Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Summer Math Assignment
for
Students Entering
Precalculus Honors in
September, 2016
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Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Precalculus Honors - Mrs. Seaboldt
June, 2016
In September you will be starting a two year program (Honors Precalculus and AP Calculus) that involves a complete and in-depth study of a wide variety of relations and functions. There are many prerequisite skills that you must be proficient with, in order to be successful with the new material. These topics have been covered in previous math classes.
The purpose of this summer work is to give you some practice in the areas of factoring, rational expressions, solving equations and inequalities, coordinate geometry, finding domains, and using function notation. We have a lot of new topics to cover, so it is important that you take responsibility for reviewing basic skills. You will be expected to have this work completed and ready to hand in on the first day of class. Please show all work on the actual sheets that have been provided to you,NOT on separate sheets of loose leaf. You will receive homework grades for these assignments.
The work will be discussed the first week of school and you will be tested on it the second week of school. Please note that this packet contains worksheets 1 through 5 and 8 through 10.
Good luck with your work ! I look forward to meeting you in September.
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Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Precalculus Honors
Assignment 1AName ___________________________ Period _______
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1.) x8 - 256
2.) x2 + 4x + 4 - 9y2
3.) 125x3 + 8
4.) 64 - 27y3
5.) a3 - 2a2b + ab2 -2b3
6.) 3x3 + 3x2 -27x -27
7.) y6 + 26y3 - 27
8.) 8x6 + 6x4 - 2x2
9.) x3 - 3x + 2
10.) 6x4 - 7x3 -12x2 + 3x + 2
FACTORINGFactor Competely
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Honors Precalc - Mrs. Seaboldt
Summer Packet - Assignment # 2
Name ___________________________ Period _____
.
1.)
2.) 4.)
.
3.)
Simplify
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Precalculus Honors
Assignment 2Name ___________________________ Period _______
. .
7.) 8.)
6.)
5.)
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Name _______________________ Period __ Honors Precalc - Mrs. Seaboldt
Summer Packet Assignment # 3ABe able to solve:
linear and quadratic equations
higher order polynomial equations
fractional equations
radical equations
literal equations
(Note: Factoring is a key element in solving equations.)
Solve each equation
1.) x3 - 4x2 - 8x + 8 = 0
2.)
3.)
4.)
5.)
6.)
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
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Solve for x in terms of y.
7.) y = x2 - 4x + 3
8.)
9.)
10.)
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
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Solve for x in terms of y.
11. x2 - 4x = y - 3 13. x2y - y = x2 + 1
12. 14.
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Name _________________________ Per ______ Honors Precalc - Mrs. Seaboldt
Summer Packet Assignment # 4ABe able to solve:
linear inequalities
quadratic inequalities
higher order polynomial inequalities
fractional inequalities
Solve each inequality:
1.)
2.) x2 + x - 2 > 0
3.) x3 - 2x2 - x + 2 < 0
4.)
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Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
5.) x3 + 2x2 > 5x + 6
6.) <
7.)
8.)
