Free Printable Summer Assignment - (summer after Precalculus)

1.

List all of the critical values (x-locations of the critical points) of the graphed function.

a)

{-2. 0}

b)

{-2, 1}

c)

{-4, -2, 0}

d)

Cannot be determined

2.

Identify the extrema.

a)

Relative max (1, 4), Relative Min (3, 0)

b)

Relative max (1, 4), Absolute Min (3, 0)

c)

Absolute max (1, 4), Relative Min (3, 0)

d)

Relative max (0, 0), Relative Min (3, 0)

3.

What type of extrema is (-3,2). Be as precise as possible.

a)

Absolute minimum

b)

Absolute maximum

c)

relative minimum

d)

Relative maximum

4.

How many relative minimums does this function have?

a)

1

b)

2

c)

3

d)

4

5.

What is the absolute max of this function?

a)

0

b)

infinity

c)

DNE

d)

2.5

6.

$Evaluate:\ \ \sum_{i=1}^3\frac{i+2}{i}$

a)

3

b)

6

c)

9

7.

Which row of Pascal's Triangle would you use to expand (x+y)³?

a)

1

b)

1 1

c)

1 2 1

d)

1 3 3 1

8.

Expand
(b - 2)³

a)

b³ - 2b² + 4b - 8

b)

5b³ - 20b² + 40b - 40

c)

b³ - 6b² + 12b - 8

d)

4b³ - 12b² + 16b - 8

9.

Find the 2nd term in the expansion of
(2b + 1)³

a)

12b²

b)

6b

c)

8b³

d)

4b²

10.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

11.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

12.

ln(e^W)

a)

e

b)

W

c)

e^W

d)

undefined

13.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

14.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

15.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

16.

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

17.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

18.

Solve the following for the unknown value of x. Round your solution to two decimal places.
5 ln (3x - 2) = 15

a)

x = 1.24

b)

x = 7.36

c)

x = 217,935.16

d)

x = 6.03

19.

What is the transformation of the logarithmic function
$f\left(x\right)=\log\ \left(x+3\right)-1$

a)

left 3, right 1

b)

right 3, down 1

c)

right 3, up 1

d)

left 3, down 1

20.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

21.

Which has a vertical asymptote?

a)

Exponential

b)

Logarithmic

c)

Both

22.

What is the end behavior of the graph?

a)

As x →∞, y→⁻∞ and as x →⁻∞, y→⁻∞

b)

As x →∞, y→∞ and as x→⁻∞, y→∞

c)

As is x →∞, y→∞ and as x→⁻∞, y→2

d)

As x →∞, y→2 and as x→⁻∞, y→∞

23.

Write the equation of the graph.

a)

f(x) = 5^x+ 2

b)

f(x) = 3^x - 2

c)

f(x) = 3^x + 2

d)

f(x) = -3^x +2

24.

Simplify the following exponential expression completely:

a)

b)

c)

d)

25.

Even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

26.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

27.

Find the Vertical Asymptotes

a)

x= 0, -2

b)

x= 2

c)

x= -3, 2

d)

x = -3,1

28.

What is the domain of the rational function?

a)

{x|x ≠ 0, -5}

b)

{x|x ≠ 2, -7}

c)

{x|x ≠ -2, 7}

d)

{x|x ≠ 0, 5}

29.

Find the oblique asymptote.

a)

y = x

b)

y = x - 8

c)

y = x - 4

d)

y = x + 4

30.

The period of a sine or cosine graph can be found by ....

a)

It's always 2π

b)

2π/B

c)

B(2π)

d)

2π+B

31.

The __________ represents the distance above or below the midline of a sine or cosine graph; we always take the absolute value of this height.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

32.

Which value represents a vertical shift in the following function y=a*sin(bx - c)+d?

a)

a

b)

b

c)

c

d)

d

33.

Which value helps identify a horizontal shift in the following function y=a*sin(bx-c)+d?

a)

a

b)

b

c)

c

d)

d

34.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

35.

Which function represents the graph?

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = sin ( ⅓ x)

d)

f(x) = sin (3 x)

36.

a)

A

b)

B

c)

C

d)

D

37.

What is the phase shift?
y=3cos(2x)

a)

π

b)

2π

c)

1/2π

d)

There is no phase shift

38.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

39.

What is the period of the function?

a)

π

b)

2π

c)

3π

d)

π/2

40.

Which trig function does this graph represent?

a)

csc

b)

sec

c)

cos

d)

sin

41.

What is cos 60°?

a)

½

b)

^√3/₂

c)

^√2/₂

d)

1

42.

How many degrees is ^π/₂ radians?

a)

30°

b)

45°

c)

60°

d)

90°

43.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

44.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

45.

Convert the following to degrees:
-8π/5 radians

a)

-288⁰

b)

-260⁰

c)

-275⁰

46.

tan (-π)

a)

undefined

b)

0

c)

1

d)

-1

47.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

48.

What quadrant is -2π/3 in?

a)

I

b)

II

c)

III

d)

IV

49.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

50.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

51.

