New Generation of ENOCHS EXCEL General Exam Tables Segment 2: EXCEL into higher GP with ENOCHS!
Pre-AP Pre-Calculus Mrs. Karolin Dodds Enochs High School ...
Transcript of Pre-AP Pre-Calculus Mrs. Karolin Dodds Enochs High School ...
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Pre-AP Pre-Calculus Mrs. Karolin Dodds Enochs High School Summer Assignment
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.
**Mastering Algebra Skills is Very Crucial Prior to Learning Pre-Calculus & Calculus Concepts**
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
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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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
, , , Rational Expressions
Simplify. 1] 12
962
2
xx
xx 2]
49
2142
23
y
yyy 3]
2
3 2
3
3 5 15
m m
m m m
Multiply or divide the given rational expressions. Make sure your final answer is simplified.
4]
2 2
2
18 3 12
3 36 1
x x y
xy x
5]
3 2 2
3 2 3
2 4 4
2 8
y y y y
y y y
6]
2
2 2
8 16 2 8
3 2 3 2
y y y
y y y y
7]
3 2 2 2
2 2
2 4 4
x y y x y xy y
x x x x
8]
3
3 2
12 8
8 6 18
y y
y y y
9]
2 2
2
2 8 4
3 12 9 18
x x x
x x x
Add or subtract the given rational expressions. Make sure your final answer is simplified.
10]
212 6
2 2
x x
x x
11]
3 1 5
8 3 12x x x 12]
9
61
3
322
xxxx
13] 5 3
3 3
x x
x x
14]
35
2y
y
Simplify each complex fraction.
15]
yx
xy
xy
yx
2
22
22
4
2
16]
2
2
2
6 98
3
x y
x xxy
x
17]
22
11
11
yx
yx
18] 1
ba
a
aa
19] 1
1 1
a b
20]
3
32
5
132
x
x
Rationalize each denominator.
21] 2
3 22]
2
5 3 23]
10
3 20 24]
4
3 11 25]
6 3
6 3
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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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
Solving Absolute Value & Rational 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
Solve each rational equation. Do Not use Calculator!
5] xxx 2
12
3
82
6] xxx 2
14
6
3
7]
6 9 1
1 4x x
8]
2
10 4 5
22 x xx x
9] 11
5
1
22
x
x
x
x 10]
6
1
2128
42
xx
x
xx 11]
2410
3211
6
1
4
22
xx
x
x
x
x
x
12] 6 2 2
44 1
x x
x x
13]
x
x
xx
3
1
3
2
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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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
Solving Linear, quadratic, & cubic Inequalities
Use the given graphs to write the solution of each inequality in Interval Notation.
1] 2 6y x x 2] 3 23 4 12y x x x
a. Solve 2 6 0x x a. Solve 3 23 4 12 0x x x
b. Solve 2 6 0x x b. Solve 3 23 4 12 0x x x
Solve each Inequality algebraically & write the solution in Interval Notation.
3] 86 13 xx 4] 7 23 5 x 5] 3 1
1 14
x 6] 2444625 xx
7] 3 2 2 3
26 8
x xx
8] 7382 x 9]
7 12 2
2 2x 10] 5284 2 xx
11] 1 3
25
2
3
xx 12] 3552 2 xx 13] 22 6 8 0x x 14] 02422 23 xxx
The examples on the next page show how to write your solution to inequalities in interval notations.
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Graphing Functions and Analyzing their Details.
1] 12 xy 2] xxf4
3)(
3] 2x 4] 3y
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
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
, 2 Set of all real #s x such that 2x
, 2 Set of all real #s x such that 2x
, Set of All real #s.
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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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: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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11] 642 2 xxy 12] 2
3 6 6y x
13] 213 xxf 14] 16)1()3( 22 yx
15]
1 32
1 12)(
2 xxx
xxxf 16]
4 , 138
3 , 1
2 , 51
)(2 xxx
x
xx
xf
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
Zero(s): .
y-intercept: .
Domain: .
Range: .
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Simplifying Radicals
Solving Absolute Value Equations
Factoring
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Solving Equations by Factoring
Multiplying Rational Expressions
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Dividing Rational Expressions
Adding & Subtracting Rational Expressions
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Multiplying Monomials
Law of Exponents
Multiplying Polynomials
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Graphing a Piecewise Function
Dividing Monomials
Greatest Integer Funtion
Solution graph
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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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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Nine Basic Funcitons of Algebra
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 .
M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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M r s . D o d d s M a s t e r Y o u r A l g e b r a S k i l l s
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Logarithmic Rules
Composition of fucntions: