PreCalculus Chapter PA Packet

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Pre-CalculusChapter P-APacket

• Prerequisites Fundamental Concepts of Algebra

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• A) Evaluate each algebraic expression for the
  given value or values of the variable(s).

Section P.1
Pg. 14

• B) List all the numbers from the given set that
  are (a) natural, (b) whole, (c) integers, (d)
  rational, (e) irrational, (f) real.

Pg. 15

• C) Simplify each expression.

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• D) Fill in the following properties of exponents

Section P.2
NOTES

• E) Simplify each exponential expression.

Pg. 25-26
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Section P.3

• I) Rationalize the denominator.

Pg. 39
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Section P.4

• J) Perform the indicated operations. Write the
  resulting polynomial in standard form and
  indicate its degree.

Pg. 49

• K) Find each product.

Pg. 49 - 50
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Section P.5
Pg. 60

• L) Factor the GCG (greatest common factor).

• M) Factor by grouping

• N) Factor the difference of two squares.

• O) Factor the perfect square trinomial.

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Section P.5
Pg. 60

• Q) Factor each trinomial, or state that it is
  prime.

• R) Write the two formulas for the Sum and
  Difference of Two Cubes

NOTES
Factor the sum or difference of two cubes.
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Section P.7
Pg. 93

• S) Solve each linear equation.

• T) Solve each formula for the specified
  variable. Do you recognize the formula? If so,
  what does it describe?

• U) Solve the absolute value equation or indicate
  it has no solution.

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Section P.7
Pg. 93 - 94

• V) Solve each quadratic equation by factoring.

• W) Solve each quadratic equation by the square
  root property.

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Section P.7
Pg. 94

• X) Solve each quadratic equation by completing
  the square.

• Y) Write the quadratic formula here

NOTES
Solve each quadratic using the quadratic
formula.
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Section P.9
Pg. 118 - 119

• Z) Express each interval in set-builder notation.
  

• In the exercises below, use interval notation to
  express solution sets.

• AA) Solve each linear inequality.

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Section P.9
Pg. 118

• In all exercises below, use interval notation to
  express solutions.

• BB) Solve the compound inequality.

• CC) Solve the absolute value inequality.

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Pre-CalculusChapter P-GPacket

• Prerequisites Fundamental Concepts of Geometry

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Pythagorean Theorem(simplify square roots NO
decimals!)

• 1) LANDSCAPING 6 congruent square stones are
  arranged in an L-shaped walkway through a garden.
  If x 15 inches, then find the total area of
  the walkway.
• 2) In the RECTANGULAR PRISM, AB 8, BC 6, BF
  8, and M is the midpoint of BD. Find BD and
  HM.

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Special Right Triangles (simplify square roots
NO decimals!)
FORMULAS Hypotenuse Long leg
FORMULA Hypotenuse
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Try These(simplify square roots NO decimals!)

• 1) Find the area of a square whose diagonal
  measures 14 cm.

• 2) Find the area of the rectangle below

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Trigonometry
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• Angles of Depression are made with a __________
  line _______to a given point.

• Angles of Elevation are made from a __________
  line _______to a given point.

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Try These
Ex.1) MISSING SIDE A boat in the water
determines that the angle of elevation from the
water level to the base of a light house on the
top of a cliff is 40. The ships captain knows
the cliff is 200 feet tall. How far is the ship
from the base of the cliff?
Ex. 2) MISSING ANGLE A plane is flying at an
altitude of 8,000 feet, and is 2 miles from the
airport. Find the angle of depression of the
plane. Note 1 mile 5,280 feet.
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Ex 3
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• Amanda is at the top of a 60 ft. Ferris wheel.
  The angles of depression to the swing ride and
  merry-go-round are 14 degrees and 32 degrees
  respectively. Find the distance between the
  swing ride and the merry-go-round.

Ex 4
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Challenges

• Find the perimeter and area of the equilateral
  triangle if the edge of the cube is 16 cm. SHOW
  NEAT ORGANIZED WORK ON SEPARATE PAPER. (simplify
  square roots NO decimals!)

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The following is taken from a disposable place
mat from Calico Kitchen, a now non-existent
restaurant Miss. M used to go to as a child. The
menu is entitled, Good Food Takes Time to
Prepare Doodle While Youre Waiting.
A square lake (whose surface area is 10,000 ft2)
has a large trees planted at each of its four
corners. How can the lake be enlarged to a
square twice its original size without replanting
the trees or submerging them in the new lake?
Include calculations with your answer to
demonstrate the new lake really is twice the size
of the original.