Precalculus

Math Resources

3-7 "Practice Test" problems:
Note: csc"(-4/3) means inverse cosine of -4/3 
1.  Graph y = 2cos(3x)
2.  Convert:  210 degrees,    17pi/6
3.  csc"(-4/3) = theta.  Find tan(theta)
4.  sec(cos"(1/10)) =
5.  cos(-17)*sec(17) = 
6.  Find two angles A,B such that sin(A) = sin(B) = -1/2
7.  (sin(A)*tan(A)/cos(A))*cot²(A)
8.  Find tan(csc"(100))
4.  Find cos(111pi / 4)
5.  Graph csc(5x)
6. Find a graph with y-int = -3 and period = pi/6

2-25 "Rambo" problems No CALC:
1.   tan(15pi/2) =
2.   sin(-6pi) + cos(-pi/4) =
3.   cot(pi/6) + csc(pi/3) =
4.   -csc(-3pi/2) + tan(-2pi/3) =
Bonus!  cot(2pi/3)*tan(2pi/3) + csc(-3pi/4) =

2-20 - "Stupid Trumpet" problems - NO CALCULATOR:
Graph each function.
1.   y = sin x
2.   y = 2 sin x
3.   y = 3 cos x
4.   y = sin (2 x)
5.   y = 0.5 (cos x)
6.   y = 100 tan x

2-19 "B Hammered" problems - NO CALCULATOR:
1.   sec(150) =
2.   csc(3pi/2) =
3.   cot(-45) =
4.   sin(7pi/6) =
5.   sec(9pi/12) =
6.   cos(17pi/2) =

2-7 - "The Golden Compass": Find each missing side, and the two missing angles from each right triangle:
1.   Leg = 1, hypotenuse = 2
2.   Leg = 2, hypotenuse = sqrt(8)
3.   Leg = sqrt(3), hypotenuse = 2
4.   Angle = 30 degrees, hypotenuse = 10

2-4 - "Pina Colada" problems:  Find sine, cosine, tangent of the angle in each situation.  Each point represents a ray beginning at the origin.
1.  (4,3)
2.  (35, 12)
3.  (8, 6)
4.  (-48, 28)
5.  (3, 3)
6.  (-5, -5) 

1-26 - FINAL REVIEW ANSWERS 

1-25 - FINAL REVIEW

1/17 - ALL ABOUT LOGS and LOG RULES

1/16 - "Malibooty" problems:

log₃27 =
log₁₀0.1 =

log₅(1/25) =

log₂8+log₈64 =

log₂8 – log₂16 =

log₂1024 =

If 3^-0.5x = 5, then 81^3x =

1/15 - "Shred Camas" problems:
1.   If 3^(2x) = y, find 9^(2x).
2.   If 2^(-3x) = 8, find -8^(-3x).
3.   If 2^(-3x) = 7, find 8^x.
4.   If 5^2x = 10, find 625^(-3x).

12/17 - "Your Grandma" assignment:
1.   Find possible rational roots, then test to find all roots of
      x³ - x² - 5x + 5
2.   Graph (find roots, y-int, asymptotes, holes):
      (x³ - x² - 5x + 5) / (x² - 1)

12/14 - "Something Appropriate" Problems:
For each of the following, provide: (a) y-int (b) roots (c) v.asymptotes (d) holes (e) h. or o. asymptotes (f) table of values (g) graph
I.   (x+5)(x-1) / ((x-1)(x+2))
II.   (x² + 5x + 4) / (x² - 1)
III.   (x^4 - 2x² + 1) / ((x+1)(x-3))

12/14 - Java Monster answers:
1. f(1)=8  f(-1)=-8  f(2)=40  f(-2)=-100
2. f(1)=-57  f(-1)=-75  f(2)=0  f(-2)=-132
3. f(1)=-31.5  f(-1)=-11.5   f(2)=-40   f(-2)=0 

12/13 - "Java Monster" problems:
Use Synthetic Division to find f(1), f(-1), f(2), f(-2) for each function:
1.   f(x) = 9x³ - 10x² - x + 10
2.   f(x) = 8x³ + x - 66
3.   f(x) = 0.5x² - 10x - 22

12/5 - Help with Polynomial Division.

12/3 - "Beowulf" problems (polynomial division):
1.   (x^3 - 9x² + x + 10)  /  (x + 1)  = 
2.   (2x^3 - 5x² + 2x - 8)  /  (2x - 1)  = 
3.   (x^4 + 0x^3 + x² + 1)  / (x + 1)  = 
4.   (x^6 + x^4 + 5)  /  (x² + 2)  = 

11/14 - Help with completing the square.

11/14 - "Blue Calculator, Red Pen" problems:
Graph, showing how you completed the square:
1. y = x² - 4x + 12
2. y = x² - 2x + 6
3. y = x² - 5x + 1
4. y - 6 = 8x + x²
Solve by completing the square:
5. x² + (2/5)x = 100
6. 2x² + (2/5)x = 100 

11/06 - Some help for Composite Functions

11/02 - Help with Function Transformations

11/01 - Understanding Domain and Range

10/15 - Mixing Problems   Example: Jar A contains 50% alcohol.  Jar B contains 80% alcohol.  You want 20mL of 60% alcohol.  How much do you use from each jar?

Put a check in the box if you understand this step. 
□ Let x = mL from jar A. 
□ Then we will use 20-x mL from jar B. 
□ We get 0.5x mL of alcohol from jar A. 
□ We get 0.8(20-x) mL of alcohol from jar B. 
□ Together, we want them to give us 0.6(20) mL of alcohol.
□  So     0.5x + 0.8(20-x) = 0.6(20)
□          0.5x + 16 – 0.8x = 12
□         -0.3x = -4
□         x = 13.3 mL
□  So we use 13.3 mL from jar A and 6.7 mL from jar B.

(2 points) Your turn:  Using the same jars, make 25 mL of a 75% alcohol mixture. 
(2 points) One more time: Jar C contains 30% alcohol.  Jar D contains 90% alcohol.  You want 30mL of 45% alcohol.  How much of each jar do you use? 
(8 points) Now try this: Use jars C and D from the previous problem.  Jar E contains 60 mL of 20% alcohol.  How much do you add to jar E (from jars C and D) to end with 300 mL of 50% alcohol?

10/8 - Precal Test 1 Review worksheet

10/8 - Topics on Friday's Test include:

• Distance and Midpoint formulas
  
• Graphing equations in various forms
• Finding equations of lines, including perpendicular and parallel
• Fraction Busters
• Inequalities in one and two variables (see below)
• Applications (including area and rate problems)

10/8 - PRACTICE FOR TEST 1

10/3 - Help with inequalities: one variable / two variable

9/29 - Video of Kenny solving an Area Model problem 

9/25 - Area Model - "Jezz is Cool" problems:
Solve by factoring.  If unfactorable, use Quadratic Formula
  1.  2x² - 11x + 5 = 0
  2.  4x² + 15 - 4 = 0 
  3.  4x² - 1 = 0
  4.  6x² + 13x - 5 = 0
  5.  x² - 2x - 24 = 0
  6.  -2x² + 4x - 1 = 0
  7.  -100x² + 200x - 100 = 0
  8.  (EC) Draw area model for 2x³ + 3x² - 7x - 4

9/21 - Fraction Busters Help

9/20 - Fraction Busters - Skillz that Killz Problems (solve for x):
   Tell if the solution is real, imaginary, or does not exist.
   1.   1/(2x) - 5/x + 2/3 + 1/(3x) + 2/5 = 1
   2.   x²/4 - x/2 + (3x + 1)/7 = 0
   3.   x(x - 4)/17 - x²/4 = 100
   4.   2/sin(x) + 3/4 - π/sin(x) = 0  

9/19 - Fraction Busters - Timmy's Face Problems (Solve for x):
   Tell if the solution is real, imaginary, or does not exist.
   1.   8/(15x) - 20/x = 7
   2.   π/10 - 2/π + 1 = 1/x
   3.   5x/2 - 4/7 + 5 = x
   4.   10/(2x) + 14/(11x) = 0
   5.   16/(πx) + 2x = 0
   6.   29(x+2)/(11x) = 0

9/10 - Exponents help:
   1. See Exponents videos in "Algebra Review"
   2. Do practice problems in "Algebra Review"
   3. Visit Exponents page at Purple Math