1

Summer Math Assignment

for

Students Entering

Precalculus Honors in

September, 2017

.

2

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

3

Honors Precalc - Mrs. Seaboldt

Summer Packet - Assignment # 2

Name ___________________________ Period _____

.

1.)

2.) 4.)

.

3.)

Simplify

4

Precalculus Honors

Assignment 2Name ___________________________ Period _______

. .

7.) 8.)

6.)

5.)

5

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.)

6

.

Solve for x in terms of y.

7.) y = x2 - 4x + 3

8.)

9.)

10.)

7

.

Solve for x in terms of y.

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

12. 14.

8

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.)

.

9

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

6.) <

7.)

8.)

10

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

11

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

12

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)

.

13

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.

14

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

15

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

5.) If f(x) = , find

.

16

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

.

17

.

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

18

.

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.

19

.

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.