, what kind of limacon?

cardiod

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40

If |a| > |b|, what kind of limacon?

dimple

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41

What does 2^x look like? (exponential function behaviors)

(0,1) & (1, b)

<p>(0,1) &amp; (1, b)</p>
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42

What does ‘k’ stand for in a*b^(x-h) +k (exponential models)

k = horiz. asymptote (not applicable for everything)

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43

Residual = ?

actual-predicted

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44

If the residual value is negative?

overestimate - predicted value too high

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45

If the residual value is positive?

underestimate - predicted value too low

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46

What does log base 2 look like?

(1,0) & (b,1)

<p>(1,0) &amp; (b,1)</p>
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47

What kind of inputs & outputs do log models have?

proportional inputs, additive outputs

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48

What kind of inputs and outputs do exponential models have?

additive inputs, proportional outputs

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