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* Solve counting problems using the Multiplication Principle.
* Solve counting problems using permutations involving n distinct objects.
* Solve counting problems using combinations.
* Find the number of subsets of a given set.
* Solve counting problems using permutations involving n non-distinct objects.
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* Calculate geometric probabilities
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* Use summation notation.
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* Use the formula for the sum of an infinite geometric series.
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* Use an explicit formula for an arithmetic sequence.
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* Write the terms of a sequence defined by a recursive formula.
* Use factorial notation.
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Let a = maximum distance = 507.4 million miles
e = eccentricity = 0.0489
c = focal radius
a^2 = c^2 + b^2
b = semi-minor axis
0.0489^2 = c^2/507.4^2 + b^2/507.4^2
c = 25 million miles
Minimum distance = a - c = 507.4 - 25 = 482.4 million miles
So the closest distance Jupiter comes to the sun is 482.4 million miles.
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* Graph parabolas with vertices at the origin.
* Write equations of parabolas in standard form.
* Graph parabolas with vertices not at the origin.
* Solve applied problems involving parabolas.
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This document discusses calculating the surface area of prisms and cylinders. It provides formulas for finding the lateral area and total surface area of prisms and cylinders. For prisms, the lateral area is calculated as the perimeter times the height, and the total surface area adds the lateral area and twice the area of the bases. For cylinders, the lateral area uses the circumference times the height, and the total surface area adds the lateral area and twice the area of the circular bases. Examples are provided to demonstrate calculating the lateral and total surface areas of specific prisms and cylinders.
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* Classify three-dimensional figures according to their properties
* Calculate the volumes of prisms and cylinders
8.2 The Hyperbola
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* Write equations of hyperbolas in standard form.
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* Recognize graphs of common functions.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Graph functions using compressions and stretches.
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1) Polynomial equations solved by factoring
2) Equations with radicals where radicals are eliminated by raising both sides to a power
3) Equations with rational exponents where both sides are raised to the reciprocal power
4) Equations quadratic in form where an algebraic substitution is made to transform into a quadratic equation
5) Absolute value equations where both positive and negative solutions must be considered.
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- A function is a relation where each input has a single, unique output
- The domain is the set of inputs and the range is the set of outputs
- Functions can be represented by ordered pairs, graphs, or equations
- The vertical line test identifies functions as those where a vertical line intersects the graph at most once
- Intercepts occur where the graph crosses the x or y-axis
9.6 Binomial Theorem
The document discusses the binomial theorem, which provides a formula for expanding binomial expressions of the form (a + b)^n. It gives the formula for finding the coefficient of the term containing b^r as nCr. Several examples are worked out applying the binomial theorem to expand binomial expressions and find specific terms. Factorial notation is introduced for writing the coefficients. The document also discusses using calculators and Desmos to evaluate binomial coefficients. Practice problems are assigned from previous sections.
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13.2 Independent & Dependent Events
* Identify events as independent or dependent
* Calculate the probabilities of independent and dependent events
9.5 Counting Principles
* Solve counting problems using the Addition Principle.
* Solve counting problems using the Multiplication Principle.
* Solve counting problems using permutations involving n distinct objects.
* Solve counting problems using combinations.
* Find the number of subsets of a given set.
* Solve counting problems using permutations involving n non-distinct objects.
13.1 Geometric Probability
* Calculate geometric probabilities
* Use geometric probability to predict results in real world situations.
9.4 Series and Their Notations
* Use summation notation.
* Use the formula for the sum of the first n terms of an arithmetic series.
* Use the formula for the sum of the first n terms of a geometric series.
* Use the formula for the sum of an infinite geometric series.
* Solve annuity problems.
9.3 Geometric Sequences
* Find the common ratio for a geometric sequence.
* List the terms of a geometric sequence.
* Use a recursive formula for a geometric sequence.
* Use an explicit formula for a geometric sequence.
9.2 Arithmetic Sequences
* Find the common difference for an arithmetic sequence.
* Write terms of an arithmetic sequence.
* Use a recursive formula for an arithmetic sequence.
* Use an explicit formula for an arithmetic sequence.
9.1 Sequences and Their Notations
* Write the terms of a sequence defined by an explicit formula.
* Write the terms of a sequence defined by a recursive formula.
* Use factorial notation.
8.4 Summary of the Conic Sections
Let a = maximum distance = 507.4 million miles
e = eccentricity = 0.0489
c = focal radius
a^2 = c^2 + b^2
b = semi-minor axis
0.0489^2 = c^2/507.4^2 + b^2/507.4^2
c = 25 million miles
Minimum distance = a - c = 507.4 - 25 = 482.4 million miles
So the closest distance Jupiter comes to the sun is 482.4 million miles.
8.3 The Parabola
* Graph parabolas with vertices at the origin.
* Write equations of parabolas in standard form.
* Graph parabolas with vertices not at the origin.
* Solve applied problems involving parabolas.
12.2 Surface Area of Prisms and Cylinders
This document discusses calculating the surface area of prisms and cylinders. It provides formulas for finding the lateral area and total surface area of prisms and cylinders. For prisms, the lateral area is calculated as the perimeter times the height, and the total surface area adds the lateral area and twice the area of the bases. For cylinders, the lateral area uses the circumference times the height, and the total surface area adds the lateral area and twice the area of the circular bases. Examples are provided to demonstrate calculating the lateral and total surface areas of specific prisms and cylinders.
12.1 Volume of Prisms and Cylinders
* Classify three-dimensional figures according to their properties
* Calculate the volumes of prisms and cylinders
8.2 The Hyperbola
* Locate a hyperbola’s vertices and foci.
* Write equations of hyperbolas in standard form.
* Graph hyperbolas centered at the origin.
* Graph hyperbolas not centered at the origin.
* Solve applied problems involving hyperbolas.
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Circle Designs
- 1. → → → → → → → → → → → → → → → → → → → → or