SUMMER REVIEW PACKET FOR STUDENTS ENTERING

PRECALCULUS HONORS or PRECALCULUS ACCELERATED

This packet contains material you have learned in Algebra 2 and Geometry.

Since you may have forgotten some of that material, this packet gives you the

opportunity to review and in some cases relearn much of the Geometry and

Algebra that you will once again need starting in the fall. This packet should be

done during August so the material is still fresh when you return to school.

Due: This packet will be collected on DAY 1 and play a role in your first quarter

effort grade. SHOW ALL WORK.

Use the ANSWER KEY to help with any problems that you don’t remember.

Also, use the ANSWER KEY to CORRECT your work.

The purpose of this packet is to refresh your Algebra and Geometry skills.

This will not be graded but IT WILL BE COLLECTED DAY 1.

Give this a good effort and the first quarter will go much smoother for you.

NAME:_______________________________________________

Approximate time : 2 Hours 15 Mins

SUMMER PREP FOR PRECALCULUS

A) Factor all of the following completely, if possible:

1) N2 – N – 6 2) 81y4 – 16x8 3) 9x2 – 15x + 6

4) (2x – 3)2 – 6(2x – 3) + 8 5) 6x2 + 3xy + 10x + 5y 6) 8A3 – 27B3

7) 36N4 + 44N3 + 24N2 8) 4x2y – 36y 9) 9x4 + 16

10) m(n – 2) – 3( 2 – n) 11) x6n – 2x3n + 1 12) ( a + b)4 – ( a – b)4

B) Solve each equation. Find ALL solutions

1) x = ( x – 6)2 2) y2 ( y –3) ( y2 – 9 ) = 0 3) x6 + 9x2 = 10x4

4) ( x – 4)3 – 4(x – 4) = 0 5) (x + 1) ( x – 5) = 7 6) y4 – 5y2 + 4 = 0

C) Write and solve an equation for the each of the following problems.

1) The product of three consecutive integers is 21 more than the cube of the smallest integer. Find the three integers

2) A rectangular garden has a perimeter of 66 ft and an area of 216 ft2 Find the dimensions of the rectangle.

3) A farmer plans to use 21 ft of fencing to enclose a rectangular corral having an area of 55 ft2. Since the Corral is

attached to the back of the barn, the farmer only needs to build 3 sides with fencing using the barn as the fourth side.

Find the dimensions of the rectangular corral.

D) Graph each solution set on a number line

1) x2 – 7x + 12 > 0 2) (x2 – 4x) ( x2 – 4) < 0

E) Given f(x) = 2x – 5 g(x) = x2 + 3 and h(x) = ½ x + 5 Evaluate each of the following, if possible

1) f( -2) 2) f(g(2)) 3) h(g(0)) 4) f( x + 2)

5) f-1(x) { Find the inverse of f(x) } 6) f(h(x)) 7) Does g-1(x) exist ? Explain

F) Evaluate WITHOUT A CALCULATOR

2 8 5

2 3

11) (2 ) _______ 2) 32 _______ 3) ______ 4) ln( ) ______ 5) Log 100 _____

81Log Log e

2 15 2 3

13 2

5 1 6

3 96) ______ 7) 27 ______ 8) 25 ______ 9) 4 8 ______ 10) ______

33

x x

Simplify #11-14 making sure to leave NO Radicals in the denominator of your answer.( Rationalize the denominator)

3

5 4 6 311) ______ 12) ______ 13) ______ 14) ______

2 2 6 2 3

Simplify:

215) ( 3 5) _________________ 16) (5 2 10)(3 2 2 10) ____________________

Solve for x :

17) 2 5 4 18) 10 15 4x x x

G) CALCULATOR ALLOWED

1) State the QUADRATIC FORMULA :

Solve by any method : ( Answers should be exact and MAY contain Radicals)

222) (5 3) 16 3) (3 1)( 3) 1 4) 4 (4 5) 5 0x x x x x

5) 22 5 8 0x x 6) 2 81x 7)

22 3 5 7x

8) An express train travels 150 km in the same time that a freight train travels 100 km. The average speed of the freight

train is 20 km/hr less than the express train. Find the speed of each train.

9) Solve by COMPLETING the square. ( SHOW ALL WORK…RELEARN COMPLETING THE SQUARE, if necessary)

a) 2 8 3 0 x x b) 22 5 1 0x x

Simplify:

10) 4 6 3 2 11) ( 3 5)( 3 5) 23)12) (5

Trigonometry and Right Triangles.

Use your knowledge of right Triangles to find ALL sides and ALL angles

13)

A = _____ a = ____ b = ____ A = ____ B = _____ b = _____

Use the Pythagorean Theorem to find missing side of the given right triangles.

14) 15)

16) A rectangle has length 12 and width of 5. Find the diagonal.

30o

4

A

B C

A

B C

5

5

13b

)

4 2

8

14

12

17) A boy is 50 ft from a tall tree. The angle from his feet to the top of the tree is 60 . How tall is the tree?

K) Polynomial and Rational Expressions

1) The graph of f(x) is given to the right.

Use the Graph to estimate the following:

a) domain of f

b) range of f

c) f(6)

d) estimate the value(s) of x if f(x)=-4

Perform the indicated operation and simplify. Leave you answer in factored form if necessary.

2)

2 2

3 2

2 1 4 4

2

x x x

x x x x

3)

2

2 3

3 12

4 8

x x x

x x

f(x)

x

4) 2

2

1

4

x

x x

5)

2 2

2 3

3 2 1

x x

x x x

6)

1 3

23

4

xx

7)

2

24

2 21

x

xx

x

8) Solve for x. 5 3

44 2x x

L)

1) Find a third degree polynomial given the Zeros are : 5, -5, and 2

2) Find all of the Zeros of the polynomial 3 2( ) 2 5 6f x x x x given that x = -3 is one of the Zeros

3) Is ( x – 4) a factor of x3 – 3x2 – 16x + 48 ? EXPLAIN/ Show how you know

4) Use your polynomial long division skills to divide : ( 5x5 - x3 - 4x2 - 233x + 28) ( x2 - 7)

Hint : Remember to use “place fillers.”

5) Solve each system of equations, if possible

) 3 9

2 4

a x y

x y

) 2 4

3 6 12

b x y

x y