Open Ended
Create a number sequence in which the first term is 4.
ANS) 4, 6, 8, 10, 12, 14, 16.
d=2
Writing in Math
Use the information about science on page 190 to explain how writing equations from
patterns is important in science. Explain the relations
Open Ended
Choose values for x and y. Then find (x+y)2.
ANS) ( x+ y ) 2 = ( 4+ 9) 2 = ( 2+3 ) 2 = 52 = 25
Writing in Math
Use the information about the worlds tall structures on page 554 to explain how you can
use radicals to determine how far a person ca
Open Ended
Write a quadratic equation with no real solutions. Explain how you know there are no
solutions.
ANS) 5x2 + 3x + 8 = 0
b2 - 4ac = -32 - 4(5)(8)
-9-160
-169 no real roots
We know that there is no real root because the discriminant is negative.
Wr
Open Ended
Create a compound interest problem that could be solved by the equation below.
A = 500[1 + (0.07/4)]4(6)
ANS) You invested $500 at a rate of 7% for 6 years compounded quarterly.
Writing in Math
Use the information about Weblogs on page 528 to e
Annaleya Hamilton
Pre-Calculus: Unit 4: Lesson 5: Apply
November 1, 2016
Describe how you can use a double-angle formula or a half-angle formula to
derive the formula for the area of an isosceles triangle. Use a labeled sketch to
illustrate your derivatio
Annaleya Hamilton
Pre-Calculus: Unit 4: Lesson 4: Apply
November 1, 2016
You can write the sum and difference formulas for cosine as a single equation:
cos (u v) = cos u cos v sin u sin v. Explain why the symbol is used on the
left side, but the symbol is
Chapter 1 Limits and Their Properties
1. Let f ( x ) =
2x 3 1
.
2x 4
(a) Find the domain of f .
(b) Complete the following table.
x
1.92
1.98
1.999
2
2.01
2.1
2.15
f
(c) Use your result from part (b) to evaluate lim
x 2
2x 3 1
.
4 2x
(d) How close to 2 sh
Annaleya Hamilton
PreCalculus: Unit 7: Lesson 5: Apply
November 22, 2016
1. Use a graphing utility to graph the polar equation shown below.
r = cos 5 + n cos , 0
For the integers n = -5 to n = 5. As you graph these equations, you should see
the graph cha
Annaleya Hamilton
PreCalculus: Unit 7: Unit Project
November 22, 2016
Annaleya Hamilton
PreCalculus: Unit 7: Unit Project
November 22, 2016
2
3
Annaleya Hamilton
4
PreCalculus: Unit 7: Unit Project
November 22, 2016
Annaleya Hamilton
7
PreCalculus: Unit
Annaleya Hamilton
PreCalculus: Unit 8: Unit Project
November 29, 2016
Annaleya Hamilton
PreCalculus: Unit 8: Unit Project
November 29, 2016
Annaleya Hamilton
PreCalculus: Unit 8: Unit Project
1
2
November 29, 2016
3
Annaleya Hamilton
PreCalculus: Unit 8:
Annaleya Hamilton
PreCalculus: Unit 8: Lesson 4: Apply
November 29, 2016
Part A
limit of this function as x> c is 0. If a rational function has a non-zero denominator for x = c the
the limit of that function can be found by direct substitution. Therefore,
Annaleya Hamilton
PreCalculus: Unit 8: Lesson 3: Apply
November 22, 2016
The notation lim x>5 f(x) = 12 means that f(x) became close to the unique number as x
approached 5 from either side, the limit of f(x) as x approached 5 is 12.
f(0) and f(2) are both
Annaleya Hamilton
PreCalculus: Unit 8: Lesson 1: Apply
November 22, 2016
In your own words, explain what is meant by a proof by mathematical induction.
A proof of mathematical induction is to prove a statement, theorem, or formula
that is asserted about e
Annaleya Hamilton
PreCalculus: Unit 8: Lesson 2: Apply
November 22, 2016
1. In your own words, explain how to form the rows of Pascals triangle.
The first & last number are always 1. Every number in between is the sum of the
numbers immediately above it.
Annaleya Hamilton
1
PreCalculus: Unit 7: Lesson 3: Apply
November 16, 2016
Write a short paragraph explaining why parametric equations are useful.
Parametric equations allow you to graph the complete position of an object over time. For
example, parametri
Annaleya Hamilton
PreCalculus: Unit 7: Lesson 2: Apply
November 16, 2016
Explain how the equation of a hyperbola and an ellipse are related. Point out any
similarities and differences between the two. Graph the equations of a hyperbola
and ellipse with th
576 Chapter 7 Linear Systems and Matrices
7 Chapter TCSt See www.0alcChat.c0m for worked-out solutions to odd-numbered exercises.
Take this test as you would take a test in class. After you are nished, check your
work against the answers given in the ba
Annaleya Hamilton
1
PreCalculus: Unit 7: Lesson 4: Apply
November 16, 2016
Write a short paragraph explaining the differences between the rectangular
coordinate system and the polar coordinate system.
The polar coordinate system and the rectangular coordi
Annaleya Hamilton
Unit 5: Lesson 5: Apply
November 11, 2016
The famous formula shown below is called Eulers formula, after the Swiss
mathematician Leonhard Euler (1707-1783).
ea + bi = ea(cos b + i sin b)
This formula gives rise to the equation ei + 1 = 0
Annaleya Hamilton
PreCalculus: Unit 6: Lesson 3: Apply
November 15, 2016
In your own words, describe the difference between a matrix in row-echelon form
and a matrix in reduced row-echelon form.
Row echelon form: Have to have a zero below the leading ones
Annaleya Hamilton
1
Precalculus: Unit 6: Lesson 1: Apply
November 15, 2016
Write a short paragraph comparing the three methods of solving systems
of equations. Describe the advantages and disadvantages of each method.
Graphing is the easiest method to sol
Annaleya Hamilton
Precalculus: Unit 6: Lesson 2: Apply
November 15, 2016
When using Gaussian elimination to solve a system of linear equations, explain
how you can recognize that the system has no solution. Give an example that
illustrates your answer.
Wh
Annaleya Hamilton
Precalculus: Unit 7: Lesson 1: Apply
November 16, 2016
Explain what each of the following represents, and how equations (a) and (b) are
equivalent.
(a) y = a(x - h)2 + k, a 0
Quadratic: Standard (Vertex) Form
(b) (x - h)2 = 4p(y - k), p
Annaleya Hamilton
Unit 5: Lesson 1: Apply
November 7, 2016
Can the Law of Sines be used to solve a right triangle? Write a short paragraph
explaining why it can or cannot be used. If it can be used, explain how to use it.
Is there an easier way to solve t
Annaleya Hamilton
Pre-Calculus: Unit 5: Lesson 2: Apply
November 7, 2016
Describe how the Law of Cosines can be used to solve the ambiguous case of
the oblique triangle ABC, where a = 12 feet, b = 30 feet, and A = 20. Is the result
the same as when the La
Annaleya Hamilton
1
Pre-Calculus: Unit 5: Lesson 3: Apply
November 8, 2016
In your own words, state the difference between a scalar and a vector.
Give examples of each.
Vectors have magnitude and direction (Ex: Displacement), scalars only have
magnitude a