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Enochs Pre-AP SM3 Summer Assignment 2017-18
Mrs. Christina Rubalcava
Enochs High School
Email: [email protected]
Phone: (209) 492-6300
Schoology Classroom Code: JCFN7-TFMNB
(login to your schoology account, click courses,
click join and type in the code)
Mrs. Rubalcava’s class materials:
- 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.
In 2017-18 school year, Pre-AP SM3 classes will be taught by Mrs. Dodds & Mrs. Rubalcava.
Both teachers require the same Summer Assignment. However, in order to acquire more
information specific to each teacher, please see below.
Mrs. Karolin Dodds
Enochs High School
Email: [email protected]
Phone: (209) 574-1719
Website: http://calccore.blogspot.com/
Mrs. Dodds’s Class Material:
- 2” Math Only Binder with Graph & Regular Paper,
- Pen, Pencil, eraser, highlighter,
- TI-83 Plus Graphing or scientific calculator.
Notes, assignments, & handouts will be organized
& saved in the Math Binder. Your binder will be your
best resource for studying & preparing for any Quiz
or Test.
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:
TAKE THE SUMMER ASSIGNMENT VERY SERIOUSLY!
The first Test in this class is at the end of The First Week of School, and it will cover the content standards assigned
in the “Summer Assignment Packet.” and there are NO RETAKES! This Test contains Free Response Questions
without a calculator; this means you are required to show the mastery of essential skills covered in this packet.
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Pre-AP Secondary Math III (SM3) Summer Assignment
Mrs. Karolin Dodds & Mrs. Christina Rubalcava
These problems must be completed on binder paper & be Ready to Turn in on the First Day of School.
Note: you must offer legible & legitimate work that supports your answer.
Use the offered resources to refresh your memory & re-learn the required skills.
Positive, Negative, & Rational Exponents
Simplify without using a calculator!
1] 08x 2]
25 3] yx 214 4]
325x 5]
7
3
x
x 6]
3
1
2
1
x
x 7]
3
2
6
5
xy
x y 8]
321
2323
cba
cba
9] 2
1
9 10] 5
3
32 11]
36
3 5
4
3
x y
x y
12] 2
1
4
6
25
9
x
x 13]
1
3125
64
14] 32 5 4
15] 8 216x y
16] 9454 yx 17]
9
3
4
23
12
15
9
8
x
yx
y
yx
18] 2841752 19] yy 5018
Solve for x without using logarithm.
20] 1000
110 x
21] 322 x 22] 6432 x
23] 162
1
x
24] 927 x 25]
4 125 4
16 5
x
Add, Subtract, & Multiply Polynomials
Perform the given operations and write the answer in standard form.
1] 45363 22 xxxx 2] 12753 22 xxx 3] 2 2 3 24 3 3 2 6 4y y y y y
4] 14 32 xx 5] mkmk 32 32 33 6] 245 yx 7] 22 35 x 8] 3
2x
9] 332 mk 10] 2 2x x 11] 43 2 2 xxx 12] 2
4 3x 13] 2
5x
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Factor Polynomials
Factor each polynomial expression completely.
1] xx 205 3 2] 3532 xxx 3] 169 2 y 4] 2216 x
5] 643 y 6] 16249 2 kk 7] 278 3 m 8] 156 2 yy
9] 210 2 12m m 10]
22 32 yxyx 11] 2 23 2a ab b 12] 22 246 xxx
13] yyy 25204 23 14] xxx 14162 23 15] xx 243 4 16] 203252x
17] 5 3 23 2 6x x x 18]
22 5 3x x 19] 24 25
3 3x
Solving Equations Algebraically
Solve each equation. Do Not use Calculator!
1] xxx 682534 2] 25124353 kkk 3] 5
4
3
2x 4]
6
1
4
1
3
1 xx
5] 4 5
2 43
xx
6]
2
1
4
5
3
1
kk 7] 31056 x 8] 27252
5
3x
9] 52 2 4 3 1x 10] 33 40 2 17x 11] 96124 4
3
x 12] 5
32 21 85x
Solving Equations by Variety of Methods
Solve each Equation using the Recommended Method. Do Not use Calculator!
