AP Calculus AB & Calculus Honors Summer …teachers.dadeschools.net/dtisdahl/2020_Calculus_Summer...AP Calculus AB & Calculus Honors Summer Assignment Ms. Sellanes The purpose of the

AP Calculus AB & Calculus Honors

Summer Assignment Ms. Sellanes

The purpose of the summer assignment is to prepare you with the necessary Pre-Calculus skills required for AP Calculus AB and Honors Calculus. Next year we will be starting off the year with Calculus and will not be reviewing any Pre-Calculus topics at the beginning of the year. Instead we will review the Pre-Calculus topics as needed.

However, to make sure you have the pre-requisites required to handle Calculus you will be given a 50-question multiple-choice Pre-Calculus test during the first/second week of school (if you are taking the AP class, you will have an additional five short answer questions). This assessment will also test your knowledge of trigonometry identities. The date of the test will be announced on the first day/week of school.

To prepare for this test, you should complete the review provided. The answers are included for you to check to see if you are answering the questions correctly. The review will not be collected. We will spend some time of the first days of school going over any questions you have on the review.

In additon to the review, complete the following:

• Memorize the unit circle (radians only) and complete the table. You will have a speed quiz on the first quadrant of the unit circle early in the 1st quarter of school followed by a speed quiz on the entire unit circle late-1st Quarter. All quiz and tests dates will be posted on teacher website site in August.

o Memorize Trigonometric Identities. See next page for list. • If you haven’t already, purchase or borrow a TI-Nspire CX CAS (*or CX II)

graphing calculator and bring it to the first day of class. You may elect to use another calculator; however ONLY the TI-inspire CX CAS series will be taught in class. Learning to use another calculator will be your own responsibility.

• Join MAST@FIU Calculus Remind for important updates over the summer. Join by clicking here or texting “@mastcalc” to 81010.

If you have any questions, please email Ms. Sellanes at [email protected] or visit the teacher website: teachers.dadeschools.net/msellanes

https://www.remind.com/join/mastcalc

mailto:[email protected]

http://teachers.dadeschools.net/msellanes/

UNIT CIRCLE

*Trig Identities: Memorize and know how to use them

MAST @ FIUCalculus (AB and Honors) Summer Assignment

Name___________________________________ Period: Date:

SHORT ANSWER.

Evaluate the exponential expression.1) (-3)-4 1)

2) -5-3 2)

Evaluate the expression without using a calculator.3) 811/4 3)

4) 274/3 4)

Simplify the exponential expression.5) x ∙ x6 5)

6) x-2

y-56)

7) (9x4)2 7)

8) -2y0 8)

9) 42x12y12

6x8y89)

10) x2y-7 10)

11) 4x4y2

z2

311)

12) xy4

x3y

-212)

Find the product.13) (x + 5)(9x2 + 7x + 4) 13)

1 MAST @ FIU Calculus Summer Assignment (Rev. 5/20/20)

Solve the problem.14) Write a polynomial in standard form that represents the volume of the open box.

x

8 - 10x

4 - 10x

14)

Factor out the greatest common factor.15) 27x4 - 9x3 + 12x2 15)

16) x2(x - 8) - (x - 8) 16)

Factor by grouping. Assume any variable exponents represent whole numbers.17) x3 - 2x2 + 3x - 6 17)

18) x3 + 9x + 5x2 + 45 18)

Factor the trinomial, or state that the trinomial is prime.19) x2 - 8x + 12 19)

20) x2 + 4x - 77 20)

21) 8x2 + 18x + 9 21)

22) 15x2 - 26x + 8 22)

23) 5x2 - 6xy - 27y2 23)

24) 12x2 + 25xy + 12y2 24)

Factor the difference of two squares.25) 64x2 - 81 25)

26) 49x2 - 121y2 26)

27) (81x4 - 16) 27)

2 MAST @ FIU Calculus Summer Assignment

Factor using the formula for the sum or difference of two cubes.28) x3 - 125 28)

29) 125x3 + 1 29)

30) 8x3 - 125 30)

Solve the problem.31) Write an expression for the area of the shaded region and express it in factored form.

2 22 2

3y2 2

2 2

3y

31)

Factor and simplify the algebraic expression.32) x7/8 - x1/8 32)

33) (x + 1)-1/5 + (x + 1)-6/5 33)

Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rationalexpression.

34) 2x + 26x2 + 16x + 10

34)

35) x2 + 14x + 49x2 + 16x + 63

35)

Add or subtract as indicated.

36) 2x2 - 3x + 2

+ 6x2 - 1

36)

37) 4xx + 1

+ 5x - 1

- 8x2 - 1

37)

Simplify the complex rational expression.

