you must show all work for every … · weekly review sheet # 1 assigned: ... you must show all...

College Pre – Calculus A Name _______________________________

Period __________

Weekly Review Sheet # 1 Assigned: Monday, 9/11/2017 Due: Friday, 9/15/2017

YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN

RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET.

NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT.

1. If 1||3)( xxf and 103.0)( 3 xxxg ,

solve for f(x) = g(x) for x rounding the nearest

thousandth.

2. Simply the expression: ).54(6 3 xixi

3. Solve 4x2 + 98 = 0 for x. 4. If 644)( 23 xxxxr , find the value

of r(2).

5. Over the set of integers, factor the expression

4x3 – x2 + 16x – 4 completely. 6. Solve 02562 xx by completing the

square, giving answer in simplest radical form.

7. The formula to determine continuously

compounded interest is rtPeS , where S is the

amount of interest earned, P is the amount of

money invested, r is the interest rate, and t is the

time (in years). Find the total interest earned if

$18,000 is invested at a rate of 1.25% for 24

months.

8. Simplify: 804

3

9. Solve algebraically for all values of x:

64 xx 10. Simplify:

57

5

11. What is the product of x2 – 2x +3 and x + 1?

12. Solve for p: 121 168 pp

13. If 132)( 2 xxxf and 5)( xxg , find

f(g(x)).

14. Factor completely: xxx 63336 23

15. Write xx 3 as a single term with a rational

exponent.

16. Solve algebraically for c: 19102

3c


Period __________





1. Express (1 – i)3 in a + bi form. 2. Solve for x:

xx 3

1

3

11

3. Simplify the expression 135

4

4. Factor Completely: 3a2 – 48b4

5. Solve for all values of x:

0 = x4 – 4x3 – 9x2 +36x

6. What is the solution set for the equation

3295 xx

7. Simplify 15

41

3

yx

yx, leaving no negative exponents

8. Solve xx

1013

algebraically and express the

result in simplest radical form.

9. Evaluate 3

2

2 )9(

x when x = 6. Express your

answer in fractional form.

10. Solve for x: xx 352 84

11. The legs of a right triangle are represented by

2x and 2x . Find the length of the

hypotenuse in terms of x.

12. If f(x) = 2x2 – 3x + 4, find f(x + 3)

Part II: Show all work and clearly identify your answers. 10 points each.

13. Solve the following system of equations

algebraically for x, y and z:

x + y + z = 1

2x + 4y + 6z = 2

-x + 3y – 5z = 11

14. Solve the system of equations algebraically:

(x – 3)2 + (y + 2)2 = 16

2x + 2y = 10


Period __________





1. Factor completely: 216 + 64x3

2. Factor: 4x2 – 20x + 25

3. Solve for x and write answer in interval

notation: |x + 3| > 4

4. Algebraically find the domain of

21112

5)(

2

xx

xxf

5. Find the equation of the line passing through the

point (-1,-2) and parallel to 2x – y + 3 = 0

6. Factor: 125 – 64x3

7. Find the distance from the point (4,2) to the line

6x + 1 = 8y

8. Find the distance between the parallel lines

3x – y + 1 = 0 and 3x – y = 7

9. Find all values of x if the distance from A (-3, 1)

and B (x, 6) is 13.

10. Solve 4x2 – 13x – 35 > 0 giving answer in

interval notation

11. Find the length of AB if A (3,-7) and

B(-1,4).

12. Solve B

b

SinA

a

sin for b.

13. Factor: 25 10 175x x

14. Factor: 215 11 12x x

15. Rewrite 85

43 xy in ax + by + c = 0 form

with no fractions.

16. Simplify: 22

2

)8(

216

64

162

x

x

x

xx


Period __________





1. What is the range of y = -3(x – 5)2 + 6?

Be sure to justify your answer.

2. What is the vertex of the y = -3(x – 5)2 + 6?

Justify your answer by listing transformations.

3. Factor: 3827 y

4. Write the equation of the line passing through

the point (2,-5) and perpendicular to the line

4x + 3y + 2 = 0 in general form.