Factoring: 1] 063 2 xx 2] 372 2 xx 3] xx 12182 2 4] 2 1 7 2x x x
Quadratic Formula: 5] 23 10 5x x 6] 0423 2 xx 7] 132 2 xx 8] 422 xx
Completing The Square: 9] 03102 xx 10] xx 1033 2 11] 216243 2 xx 12] 0232 xx
Extracting The Root: 13] 15217322
x 14] 21
5 123
x 15] 2
5 7 6 141x
Solve each equation using your method of choice. Should you check for extraneous solutions!
16] xx 3230 17] 327 xx 18] 1462 xx 19] 2 8 2 2 1x x
20] 3 30 2x x 21] 2 8 3 2x x
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Solving Absolute Value Equations
Solve each absolute value equation. Do Not use Calculator!
1] 4 2 5 9 3x 2] 1892
3x 3] 7 3 10 2x 4] 3 2 4 5x x
Operations with Complex Numbers
Write the sum or difference in standard form. 1] ii 4332 2] ii 932
3] 5 3 2 9i 4] 8157 2 i 5] 33 25 8 9
Write the product in standard from. 6] ii 31 4 7] 3 5 4 2i i 8] 4 6 5i i
Multiply each complex number with its conjugate & write the result in standard form.
9] i65 10] 1 2 i 11] 4 3i
Write each complex number in standard form.
12] 7
2i 13]
i
i
3
2 14]
i
i
2 15]
i
i
42
3
16]
6
3 i
Solve using quadratic Formula. 17] 1942 xx 18] 23 8 19 5x x
The examples below show how to write the solution to an inequality in interval notations.
Also, interval notations are used to express the domain, range, increasing, & decreasing intervals of a function.
Interval Notation Inequality
1,2 Set of all real #s x such that 1 2x
1,2 Set of all real #s x such that 1 2x
1, 2 Set of all real #s x such that 1 2x
1, 2 Set of all real #s x such that 1 2x
1, Set of all real #s x such that 1x
1, Set of all real #s x such that 1x
Set of all real #s x such that
Real Number Line Graphs
−∞ ∞
-5 -4 -3 -2 -1 0 1 2 3
−∞ ∞
, 3 1,
-5 -4 -3 -2 -1 0 1 2 3 −∞ ∞
, 3 1
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Solving Linear Inequalities
Solve each Inequality algebraically & write the solution in Interval Notation.
1] 86 13 xx 2] 7 23 5 x 3] 3 1
1 14
x 4] 2444625 xx
5] 3 2 2 3
26 8
x xx
6] 7382 x 7]
7 12 2
2 2x 8] 1
3
25
2
3
xx
Graphing Functions and Analyzing their Details.
1] 12 xy 2] xxf4
3)(
3] 2x 4] 3y
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: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
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Enochs Pre-AP SM3 Summer Assignment 2017-18
5]
11 4
2y x 6] 2 xy
7] 412 xy 8] 12 xy
9] 35 xy 10] 542 xxy
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: .
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:
.
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Enochs Pre-AP SM3 Summer Assignment 2017-18
11] 642 2 xxy 12] 2
3 6 6y x
13] 16)1()3( 22 yx
14]
1 32
1 12)(
2 xxx
xxxf 15]
4 , 138
3 , 1
2 , 51
)(2 xxx
x
xx
xf
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: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
Zero(s): .
y-intercept: .
Domain: .
Range: .
Increasing Intervals:
.
Decreasing Intervals:
.
Max/Min Values:
.
.
PAGE 8
Enochs Pre-AP SM3 Summer Assignment 2017-18
DayTwo
DayOne
At thebeginning
For 7-8, write as a single fraction.
Sequences/Functions
Determine if the pattern given is linear, exponential, quadratic, or neither. Next, give the recursive & explicit equations.
1.
Type of Sequence: ___________________ Recursive Rule: __________________ Explicit Rule:___________________
2.
Type of Sequence: ___________________ Recursive Rule: __________________ Explicit Rule: ____________________
3. Describe the pattern of change or rate of change for a linear, exponential, and a quadratic function.
Linear-
Exponential-
Quadratic-
4. Which type of function grows the fastest?
Fraction Operations (Answers in Reduced Form)
1. 2x5
6x∙5
8 2.
7
9n∙5n
8n 3.
4x2
10÷
3𝑥2
4x 4.
8x3
3x÷
6
7𝑥3
5. 5
6+
4
9 6.
7
15−
3
10 7.
5
6x+
3
10x2 8.
5
14𝑥2−
4
6x
Figure 1 Figure 2 Figure 3 Figure 4
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Enochs Pre-AP SM3 Summer Assignment 2017-18
vertex:________________
x-intercepts:___________
y-intercepts:___________
stretch or compress:_______
vertex:________________
x-intercepts:___________
y-intercepts:___________
stretch or compress:_______
Quadratic Functions
Use each function to identify the vertex, intercepts, vertical stretch, and graph it.
1. 2 10 24y x x 2. 3 3y x x 3. 22
3 63
y x
vertex:________________
x-intercepts:___________
y-intercepts:___________
stretch or compress:_______
Write the equation in vertex form.
5. 2 6 9y x x 6. 2 7 1y x x 7. 22 12 9y x x
Inverse Functions
Find the inverse of the function, graph both the original function and its inverse on the graph provided.
1. 1
( ) 32
f x x
Find the inverse of the given function.
2. 2 2f x x 3. 5 1f x x
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Enochs Pre-AP SM3 Summer Assignment 2017-18
A
B C
1
3
Absolute Value Functions
Graph the absolute value function and write it as a piecewise function.
1. Absolute Value: 1 2f x x 2. Absolute Value: ( ) 4f x x
Piece-Wise: ( )f x { Piece-Wise: ( )f x {
Right Triangle Trigonometry
Use the figure to write the following trigonometric ratios.
1. sin( )A 2. cos( )A 3. tan( )A
4. sin( )B 5. cos( )B 6. tan( )B
Solve the right triangles (list all side and angle measures for the triangle).
7. 8.
8. 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 to how high up the building the ladder is to the nearest hundredth of a foot.
X Y
12
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Radian & Degree Measure
Write the radian measure of the angle given in degrees.
1. 122° 2. 50° 3. 270° 4. 0° 5. 1°
Write the degree measure of the angle given in radians.
6. 𝜋
2 7.
2𝜋
3 8. π 9.
3𝜋
4 10.
9𝜋
4
For problems 11 & 12, find the arc length and sector area in degrees. Give EXACT answers.
11. 12.
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Enochs Pre-AP SM3 Summer Assignment 2017-18
You are advised to use the next few pages of examples to help refresh your memory or relearn the
essential mathematical skill that you may have not fully mastered.
Simplifying Radicals
Solving Absolute Value Equations
Factoring
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Solving Equations by Factoring
Multiplying Rational Expressions
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Dividing Rational Expressions
Adding & Subtracting Rational Expressions
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Multiplying Monomials
Dividing Monomials
Law of Exponents
Multiplying Polynomials
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Graphing a Piecewise Function
Greatest Integer Funtion
Solution graph
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Enochs Pre-AP SM3 Summer Assignment 2017-18
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 2017-18
Nine Basic Funcitons of Algebra
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Enochs Pre-AP SM3 Summer Assignment 2017-18
Complex Numbers:
The complex number system contains a number, denoted i , such that 2 1i .
Every complex number can be written in standard form a bi .
PAGE 20
Enochs Pre-AP SM3 Summer Assignment 2017-18
Logarithmic Rules
Composition of Fucntions:
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