Summer Math Assignment for Students Entering … Packet for Students Entering Honors...

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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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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May 17, 2016

Precalculus Honors

Assignment 1AName ___________________________ Period _______

.

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


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May 17, 2016

Honors Precalc - Mrs. Seaboldt

Summer Packet - Assignment # 2

Name ___________________________ Period _____

.

1.)

2.) 4.)

.

3.)

Simplify


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May 17, 2016

Precalculus Honors

Assignment 2Name ___________________________ Period _______

. .

7.) 8.)

6.)

5.)


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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.)


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May 17, 2016

.

Solve for x in terms of y.

7.) y = x2 - 4x + 3

8.)

9.)

10.)


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May 17, 2016

.

Solve for x in terms of y.

11. x2 - 4x = y - 3 13. x2y - y = x2 + 1

12. 14.


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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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May 17, 2016

5.) x3 + 2x2 > 5x + 6

6.) <

7.)

8.)


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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


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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


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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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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.


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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


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May 17, 2016

4.) If f(x) = x2 + 3x, find f(a+b) - f(a-b)

5.) If f(x) = , find

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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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May 17, 2016

.

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


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May 17, 2016

.

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.


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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.

Summer Math Assignment for Students Entering … Packet for Students Entering Honors...

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