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Name ____________________________ Per _____ Honors Precalc - Mrs. Seaboldt
Summer Packet - Assignment 5A
1.) Given: A (-1, 2), B (5, 4)
a.) Find AB (in simplified radical form)
b.) Find the midpoint of
2.) Given: A (-5, 7), M (2, 4)
If M is the midpoint of , find B
3.) If A is a point on the x-axis and
B is the point (3, 8), find all points A such
that AB = 10
4.) Given: A (4, 0), B (2, 1), C (-1, -5)
a.) Prove that ABC is a right triangle
b.) Find the area of ABC
5.) Find the x and y intercepts
a.) 2x - 3y - 6 = 0
b.) x = y2 -2y -8
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
6.) Write an equation for each circled described:
a.) radius is , center is (-1, -4)
b.) center is (-5, 4), circle is tangent to the x axis
c.) radius is 3, center is in quadrant IV and is tangent to both axes
d.) center is (1, 3), circle passes through the point (-2, 2)
e.) endpoints of a diameter are (-3, 1) and (5, -5)
7.) Find the center and radius of each circle:
a.) x2 + y2 + 4x - 6y + 9 = 0b.) 4x2 + 4y2 + 8y + 3 = 0
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
8. Calculate the equation of a line satisfying the given conditions:
a.) passes through the points (4, -3) and (4, 2)
b.) passes through the points (3, -1) and (-5, -1)
c.) passes through the point (-3, 4) and has a slope of -2
d.) passes through the points (-2, -2) and (2,4)
e.) is parallel to the line 4x +3y - 3 = 0 and has a x intercept of 6
f.) is perpendicular to the line x + 3y + 6 = 0, and has a y intercept of -1
g.) the perpendicular bisector of given A (-1, -2) and B (3, 6)
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Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
9.) f(x) = 6x + 1
10.) f(x) = -x + 10
11.) f(x) = 2x2 - 3
12.) f(x) =
Name __________________________ Per _____ Honors Precalc - Mrs. Seaboldt
Summer Packet - Assignment # 8A
Use the functions below to substitute into the following fraction and the simplify.
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Name _____________________________ Per ____ Honors Precalc - Mrs. Seaboldt
Summer Packet - Assignment # 9
1.) If f(x) = x3 + Ax2 + Bx -3 and if f(1) = 4 and f(-1) = -6, What is the value of 2A + B ?
A.) 12 B.) 8 C.) 0 D.) -2 E.) It can't be determined with the given information.
2.) If f(x) = , then f( ) equals:
A.) f(x) B.) f( ) C.) -f(-x) D.) -f(x) E.) none of the above
For questions 3 - 5, express results in simplified form.
3.) If f(x) = , find f( ).
.
Show all calculations
Summer Packet for Students Entering Honors Precaculus.notebook
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4.) If f(x) = x2 + 3x, find f(a+b) - f(a-b)
5.) If f(x) = , find
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Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
Name ________________________ Per ______ Honors Precalc - Mrs. Seaboldt
Summer Packet - Assignment 10
1.) If f(x) = 2x3 + Ax2 + Bx - 5 and if f(2) = 3 and f(-2) = -37, what is the value of A + B ?
A.) -6 B.) -3 C.) -1 D.) 2 E.) It can't be determined with the given information
2.) If f(x) = , which of the following statements must be true for x 0.
I. f(-x) = -f(x)
II. f( ) = -f(x)
III f(x2) = [f(x)]2
3.) If f(x1) + f(x2) = f (x1 + x2) for all real numbers x1 and x2, which of the following
could define x ?
A.) f(x) = x + 1 B.) f(x) = 2x C.) f(x) = D.) f(x) = 2x E.) f(x) = x2
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Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
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5.) If g(x+3) = x2 + 2, then g(x) equals
A.) B.) (x-3)2 + 2 C.) (x-3)2 -2
D.) E.)
4. If f(x) = 4x, then f(x+1) - f(x) = ?
A.) 4 B.) f(x) C.) 2f(x) D.) 3f(x) E.) 4f(x)
6. If f(x) = , which of the following is not true ?
A.) f( ) = - f(x) B.) f( ) = f (-x) C.) f(x) = f(-x)
D.) f(-x) = -f(x) E.) None of these
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
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7. If f(x+1) = x2 - 3x + 2 for all real x, then f(3) = ?
A.) 6 B.) 0 C.) 2 D.) -2 E.) 8
8. If x < 0 and f(x) = , the f( ) is equal to
A.) x B.) -x C.) D.) E. undefined
9. If f(x) = , find f( ). Express answers in
simplest form.
Summer Packet for Students Entering Honors Precaculus.notebook
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May 17, 2016
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10. If f(x) = 2x - 3, find f(a + b) - f(a - b).
11. If f(x) = , find .
Express answers in
simplest form.
Express answers in
simplest form.