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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
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 2 Assigned: Monday, 9/18/2017 Due: Friday, 9/22/2017
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. 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
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 3 Assigned: Monday, 9/25/2017 Due: Friday, 9/29/2017
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. 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
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 4 Assigned: Monday, 10/2/2017 Due: Friday, 10/6/2017
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. 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: _________________________
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 5 Assigned: Monday, 10/16/2017 Due: Friday, 10/22/2017
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. 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? _____________________________
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 6 Assigned: Monday, 10/23/17 Due: Friday, 10/27/17
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. 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: ______________________
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 7 Assigned: Monday, 10/30/17 Due: Friday, 11/3/2017
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 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
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 8 Assigned: Monday, 11/13/2017 Due: Friday, 11/17/2017
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. 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:
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 9 Assigned: Monday, 11/27/2017 Due: Friday, 12/1/2017
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. 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:
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 10 Assigned: Monday, 12/4/2017 Due: Friday, 12/8/2015
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. 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 ____
Weekly Review Sheet # 11 Assigned: Monday, 12/11/2017 Due: Friday, 12/15/2017
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. 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)
College Pre – Calculus A Name _______________________________
Period __________
Weekly Review Sheet # 12 Assigned: Monday, 1/8/2018 Due: Friday 1/12/2018
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. 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: __________________________
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