5. Solve: 910 24 xx = 0

6. Find the distance between the two parallel lines

5x – 4y = -5 and 5x – 4y – 7 = 0

7. Solve for CosB: b2 = a2 + c2 – 2acCosB

8. Algebraically find the domain of 3

1)(

xxf

9. Find the range of |102|5)( xxg Note: If using a graph, you must draw the complete graph

10. Algebraically find the domain of

152

12)(

2

xxxh

11. Algebraically find the range of 7

122)(

x

xxh

12. Find the distance from the point (4,-7) to the

line 3x – 2y = 5 in simplest radical form.

13. What is the equation of the horizontal line

passing through the point (-7,6)? Be sure to justify your answer

14. Write the equation of the line parallel to the

line segment with endpoints (-3,5) and (4,7)

and contains the point (-1,6) in general form

15. Simplify:

xx

x

x

4

14

21

16. What is the slope of the line perpendicular to

the line containing the points (2,7) and (3, -1)

16. Find the (x, y) table of values for each part of the function, sketch the piecewise graph and then

find the domain and range. [10 Points]

0,1

0,)(

2

xx

xxxf

Domain: _______________________ Range: _________________________


Period __________





1. Find all values of x if the distance from A (x,3)

to B (5,7) is 5.

2. Factor: 912 27125 ba

3. Find the distance from the point (-2,2) to the

line 5x = 3y -1

4. Solve: x2 – 8x – 29 = 0 by completing the

square, giving answer in simplest radical form.

5. Algebraically find the domain of 7

12)(

x

xxf

6. If 216)( xxf and 4)( xxg ,

find )(xg

fin simplest form.

7. If 62)( 2 xxxf and 9)( xxg ,

find ))(( xgf

8. Write the equation of the line parallel to

3y – x = 5 and passing through the point (6,-1)

in general form.

9. Complete the square to write the equation of

6105)( 2 xxxg in standard form of a

quadratic equation for graphing

10. What is the range of 6105)( 2 xxxg

(question #9)? Justify your answer by identifying

transformations.

Part II: 20 Points

11. An object 160 feet above the ground is shot straight up with an initial velocity of 485 ft/sec.

a. Write the general formula for projectile motion ______________________________

b. Write the equation that would be used to

represent this problem ______________________________

c. Draw the graph that represents the problem situation:

Be sure to write all unrounded values for each part of this question before you round

d. When will the object reach is maximum height? _____________________________

e. What is the maximum height? _____________________________

f. When will the object be exactly 2275 feet above the ground? _____________________________

f. When will the projectile hit the ground? _____________________________


Period __________





1. Determine the number of real zeros of the

quadratic function 753)( 2 xxxf

2. Solve by completing the square:

020122 2 xx

3. Algebraically find the range of 32

4)(

x

xxf

4. Draw a complete graph and find the range of

)3(

)6()(

2

x

xxf Hint: look at the window HW#9, question #19

5. What is the equation of the line, in general form,

passing through the points (5,-4) and (-3,2)?

6. Find the difference quotient for the function

8123)( 2 xxxf

7. Factor completely: 32128 23 xxx

8. Complete the square and find the vertical shift

of the function 68)( 2 xxxf

9. Write the equation of the function that would be

used to represent the area of a sidewalk with a

10. A rectangular fence is used to enclose a plot of

land with an existing wall as one side. If only 675

uniform width x surrounding a rectangular

garden that is 19 feet wide and 27 feet long.

feet of fencing is used, write the equation used to

find the area of the plot of land.

11. Graph the function from #9 above and find the

width of the sidewalk if the area of the

sidewalk is 350 square feet. [8 Points]

Width of sidewalk: _____________________

12. Graph the function from #10 above and find

the maximum area of the plot of land and the

dimension of the plot that produces that

maximum area. [8 Points]

Maximum Area: ___________________

Dimensions of the plot: _____________________

Part II: 14 Points

13. Complete the square on the quadratic equation 5142 2 xxy and list all transformations from

the graph of y = x2, then find the vertex, axis of symmetry, domain and range

List all transformations:

Vertical stretch or shrink: ______________________________ Reflect over x – axis? _____________

Horizontal Shift: _______________________ Vertical Shift: _________________________

Vertex: _________________ Equation of Axis of Symmetry: _________

Domain: ________________ Range: ______________________


Period __________





1. If 98)( xxf and 173)( xxg , find

)4(gf .

