Probability + Trigonometry Equations
Systems of Equations & Absolute Value
Exponents, Radicals & Trinomials
Factoring, Trigonometry, Inverse Trigonometry
Graphing parabolas. From an equation, create a table of values, identify the x and y-intercepts, graph
100
What is the fraction used for probability?
Probability =
(# of favorable events)/(# of total possible events)
100
|-18 * 3| = ?
|-18 * 3|
= |-54|
= 54
100
Simplify:
(4a5) (8a2)
(4a5) (8a2)
= (4 * 8)(a5 * a2)
= 32a5+2
= 32a7
100
Maya has determined that she needs to use tangent in her problem. Which fraction should she use to create her equation? (Use Hypotenuse, Adjacent, and Opposite)
Opposite/Adjacent
SOH CAH TOA
100
Identify the x and y-intercepts
x - intercepts: (-1,0) & (3,0)
y - intercept: (0, -3)
200
Bag 1 Contains 2 red candies, 3 green candies, and 1 purple candy
What's the probability of pulling out a purple candy? That is, what is P(Purple Candy)?
1/6 or 0.1667 or 16.67%
200
On a graph, where do I find the solution of a system of equations?
It is the coordinate points of where they intersect (cross) each other.
200
Simplify:
(x+1)(x+2)
(x+1)(x+2)
= x2 + 3x + 2
200
Factor
x2 + 4x - 12
(x + 6)(x - 2)
200
Identify the a, b, and c terms. Why is c important for graphing?
y = x2 - 3x - 18
a = 1
b = -3
c = -18, which is the y-intercept (0.-18)
300
What ratio do you use to solve for the missing side (x)?
What's the equation?
Tangent Ratio
tan(22) = x/16
300
What is the solution to the following system of equation?
y = 3x
2x +3y = 33
2x + 3(3x) = 33
2x + 9x = 33
11x = 33
x = 3
y = 3(3)
y = 9
Solution: (3,9)
300
Simplify:
(4a3b) (3a2b-8)
(4a3b) (3a2b-8)
= (4 * 3)(a3 * a2)(b*b-8)
= 12a3+2b1-8
= 12a5b-7
=(12a5)/b7
300
Factor
2x2 + 5x - 7
(2x + 7)(x - 1)
Use t-chart and generic rectangles
300
What is the vertex for the equation
y = x2 - 6x - 18
a = 1, b= -6, c = -18
Axis of Symmetry:
x=-b/2a = -(-6) / 2(1) = 3
y = (3)2 - 6(3) -18 = 9 - 18 - 18 = -27
Vertex: (3,-27)
400
A spinner has 6 spaces. If you spin it 5 times, how many different outcomes are possible?
Fundamental Counting Principle:
6*6*6*6*6 = 7776 different possible outcomes
400
What is the solution to the following system of equation?
2x - 3y = -18
5x +3y = 39
2x - 3y = -18
5x + 3y = 39
-----------------
7x = 21
x = 3
5(3) +3y=39
15 +3y = 39
3y = 24
y = 8
Solution: (3, 8)
400
What is the Quadratic Equation?
x = [-b +/- sqrt(b2-4ac)]/2a
400
What is the missing angle (x) in degrees?
SOH CAH TOA
x = Sin-1 (8/11)
x is approximately 46.66 degrees
400
Find the equation from the table/graph in standard form
Identify x-intercepts as (1,0) & (5,0)
(x - 1)(x - 5) by Zero Product Property
y = x2 - 6x + 5
Check y-intercept (0,5) matches equation ✅
y= x2 - 6x + 5 or y = (x - 3)2 -4
500
Bag 1 contains 2 red candies, 3 green candies, and 1 purple candy
Bag 2 contains 2 red candies, 2 green candies, and 2 purple candies
What's P(Green from Bag 1 and Purple from Bag 2)?
Use Multiplication Rule because of "AND"
3/6 *2/6
= 1/2 * 1/3
= 1/6 = 0.1667 = 16.67%
500
Solve and graph the Absolute Value Inequality
|6x+8| < 10
-10 < 6x+8 < 10
-18 < 6x < 2
-3 < x <1/3
(Mr. Tao will graph solution)
500
Simplify:
Sqrt(5) * Sqrt(60)
(Mr. Tao need to write this)
Sqrt(5) * Sqrt(60)
= Sqrt(5) * Sqrt(5*22*3)
= Sqrt(52*22*3)
=5*2 Sqrt(3) = 10 Sqrt(3)
(Mr. Tao need to write this)
500
Solve for side x using Trigonometry
SOH CAH TOA
tan(22) = 7 / x
x = 7/tan(22)
x is approximately 17.33 meters
500
Tell me the equation in standard form, if the x-intercepts are (-1,0) & (4.0) and the y-intercept is (0,4)
x-intercepts are (-1,0) & (4,0)
Graph is negative, because it opens down
y = -(x+1)(x-4) by ZP
y = - (x2 - 3x - 4)
So, y = - x2 + 3x + 4 which matches the y-intercept of (0,4)