Enochs Pre-AP SM3 Summer Assignment SM3 Summer... · 2019-05-22 · PAGE 3 Enochs Pre-AP SM3 Summer...
Transcript of Enochs Pre-AP SM3 Summer Assignment SM3 Summer... · 2019-05-22 · PAGE 3 Enochs Pre-AP SM3 Summer...
PAGE 1
Enochs Pre-AP SM3 Summer Assignment 2019-20
Mrs. Christina Rubalcava
Email: [email protected]
Phone: (209) 492-6300
Mrs. Rubalcava’s Class Material:
- Graph-ruled notebook (at least 2),
- Math binder or section of a binder,
- Colored pencils, pencils/erasers, pens,
- Highlighters & Pen tip whiteboard marker
- Graphing or scientific calculator.
All notes, which include important definitions,
formulas, & examples shown in class should be
done in your notebook. The teacher has the
discretion to perform random notebook checks
for a grade.
Mrs. Dodds and Mrs. Rubalcava will teach Pre-AP SM3 classes during 2019-20 school year. Both teachers
require the same Summer Assignment. You can find additional resources for the summer assignment
by logging into Schoology, clicking “courses”, clicking “join”, & then typing in the code: 8MZQM-FZB9J.
Mrs. Karolin Dodds
Email: [email protected]
Phone: (209) 574-1719
Mrs. Dodds’s Class Material:
- 2 inch 3-ring Binder for Math ONLY.
- Pen, Pencil, Eraser, & color pens or highlighters.
- TI-83 Plus Graphing or scientific calculator.
- Date & name all your notes & assignments.
- File related notes, assignments, handouts, &
returned quizzes together by date they were done.
- Have enough graph & lined paper in your binder.
- Your best resource for studying & preparing for any
Quiz or Test is your Math Binder.
In fairness to all, calculators with a computer algebraic system (CAS) will NOT be used on Quizzes or Tests.
Be noted that you will be taught to do calculations in this class with & without a calculator;
thus, you will be Quizzed and Tested in both ways.
SUMMER ASSIGNMENT:
We strongly suggest that you take this assignment seriously. If you have difficulty with a question,
DO NOT SKIP IT – RESEARCH IT. That research can be in the form of a textbook, a parent, a friend,
free on-line help, or your old math notebook. You may also refer to the websites below as a resource.
In addition, you can study the examples offered at the last few pages of this summer assignment.
Virtual Math Lab http://www.wtamu.edu/academic/anns/mps/math/mathlab/
Algebra Help https://www.wyzant.com/resources/lessons/math/algebra
Purple Math http://www.purplemath.com/
Khan Academy https://www.khanacademy.org/
MathBits.com http://mathbits.com/
The Math Page http://www.themathpage.com/
Math Open Reference http://www.mathopenref.com/
You must offer legible & legitimate work that supports your answer. The Summer Assignment will be
collected & graded based on completion & correctness on the 1st day of school, August 12th.
Points will be deducted if the packet is turned in late. You will be tested on the topics from the Summer
Assignment on Monday, August 19th. There will be NO RETAKES for a Poor Test Score, so seek out all
the help that you require prior to this test. The test will assess your mastery & retention of the
prerequisite math skills needed to succeed in Pre-AP SM3.
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Rules of Exponents Simplify without calculator. Answers MUST be in terms of Positive Exponents.
1] 08x 2]
32 5 4 3] 214x y
4] 3
25x 5] 4
5 23x y 6] 7
3
x
x
7]
1
2
1
3
x
x
8] 3
2
6
5
xy
x y 9]
2 3 2
31 2
3a b c
a b c
10]
1
481 11] 5
3
32 12] 2
1
4
6
25
9
x
x
13]
1
3125
64
14] 4 954x y 15] 6
4
25
49
x
y
16]
36
3 5
4
3
x y
x y
17] 18 50y y 18] 3 2 3
4 9
8 15
9 12
x y x y
y x
Solve for x without using logs or calculator. “SHOW WORK SUPPORTING YOUR ANSWER”
21] 3 12
8
x
x
22] 3 116
32
x 23] 6432 x
24] 4
27 25
125 9
x
25] 4 1
25 4
16 5
x
26] 3 232 8x x
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Add, Subtract, & Multiply Polynomials Write your answer in Standard Form, 2ax bx c .
1] 2 23 5 7 12x x x 2] 2 23 2 4 5x x x 3] 14 32 xx
4] 2 2 3 24 3 3 2 6 4y y y y y 5] 22 3 4x x x 6] 2
7x
7] 2
5 4x y 8] 2
4 3x 9] 7 7x x
10] 2 2x x 11] 3 32 4 2 4k m k m
Factor Polynomials Apply various factoring techniques to Factor Completely.
12] 212 18x x 13] 3532 xxx 14] 169 2 y 15] 24 25
9 16m
16] 16249 2 kk 17] 156 2 yy 18] 22 5 3x x 19] 24 12 9x x
20] 22 246 xxx 21] 5 3 23 5 15x x x 22] xxx 14162 23 23]
2 23 2a ab b
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Solving Equations Do Not use Calculator! “SHOW WORK SUPPORTING YOUR ANSWER”
1] 4 3 5 2 8 6x x x 2] 1 1 1
3 4 6x x 3]
4 52 4
3
xx
4] 1 5 1
3 4 2
k k 5] 6 5 10 3x 6]
32 25 7 2
5x
7] 52 2 4 3 1x 8]
3
44 12 96x 9]
5
32 21 85x
Solving Absolute Value Equations “SHOW WORK SUPPORTING YOUR ANSWER”
10] 2 6 4x 11] 4 2 5 9 3x 12] 1892
3x
13] 7 3 10 2x 14] 3 2 4 5x x 15] 4 3 6 2x
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Enochs Pre-AP SM3 Summer Assignment 2019-20
1. Solve by Factoring: “SHOW WORK SUPPORTING YOUR ANSWER”
1] 063 2 xx 2] 372 2 xx
3] xx 12182 2 4] 24 9 3 2x x x
2. Solve using Quadratic Formula:
5] 132 2 xx 6] 0423 2 xx
7] 24 12 9x x 8] 422 xx
3. Solve by Completing the Square:
9] 03102 xx 10] xx 1033 2
11] 216243 2 xx 12] 0232 xx
Various Methods used to Solve Quadratic Equations
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Enochs Pre-AP SM3 Summer Assignment 2019-20
4. Solve by taking the Square Root:
1] 15217322
x 2] 21
5 123
x 3] 2
5 7 6 141x
Solve Square Root Equations: Make sure to check for extraneous solutions!
4] xx 3230 5] 327 xx
6] 2 8 2 2 1x x 7] 2 8 3 2x x
Add, Subtract, & Multiply Complex Numbers a bi Write the result in Standard Form, a bi .
10] ii 4332 11] ii 932 12] 5 3 2 9i
13] 8157 2 i 14] 33 25 8 9 15] ii 31 4
16] 3 5 4 2i i 17] 4 6 5i i
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Multiply each complex number by its conjugate.
1] i65 2] 1 2 i 3] 4 3i
Rationalize & write each complex number in standard form, a bi . Meaning 5 3
4 2i and NOT
5 6
4
i
4] 7
2i 5]
i
i
3
2
6] 6
3 i 7]
i
i
42
3
Solve using quadratic Formula & write your answer in standard form, a bi .
8] 1942 xx 9] 23 8 19 5x x
Solving Linear & Compound Inequalities Write the final answer in Interval Notations. Example: ,5
10] 3 2 2 3
26 8
x xx
11] 2444625 xx 12] 7382 x
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Enochs Pre-AP SM3 Summer Assignment 2019-20
A
B C
12
Right Triangle Trigonometry Find the trigonometric ratios of the given triangle. If possible, reduce your answers.
1] sin( )A 2] cos( )A 3] tan( )A
4] sin( )B 5] cos( )B 6] tan( )B
Solve the given right triangles (find the measure of all sides & angles for each triangle). You may use a calculator
when necessary & round your answers to the hundredth.
