Exponents and Complex Numbers
i=
i2=
i3=
i4=
i10=
i= square root of -1
i2= -1
i3= square root of 1
i4= 1
i10= -1
List the 6 ways of factoring
1. GCF
2. Quadratic
3. Grouping
4. Difference of Squares
5. Difference of Cubes
6. Sums of Cubes
List the 6 trig ratios (Name or abbreviation)
1. Sine : Sin
2. Cosine: Cos
3. Tangent: Tan
4. Cosecant: Csc
5. Secant: Sec
6. Cotangent: Cot
Write an equation given the following information:
a point (-5,-4) and is parallel to y = 9/5x -4
y= 9/5x +5
Write the inequality/ equation: In order to enter the club, not only do you have to have your id card, you must also be 18 and up.
x>18
Multiply: (5-i)(3+2i)(2+i)
27+31i
Divide: (2v3-13v2+16v +8) / (2v-5)
v2-4v-2 Remainder: -2/ 2v-5
Write the Law of Sins and draw a diagram
Formula: a/Sin A = b/ Sin B = c/ Sin C
Diagram: Couldn't add a picture -> Angle A across from side a, Angle B across from side b, and Angle C across from side C
Is it a function? Domains? Ranges?
(1,7)
(2,-7)
(-9,-7)
(4,3)
(-3,3)
Is it a function: Yes
Domain: {-9, -3, 1, 2, 4}
Range: {-7, 3, 7}
How many solutions are there and how do you know?
-3x = -3 - y
-4 = 3x - y
No solution: Different y-intercept; same slopes
Divide: (6-i) / (1-4i)
10/17 + 23i/17
Factor and Name the Method: 2000x3+54y3
Answer: 2(10x+3y)(100x2-30xy+9y2)
Methods: GCF and Sum of Cubes
Surface area and volume of a Cone and Sphere
Cone: Surface Area- 1/3πr2l; Volume- πr2h
Sphere: Surface Area- 4πr2; Volume- 4/3πr3
Write a polynomial function with the roots : 4, -1, 1
x3 - 4x2 - x + 4
Solve by substitution:
9x + 2y = 21
3x - 3y = -15
(1, 6)
Solve for X: [(3x-2) to the power of 5/2] - 7 = 25
X= 2
Solve for a: 1/a - 7/a2-7a = 1/ a2-7a
a= 15
Alexis baked a round layer cake with three cylindrical layers of equal height. The cake is 9 inches high, and the radii of each of the three layers are 5 inches, 4 inches, and 3 inches, respectively. Calculate the total amount of cake Alexis made.
Alexis made 150π cubic inches of cake.
Graph: - (square root of x+4) -1
Couldn't insert a picture
Solve for p and graph on a number line:
3 (p-2) > 7p - 54
Inequality: 12 > p or p < 12
Number Line: Open circle, on the left side
Yareli recently played the game of her lifetime scoring a record-breaking 30 points for her basketball team. After playing, her arms were sore, so she took a pill containing 600 mgs of Ibuprofen. The half life of the pill of 6 hours. Write an equation that shows the amount left in her body over time and explain what X is.
Option 1: y= 600 * .5 x -> x= # of 6 hour periods
Option 2: y = 600 * .5 x/6-> x= # of hours
Solve for n: 1/ n-2 = n+5/ n3-2n2 + 1/ n3-2n2
*Hint: More than 1 solution
n = 3, -2
Isaiah was sneak-eating Dorito chips in math class one day when he realized he was about to eat a chip that was literally a perfect equilateral triangle. As he paused to marvel at this beautiful mathematical object, he observed that the chip was exactly 5 cms tall. How long were the sides of the chip? (SPECIAL RIGHT TRIANGLE)
Each side of the chip was (10 square root of 3) over 3 cms long (5.77 cm)
Draw the 11 parent functions and write the equation
1. f(x)= |x|
2. f(x)= x2
3. f(x)= x3
4. f(x)= ax
5. f(x)= square root of x
6. f(x)= cubic root x
7. f(x)= 1/x
8. f(x)= 1/x2
9. f(x)= x
10. f(x)= a
11. x= a
Solve for b:
-9|2b +1| > 108
No solution -> an absolute value can not be less than or equal to a negative number