38) x8

- 1

x - 838)


39)1 - 9

x

1 + 9x

39)

40) x - x

x + 4x + 3

40)

First, write the value or values of the variable that make a denominator zero. Then solve the equation.

41) 9x

= 12x

+ 68 41)

42) 7x - 9

+ 1 = 6x - 9

42)

Solve the formula for the specified variable.

43) V = 13

Bh for h 43)

44) S = 2πrh + 2πr2 for h 44)

Solve the quadratic equation by the method of your choice.45) (2x + 7)2 = 16 45)

46) 2x2 = 3x + 5 46)

47) x2 + 8x = 7 47)


Use the graph to find the indicated function value.48) y = f(x). Find f(5).

a) Find the domain.b) Find the range.c) Intervals in which the function is increasing.d) Intervals in which the funciton is decreasing.e) Intervals in which the function is constant.f) The minimum value.g) The maximum value.

x-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

y8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

x-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

y8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

48)

Evaluate the piecewise function at the given value of the independent variable.

49) g(x) =x2 - 7x + 2

if x ≠ -2

x - 8 if x = -2

; g(-5) 49)


Graph the piecewise-defined function.

50) f(x) = -5 - x, x < 13, x ≥ 1

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

50)

Graph the function.

51) f(x) = x + 4 if -9 ≤ x < 3-8 if x = 3-x + 4 if x > 3

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

51)

Find and simplify the difference quotient f(x + h) - f(x)h

, h≠ 0 for the given function.

52) f(x) = 7x + 9 52)

53) f(x) = 3x2 53)

Use the given conditions to write an equation for the line in point-slope form.

54) Slope = 89

, passing through (4, 3) 54)

55) Passing through (-2, -6) and (-4, -7) 55)

56) Passing through (1, -7) with x-intercept = -1 56)


57) Match each graph in each set to the function (a-f)

x-5 -4 -3 -2 -1 1 2 3 4 5

y

4

3

2

1

-1

-2

-3

-4

Set 1

x-5 -4 -3 -2 -1 1 2 3 4 5

y

4

3

2

1

-1

-2

-3

-4

Set 1

x-5 -4 -3 -2 -1 1 2 3 4 5

y

4

3

2

1

-1

-2

-3

-4

Set 2

x-5 -4 -3 -2 -1 1 2 3 4 5

y

4

3

2

1

-1

-2

-3

-4

Set 2

57)

a) Absolute Value Function Set 1 Blue: ________________b) Constant Function Set 1 Green: ________________c) Cube Root Function Set 1 Black: ________________d) Exponential Function Set 1 Red: ________________e) Linear Function Set 2 Blue: ________________f) Natural Log Function Set 2 Green: ________________g) Sqaure Root Function Set 2 Black: ________________h) Quadratic Function Set 2 Red: ________________

Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the givenfunction.

58) g(x) = - 12

(x + 2)2 + 3

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

58)


Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph thegiven function.

59) g(x) = 12

x - 5 - 6

Domain: ___________ Range: ____________

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

59)

Begin by graphing the standard square root function f(x) = x . Then use transformations of this graph to graph the givenfunction. Describe how the graph of h is related to the graph of f.

60) h(x) = -x + 2 - 1

Domain: ___________ Range: ____________

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

60)

Graph the function.61) Use the graph of f(x) = ex to obtain the graph of g(x) = ex + 3.

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

61)


62) Use the graph of f(x) = ln x to obtain the graph of g(x) = 3 ln x.

Domain: ___________ Range: ____________

x-5 5

y

5

-5

x-5 5

y

5

-5

62)

Find the domain of the function.

63) f(x) = xx2 + 18

63)

64) h(x) = x - 3x3 - 81x

64)

65) f(x) = 6 - x 65)

66) xx - 6

66)

Find the domain of the logarithmic function.67) f(x) = log 4 (x + 2) 67)

68) f(x) = ln 1x + 5

68)

For the given functions f and g , find the indicated composition.

69) f(x) = 3x + 7

, g(x) = 67x

(f∘g)(x)

69)

70) f(x) = x - 24

, g(x) = 4x + 2

(g∘f)(x)

70)

Solve the problem.71) If f(x) = -2x + 6 and g(x) = 6x + 9, find g(f(x)). 71)


Find functions f and g so that h(x) = (f ∘ g)(x).72) h(x) = (6x + 6)6 72)

Find the inverse of the one-to-one function.73) f(x) = (x + 8)3 73)

74) f(x) = x + 6 74)

75) f(x) = 2x + 6 75)

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates ofthe minimum or maximum point.

76) f(x) = x2 - 2x - 7 76)

77) f(x) = x2 + 2x + 1 77)

Solve the problem.78) A developer wants to enclose a rectangular grassy lot that borders a city street for parking.

If the developer has 332 feet of fencing and does not fence the side along the street, what isthe largest area that can be enclosed?

78)

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis andturns around, at each intercept.

79) f(x) = (x + 1)(x - 3)(x - 1)2 79)

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses thex-axis or touches the x-axis and turns around, at each zero.

80) f(x) = 2(x + 1)(x + 3)4 80)

Sketch the polynomial function using the zeros, multiplicity of each zero, and end behavior.81) f(x) = x(x + 1)(x + 2)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

81)


82) f(x) = x4 - 4x2

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

82)

Find the y-intercept of the polynomial function.83) f(x) = (x + 1)(x - 4)(x - 1)2 83)

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.84) f(x) = -4x4 - 3x3 - 4x2 + 4x + 5 84)

85) f(x) = (x + 1)(x + 4)(x + 5)2 85)

Find the zeros of the polynomial function.86) f(x) = x3 + x2 - 42x 86)

87) f(x) = x3 + 3x2 - x - 3 87)

Divide using synthetic division.

88) -3x3 - 22x2 - 22x + 12x + 6

88)

89) x5 + x2 - 1x - 2

89)

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots.90) x3 + 3x2 - x - 3 = 0 90)

91) x3 - 8x2 + 14x - 4 = 0 91)


Solve the problem.92) A box with an open top is formed by cutting squares out of the corners of a rectangular

piece of cardboard and then folding up the sides. If x represents the length of the side ofthe square cut from each corner, and if the original piece of cardboard is 13 inches by 11inches, what size square must be cut if the volume of the box is to be 126 cubic inches?

92)

Use the graph of the rational function shown to complete the statement.93)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

As x→-3-, f(x)→ ?

93)

Find the vertical asymptotes, if any, of the graph of the rational function.

94) f(x) = xx2 + 8

94)

95) g(x) = x - 2x(x - 2)

95)

Find the horizontal asymptote, if any, of the graph of the rational function.

96) f(x) = 15x5x2 + 1

96)

97) g(x) = 15x2

3x2 + 197)

98) h(x) = 6x3

3x2 + 198)


Write the equation in its equivalent logarithmic form.

99)3

216 = 6 99)

Evaluate the expression without using a calculator.100) log 6 6 100)

101) log8 18

101)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluatelogarithmic expressions without using a calculator.

102) log 2x - 1x4

102)

103) logb xy3

z5103)

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whosecoefficient is 1. Where possible, evaluate logarithmic expressions.

104) 3 log b m - log b n 104)

105) 17

[5ln (x + 9) - ln x - ln (x2 - 8)] 105)

Solve the exponential equation. Express the solution set in terms of natural logarithms.

106) 5 9x = 4 106)

107) e x + 3 = 6 107)

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for thesolution.

108) e5x - 1 - 8 = 1243 108)

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmicexpressions. Give the exact answer.

109) log 2 (x + 1) = -1 109)

110) ln x + 7 = 9 110)

111) log4

(x + 2) - log4

x = 2 111)


Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of thegiven angle. Give an exact answer with a rational denominator.

112) Find sin θ.

7

4

112)

113) Find tan θ.3

10

113)

Find the exact value of the real number y.

114) y = sin-1 32

114)

115) y = arctan 1 115)

Find the intervals on which the function is continuous.116) y = 5x + 8 116)

117) y = 1(x + 3)2 + 6

117)

Find the points of discontinuity.Identify each type of discontinuity (Hole/removable or Vertical Asymptote/non-removable).

118) y = x + 1x2 - 12x + 35

118)

119) y = 5(x + 5)2 + 10

119)

120) y = 2x -4x2 - 4

120)


Answer KeyTestname: 2020_SUMMERASSIGNMENTREVIEW_VERSION4(NOLIMITS)

1) 181

2) - 1125

3) 34) 815) x7

6) y5

x2

7) 81x88) -29) 7x4y4

10) x2

y7

11) 64x12y6

z6

12) x4

y6

13) 9x3 + 52x2 + 39x + 2014) 100x3 - 120x2 + 32x15) 3x2(9x2 - 3x + 4)16) (x - 8)(x2 - 1)17) (x - 2)(x2 + 3)18) (x + 5)(x2 + 9)19) (x - 2)(x - 6)20) (x + 11)(x - 7)21) (4x + 3)(2x + 3)22) (5x - 2)(3x - 4)23) (5x + 9y)(x - 3y)24) (3x + 4y)(4x + 3y)25) (8x + 9)(8x - 9)26) (7x + 11y)(7x - 11y)27) (9x2 + 4)(3x + 2)(3x - 2)28) (x - 5)(x2 + 5x + 25)29) (5x + 1)(25x2 - 5x + 1)30) (2x - 5)(4x2 + 10x + 25)31) (3y + 4)(3y - 4)32) x1/8(x3/4 - 1)