2. Find )(" xf if

106236)( 245 xxxxxf

3. Find the difference quotient for

5147)( 2 xxxf

4. Express as a single fraction, ))(( xgf if

3)( 2 xxf and 4

)5()(

xxg

5. Solve graphically 782)( 2 xxxf

6. Solve by completing the square

036204 2 xx

7. Find the distance between the parallel lines

054 yx and 114 yx

8. Algebraically find the range of

4

3;

32

75

x

x

xy

9. Factor Completely: 3613 24 xx 10. Solve and write answer in interval notation

102

327

x

11. Complete the square and identify the vertical

shift of the graph of 1123 2 xxy

12. What is the horizontal shift of the graph

1123 2 xxy ? (use your work from #11)

13. Write the equation of the line perpendicular to

0243 yx and passing through the

point (1,-5) in general form.

14. Solve using a sign chart:

04

21112 2

x

xx


Period __________





1. Graphically find the solution to

1574 23 xxx in interval notation

Zeros:

Answer:

2. The cost equation for manufacturing

calculators is 3110)( 2 xxxc where c(x)

is the cost in thousands of dollars for x

calculators. Graphically find the number of

calculators manufactured for a cost of 625

thousand dollars.

3. Factor Completely: 47 125216 xyyx

4. Find the center and the radius of the circle

027101622 yxyx (radius in simplest radical form)

5. Algebraically find the range of

83

57)(

x

xxf ,

3

8x

6. Find the inverse, f -1 (x), if

83

57)(

x

xxf ,

3

8x

7. Solve using sign patterns and write answer in

interval notation: 04

72

xx

x

8. Solve using sign patterns and write answer in

interval notation: 10x3 + 7x2 – 6x < 0

9. Solve by completing the square:

ax2 + bx + c = 0 (10 Points)

10. An object 47 feet above the ground is shot straight

up with an initial velocity of 375 feet per second. For

what period of time will the object be at least 850 feet

the ground? (15 Points)

Identify variables and write equation here:

Graph the problem situation here:

Completely answer the problem here:


Period __________





1. Use a sign chart to solve 05

32 2

x

xx

2. Find the inverse, )(1 xf , if

4;4

73)(

x

x

xxf

3. Determine all real zeros of

1111)( 23 xxxxf by factoring

4. Find the difference quotient of

653)( 2 xxxf

5. Solve for x: 12

25

3

3

xx

6. Find the equation of the line perpendicular to

2x + 5y – 6 = 0 and passing through (-3,7) in

general form

7. Solve by completing the square

01293 2 xx giving answer in simplest radical

form

8. Complete the square and identify the horizontal

shift of 5124)( 2 xxxf .

9. Find the center and radius of

03710822 yxyx

10. Find the coordinates of the x-intercept(s) of

4x2 + 9y2 = 36

11. Draw a complete graph and find all intervals

where )(xf is increasing and decreasing if

652)( 24 xxxxf (5 Points)

Increasing: _______________________________

Decreasing: ______________________________

12 Draw a complete graph and find all local

extrema of

1577)( 23 xxxxf (5 Points)

Local Maxima: ____________________________

Local Minimum: __________________________

13. A candy box (probably to hold some chocolate for Mrs. Wiech) is to be made out of a piece of cardboard

that measures 12 inches by 15 inches. Squares of length x will be cut from each corner and then the ends will

be folded up to create the box. Find the value of x that will allow the maximum volume of the candy box

created ( holding the maximum amount of chocolate)

Draw picture here: Draw a graph of the problem situation here:

Identify variables and write equation here: Completely answer the problem here:


Period __________





1. Write the equation of a circle in general form

that has a center of (7,-3) and a radius of 5 .

2. Use Horner’s Algorithm to find the quotient

and remainder when 17125)( 3 xxxf is

divided by x – 3.

3. Find the remainder when

2752)( 23 xxxxf is divided by x – 3.

4. Given: 35634)( 2345 xxxxxf ,

find )(" xf .

5. Given the function, 124

72)(

2

xx

xxf , what

is the equation(s) of the vertical asymptote(s)?

