MATH C

STUDY GUIDE FOR FINAL EXAM

 

DATE:___________________      TIME:____________

 

 

FORMULAS

 

                            

 

                                                    

 

 

 

 

 

Page

Problem Number(s)

 

Page

Problem Number(s)

p.  91

68

 

p.  487

85,  87

p. 114

31,  33

 

p.  488

102

p. 146

63,  65

 

p. 496

47,  49,  51,  53

p. 193

41a,  43a

 

p. 497

119,  123

p. 194

59

 

p.  515

132

p. 212

126

 

p. 521

37,  39

p. 239

71, 73

 

p.  531

41

p. 239

67

 

p. 542

57, 61

p. 250

13, 15

 

p. 563

27,  31

p. 276

57

 

p. 584

85

p. 285

25,  27

 

p. 584

77,  79

p. 306

25,  31

 

p. 598

69, 71

p. 323

25,  27

 

p. 608

3,  7

p. 335

87,  89,  91,  97

 

p. 610

111,  117

p. 357

39,  53,  55

 

p. 644

19

p. 414

31,  33

 

p. 660

27,  29

p. 423

29,  51

 

p. 671

27,  29

p. 462

9

 

p. 681

1,  3,  11,  13

p. 486

39,  43

 

 

 

 

Additional topics and practice problems

 

Examples:

(1)  Find the determinant                                         (2)  Solve for x: 

 

 

 

 

 

Examples: 

(1)                                                                       (2) 

 

 

 

Examples:  Given .

Find

(1)                                                                     (2) 

 

(3)                                                             (4) 

 

 

 

 

Example:  A principle of $25,000 is invested in an account paying an annual rate of 5%.  Find the amount in the account after 2 years if the account is compounded

(1)    Semiannually

 

(2)   Annually

 

(3)   Monthly

 

Example:  Mrs. Meidinger has only dimes and nickels in her purse.  She has 38 coins in all and worth a total of $2.55.  How many dimes and nickels does she have?

 

 

 

 

Type of Problem:

 

Solve a Quadratic Equation by the “Perfect Square” Method

 

1.  Isolate the x2  term.

2.  Simplify other side, if possible

3.  Square root on both sides, with ±

 

 

 

 

 

Type of Problem:

 

Solve a Quadratic Equation by the “Factoring” Method

 

 

 

1.  Descending order on one side, zero on other side.

2.  Factor one side, bring down zero

3.  Set each factor equal to zero

4.  Solve each new equation for x

 

 

 

 

 

Type of Problem:

 

Solve an Radical Equation

 

 

1.  Isolate the radical

2.  Square both sides

3.  Check the answer, or you’re fried!

 

 

 

 

 

Type of Problem:

 

Simplify or Multiply Rational Expressions

 

 

 

 

 

1.  Factor the numerators

2.  Factor the denominators

3.  Cross out factors (not terms) of one or negative one.

 

 

 

 

Type of Problem:

 

Add or Subtract Rational Expressions

 

1. Find LCD

    Factor denominators

    Multiply each fraction by what you need, top and bottom, to get the LCD

2.  Add (subtract) the tops

     (Distribute, combine like terms)

 

 

 

Type of Problem:

 

Solve a Rational Equation

 

1.  Multiply each term by the whole LCD to get rid of the fractions

2.  Simplify each side separately.

3.  Move all x terms to one side

4.  Move all other terms to other side

5.  Divide by the coefficient of x

6.  Check to be sure the answer won’t make any terms undefined.

 

 

Type of Problem:

 

Simplify a Complex Fraction

 

1.  Multiply each term in the numerator and denominator by the whole LCD to get rid of the little fractions.

2.  Simplify top & bottom separately, then reduce if possible