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

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


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


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


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.


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, 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


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: .


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: .


Simplifying Radicals

Solving Absolute Value Equations

Factoring


Solving Equations by Factoring

Multiplying Rational Expressions


Dividing Rational Expressions

Adding & Subtracting Rational Expressions


Multiplying Monomials

Law of Exponents

Multiplying Polynomials


Graphing a Piecewise Function

Dividing Monomials

Greatest Integer Funtion

Solution graph


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.


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 .


Logarithmic Rules

Composition of fucntions:

Pre-AP Pre-Calculus Mrs. Karolin Dodds Enochs High School ...

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