6. Factor Completely: 64164 23 xxx

7. Find )(1 xf if 2

3;

23

57)(

x

x

xxf

8. Solve for x and give answer in interval notation:

497

5214

x

9. Write the equation of the absolute value

Function whose graph has a vertical stretch of

5, reflects over the x-axis, a horizontal shift right

of 4 and vertical shift down of 3.

10. Express as a single fraction, ))(( xgf if

3)( 2 xxf and 2

)3()(

xxg

11. Graph 25xx3xf(x)234 and find all zeros, local maximum and local minimum, and intervals

where f(x) is increasing and decreasing (Be sure to include all unrounded values)

a. Draw a complete graph of f(x): b. Find all zeros:

Zeros: _______________________________________________

c. Find all local extrema:

Local minima: _____________________________ Local maxima: _____________________________

d. Intervals where f(x) is increasing and decreasing:

Increasing: _________________________________ Decreasing: ____________________________

12. For the piecewise function, find (x, y) values, graph and find domain and range and identify intervals where

)(xf is continuous and discontinuous if

1,

1,22)(

2

xx

xxxxf

Domain: ____________________ Range: ____________________ What type of discontinuity

does f(x) exhibit?

Continuous: _________________ Discontinuous: _____________ ____________________

College Pre – Calculus A Name _______________________________ Period ____





1. What is the equation of the quadratic function

whose roots are i73 ?

2. Solve by completing the square, giving answer

in simplest radical form:

09213 2 xx

3. Given 20015.100 xp , find the production

level, x, is the price, p, is $14.50

4. If 8116)( 2 xxf and 94)( xxg ,

find )(xg

f

.

5. Determine the number of possible negative real

roots for the function 623)( 234 xxxxf .

Be sure to justify your answer.

6. Factor: 27a3 + 64b9

7. Algebraically, find the range of

5

4;

45

33)(

x

x

xxf

8. What is the equation of the line, in general form,

which is perpendicular to the line 0652 yx

and passes through the point (-3, 7)

9. Given: 608112)( 234 xxxxxf

Algebraically determine if 6 is a real zero

of f(x). Write yes or no on answer sheet and

justify your answer below.

10. What is the upper bound of

3242)( 23 xxxxf ?

(be sure to justify your answer)

11. Find the distance from the point (5, 3) to the

line 6x – y + 4 = 0

12. Simplify:

14

21

2

a

a

13. What is the local maximum of the function

?4642)( 23 xxxxf Be sure to include a complete graph

14. Find the difference quotient for the function

523)( 2 xxxf

15. Evaluate 423 )5y(2x …..show all work and clearly identify your answer on the bottom of the

answer sheet. Do not write your answer on line #15…it’s too long. (5 Points – no partial credit)


Period __________

Weekly Review Sheet # 12 Assigned: Monday, 1/8/2018 Due: Friday 1/12/2018




1. Find the reciprocal of i

i

3

4 in simplest bia

form

2. Solve for x and y:

iiyxyx 415)23()2(

3. When the polynomial f(x) is divided by 12 x ,

the quotient is 42 xx and the remainder is 3.

Find f(x)

4.Write a polynomial of degree 3 with zeros of 3

and i45

5. Simplify: 22

44

ba

ba

6. Solve using sign patterns:

32

12

x

xx

7. Given the function 6532)( 23 xxxxf ,

determine the number of possible negative real

roots.

8. Find the equations of the vertical and

horizontal asymptotes for 25

96)(

x

xxf

9. Algebraically find all zeros of

10021)( 24 xxxf 10. Solve for x in fractional form: xx

354

3

927

11. Solve Graphically: 307

543

25

x

xx

12. Given the function: 223314

4

1)( xxxxf

a. Use the first derivative and a sign chart to find interval(s) where f(x) is increasing and decreasing.

Be sure to clearly identify your answers.

First Derivative: Sign Chart for Finding Interval(s) of

Increasing and Decreasing

Clearly identify interval(s):

Increasing: ______________________________________________________

Decreasing: ____________________________________________________

b. Using the sign chart from above, find all local extrema in fractional form of f(x)

Local Maxima: ___________________________ Local Minima: __________________________

you must show all work for every … · weekly review sheet # 1 assigned: ... you must show all...

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