What are the negative and positive coterminal angles of -225 degrees?

a)

375°, -600°

b)

125°, -356°

c)

135°, -585°

d)

60°, -120°

52.

What are the negative and positive coterminal angles of -300 degrees?

a)

60°, -600°

b)

135°, -476°

c)

60°, -125°

d)

220°, -340°

53.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

54.

*

a)

cos x

b)

csc x

c)

sec x

d)

cot x

55.

180 degrees equals _____ radians

a)

100

b)

1

c)

14

d)

$\pi$

56.

$\sin\ \pi\ =$

a)

1

b)

0

c)

-1

d)

$\frac{\sqrt{2}}{2}$

57.

$\cos\ \frac{3\pi}{2}\ =$

a)

1

b)

0

c)

-1

d)

$\pi$

58.

a)

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

b)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

c)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

d)

The end behavior of the graph is x →∞,y→⁻∞ and x→∞, y→⁻∞

59.

a)

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

b)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

c)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→0

d)

The end behavior of the graph is x →∞,y→∞and x→⁻∞, y→⁻∞

60.

Which of the following helps determine end behavior?

a)

The leading coefficient

b)

The number of terms in the function

c)

The y-intercept

d)

The x-intercepts

61.

Based on the end behavior of the polynomial, what best describes the leading coefficient?

a)

a negative real number

b)

a positive real number

c)

an even real number

d)

an odd real number

62.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

63.

In the above graph complete the following end behavior:

As x --> -∞, f(x) --> ____

As x --> +∞, f(x) --> ____

a)

down, down

b)

up, down

c)

down, up

d)

up, up

64.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

65.

A function is continuous on a number if and only if f(c) = lim f(x) as x approaches a number c.

a)

TRUE

b)

FALSE

66.

One of the conditions a function must satisfy to be continuous at a number is "f(c) must exist"

a)

TRUE

b)

FALSE

67.

Evaluate

a)

-7

b)

0

c)

1

d)

DNE

68.

Which of the following best describes the continuity at x = 5?

a)

Continuous

b)

Removable discontinuity

c)

Non-removable discontinuity

69.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

DNE

d)

-2

70.

Find the limit of the function as x approaches 2⁺.

a)

1

b)

-1

c)

5

d)

DNE

71.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

72.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

73.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

74.

Which of the following graphs presents an infinite discontinuity at x = 1?

a)

b)

c)

d)

75.

Which of the following graphs presents a removable/hole discontinuity at x = -2?

a)

b)

c)

d)

76.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

a)

y = 6.80 + .65x
y=7.30+.90x

b)

x + y = 6.80
x + y = 7.30

c)

y = 6.80+.90x
y = 7.30 + .65x

d)

y + .90x = 6.80
y + .65x = 7.30

77.

Which system of inequalities is shown?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 3

78.

Convert the rectangular coordinates to polar coordinates
(6√3, 6)

a)

(12, π/6)

b)

(6, 7π/6)

c)

(6, π/6)

d)

(12, 7π/6)

79.

Find the rectangular coordinates of each polar point. (4, 3π/2)

a)

(4,4)

b)

(4,0)

c)

(0,4)

d)

(0,1)

80.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

81.

Find m<B to the nearest whole number.

a)

A

b)

B

c)

C

d)

D

82.

If the blue graph is f(x) = x^2,then the red graph must be

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

83.

If the blue graph is f(x)=|x|, the red graph must be:

a)

g(x)=|x+2|

b)

g(x)=|x|+2

c)

g(x)=|x-2|

d)

g(x)=|x|-2

84.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

85.

Find the vector with initial point P(4, 3) and terminal point Q (8, 1)

a)

〈4, -2〉

b)

〈-4, 2〉

c)

〈-4, -2〉

d)

〈8,1〉

86.

Given that u = 〈11, 7〉 and v = 〈9, -8〉,
find 2u - 5v

a)

〈-23, 54〉

b)

〈67, -26〉

c)

〈23, -54〉

d)

〈26, -67〉

87.

Find S_n for the given series:
a₁=22
d=-8
n=21

a)

1911

b)

-1449

c)

-2436

d)

-1218

88.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

89.

Find the geometric mean of 12 and 192

a)

4

b)

16

c)

48

d)

2304

90.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

91.

a)

A

b)

B

c)

C

d)

D

92.

a)

A

b)

B

c)

C

d)

D

93.

Simplify.

a)

b)

c)

d)

94.

Simplify.

a)

b)

c)

d)

95.

a)

A

b)

B

c)

C

d)

D

96.

a)

A

b)

B

c)

C

d)

D

97.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

98.

₇P₂

a)

0

b)

7

c)

42

d)

210

99.

A group of 25 people are going to run a race. The top 8 finishers advance to the finals.

a)

200

b)

4.3609 x 10¹⁰

c)

0

d)

1,081,575

100.

A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there?

a)

64

b)

14

c)

24,024

d)

2184

Summer Assignment - (summer after Precalculus)

Total questions: 100

Worksheet time: 4hrs 18mins

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