33) (x + 2)(x+ 1)6/5

34) 13x + 5

, x ≠ - 53

, x ≠ - 1

35) x + 7x + 9

, x ≠ -9, -7

36) 8x - 10(x - 1)(x + 1)(x - 2)

37) 4x - 3x - 1

38) 18

39) x - 9x + 9

40) xx + 4

41) 0; 18

42) 9; {8}

43) h = 3VB

44) h = S - 2πr22πr

45) - 112

, - 32

46) 52

, -1

47) {-4 - 23, -4 + 23}48) 2

a) Domain: [-6,6]b) Range: [0,6]c) Increasing: (0,1)U(1,6] OR (0,6]d) Decreasing: [-6,0)e) Constant.: NAf) The minimum value: 0g) The maximum value: 6

49) - 6



50)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

51)

x-10 -5 5 10

y

10

5

-5

-10

(-9, -5)

(3, 7)

(3, -8)

(3, 1)

x-10 -5 5 10

y

10

5

-5

-10

(-9, -5)

(3, 7)

(3, -8)

(3, 1)

52) 753) 3(2x+h)

54) y - 3 = 89

(x - 4)

55) y + 6 = 12

(x + 2) or y + 7 = 12

(x + 4)

56) y + 7 = - 72

(x - 1) or y = - 72

(x + 1)

57) Set 1 Blue: a) Absolute Value functionSet 1 Green: e) Linear FunctionSet 1 Black: h) Quadratic FunctionSet 1 Red: b) Constant FunctionSet 2 Blue: g) Sqaure Root FunctionSet 2 Green: c) Cube Root Function Set 2 Black: d) Exponential FunctionSet 2 Red: f) Natural Log Function

58)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

59) Domain: all real numbers OR (-∞ , ∞ ) Range: [-6,∞ )

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

60) Domain: (-∞ , 2]Range: [-1,∞ )

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5



61)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

62) Domain: (0,∞ )Range: all real numbers OR (-∞ ,∞ )

x-5 5

y

5

-5

x-5 5

y

5

-5

63) (-∞, ∞)64) (-∞, -9) ∪ (-9, 0) ∪ (0, 9) ∪ (9, ∞)65) (-∞, 6]66) (6, ∞)67) (-2, ∞)68) (-5, ∞)

69) 21x6 + 49x

70) x71) -12x + 4572) f(x) = x6, g(x) = 6x + 6

73) f-1(x) = 3

x - 874) f-1(x) = x2 - 6

75) f-1(x) = x - 62

76) minimum; 1, - 877) minimum; - 1, 078) 13,778 ft279) -1, crosses the x-axis;

3, crosses the x-axis;1, touches the x-axis and turns around

80) -1, multiplicity 1, crosses x-axis; -3, multiplicity 4,touches x-axis and turns around

81)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

82)

x-8 -6 -4 -2 2 4 6 8

y20

16

12

8

4

-4

-8

-12

-16

-20

x-8 -6 -4 -2 2 4 6 8

y20

16

12

8

4

-4

-8

-12

-16

-20

83) -484) falls to the left and falls to the right85) rises to the left and rises to the right86) x = 0, x = - 7, x = 687) x = -1, x = 1, x = - 388) -3x2 - 4x + 2

89) x4 + 2x3 + 4x2 + 9x + 18 + 35x - 2

90) {1, -1, -3}91) {2, 3 + 7, 3 - 7}92) 2 in. by 2 in. square93) -∞94) no vertical asymptote95) x = 0 and x = 296) y = 097) y = 598) no horizontal asymptote

99) log 216 6 = 13

100) 12

101) -117 MAST @ FIU Calculus Summer Assignment


102) log 2 (x - 1) - 4 log 2 x

103) logbx + 3logby - 5logbz

104) log bm3n

105) ln 7 (x + 9)5

x(x2 - 8)

106) ln 49 ln 5

107) {ln 6 - 3}108) 1.63

109) - 12

110) {e18 - 7}

111) { 215

}

112) 7 6565

113) 310

114) π3

115) π4

116) - 85

, ∞

117) (-∞,∞)118) x = 5, x = 7, both Vertical Asypmtotes

(non-removable discontinuities)119) None120) x= 2 (Hole/removable discontinuity)

x= -2 (Vertical Asymptote/non-removablediscontinuity)


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AP Calculus AB & Calculus Honors Summer …teachers.dadeschools.net/dtisdahl/2020_Calculus_Summer...AP Calculus AB & Calculus Honors Summer Assignment Ms. Sellanes The purpose of the