7] 8]
9] A 24-foot ladder forms a 65 angle with the ground. The top of the ladder rests against a building. Draw a diagram
to find how high up the building the ladder is to the nearest hundredth of a foot.
Radian & Degree Measure
Write the radian measure of the angle given in degrees.
10] 135° 11] 60° 12] 270° 13] 120° 14] 30°
Write the degree measure of the angle given in radians.
15] 𝜋
2 16]
2𝜋
3 17] 𝜋 18]
3𝜋
4 19]
5𝜋
6
For problems 11 & 12, find the arc length and the area of the sector. No calculator, give EXACT answers.
20] 21]
x y
12
B
z
5
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Graphing Functions & Analyzing their Details. Follow these instructions.
Do not use a calculator. Graph neatly & show all the important details of each specific graph.
“x-intercepts” are also known as, “zeros” or “roots”.
Calculate x-intercept & y-intercept Algebraicaly & make sure they agree with what your graph displays.
Write x & y-intercepts as points (x, 0) and (0, y).
Write domain, range, increasing or decreasong intervals in Interval Notations. Example: , 4
Min/Max value refers to the Highest or Lowest y-value on the entire graph.
1] 12 xy 2] xxf4
3)(
3] 2x 4] 3y
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
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y-intercept: .
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Range: .
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.
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.
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y-intercept: .
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.
Decreasing Intervals:
.
Max/Min Values:
.
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Enochs Pre-AP SM3 Summer Assignment 2019-20
5] 24
3y x 6] 2 3 6y x
7] 412 xy 8] 12 xy
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
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.
Decreasing Intervals:
.
Max/Min Values:
.
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
.
Increasing Intervals: .
Decreasing Intervals: .
Max/Min Values: .
9] 35 xy
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Enochs Pre-AP SM3 Summer Assignment 2019-20
10] 542 xxy 11] 642 2 xxy
12] 2
2 1 6y x 13] 2 2 9x y
14] 2 2
19 25
x y
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
.
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y-intercept: .
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.
Decreasing Intervals:
.
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.
.
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y-intercept: .
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.
Decreasing Intervals:
.
Max/Min Values:
.
.
Zero(s): .
y-intercept: .
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Range: .
.
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Enochs Pre-AP SM3 Summer Assignment 2019-20
15] 16)1()3( 22 yx 16]
2 22 3
116 4
x y
17]
1 32
1 12)(
2 xxx
xxxf 18]
4 , 138
3 , 1
2 , 51
)(2 xxx
x
xx
xf
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
.
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Enochs Pre-AP SM3 Summer Assignment 2019-20
You DO NOT need to print these pages; they are for your reference only!
You are advised to use the next few pages of examples to help refresh your memory or relearn the
essential mathematical skills that you may have forgotten or not fully mastered.
Simplifying Radicals
Solving Absolute Value Equations
Law of Exponents
Multiplying Monomials
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Factoring
Multiplying Polynomials
Dividing Monomials
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Graphing a Piecewise Function
Greatest Integer Funtion
Solution graph
Solving Equations by Factoring
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Quadratic Function (Polynomial of degree 2): Shape of the graph of a quadratic function is a Parabola. Three parabolas are shown below with important points labeld.
The graph of a quadratic funciton: - can open either upward or downward
- always has a vertex which is either the maximum or minimum
- always has exactly one y-intercept
- can have 0, 1, 2 x-intercepts
* A parabola is symmetric about a line through the vertex called the axis of symmetry.
* A quadratic function can be written in Transformation Form which is 2
f x y a bx h k
* In Transformation Form, the vertex is ,h
kb
and line of symmetry is h
xb
.
* A quadratic function can be written in Polynomial Form which is 2 f x y ax bx c
* In Polynomial Form, the vertex is , 2 2
b bf
a a
and line of symmetry is 2
bx
a
.
Changing from Polynomial Form to Transformation Form.
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Nine Basic Funcitons of Algebra
Complex Numbers: The complex number system contains a number, denoted i , such that 2 1i .
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Every complex number can be written in standard form a bi .
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Enochs Pre-AP SM3 Summer Assignment 2019-20
Logarithmic Rules
Composition of Fucntions: