# PreCalc Chapter 1

Ch 1 Topics from Algebra

Ch 1.1 Real Numbers

Definitions of Real Numbers, Rational Numbers, Integers, Fractions, Absolute Values

Writing  |3-e| and |e-3| without Absolute Value ;
Writing 513 in Scientific Form ;
Writing 930000000 in Scientific Form ;
Writing 0.0000000852 in Scientific Form ;
Writing  -7.854×10-8 in Decimal Form;

Simplifying 5³;
Simplifying (-1/3)³;
Simplifying  (-1/3)4;
Does  -3²=(-3)² ?
Does  2(3)4=2(81)=162 or Does 2(3)4 =64 = 1296 ?
Simplifying a0;
Simplifying 5-2;
Simplifying  1/8-3;
Simplifying 5253;
Simplifying  (24)3;
Simplifying  25 / 22;
Simplifying  5√0;
Simplifying  4√16;
Simplifying  3√27;
Simplifying  3√-8;
Simplifying  4√-16;
Does  (3+4)2 = 32+ 42?
Does  √a2+b2 = a+b?
Does  √32+42 = 3+4?
Does  √a+b = √a+√b?
Does  √9+16 = √9+√16?
Simplifying 272/3;
Simplify  95/2;
Simplifying (-4b3)(1/6b2)(-9b4)

Simplifying  6-3;
Simplifying  (-2)-4;
Simplifying  (1/2)-5;
Simplifying  3-532;
Simplifying  2-142;

Simplifying  a-3/b-4;
Simplifying  1 / 5p-7;
Simplifying  a4 / (a3)2;
Simplifying (5x3)2 / x-4

Simplifying  (x-4y3)-5;
Simplifying  (24z6 / 8z4)-3;
Simplifying (2x4)5· x-7

Simplifying  (6x4 y0)·(4x0);
Simplifying  (2xy2z6 / 3x5y6z4)-2;
Simplifying (x4y)5 (x2y)-3 / x7 y6

Simplifying  (4a2b / a3b2)(5a2b / 2b4);
Simplifying  <2x2y-5)(6x-3y)(1/3x-1y3;
Simplifying  (3x1/2)(-2x5/2);
Simplifying  (c-4 / 16d3)3/4;
Writing √(a+Vb) as an Exponent ;
Writing (4x)3/2 as a Radical ;
Simplifying √1/7 ;
Simplifying 4V81r5s8 ;
Simplifying √1/3x3y ;
Simplifying 5√(3x11y3 /9x2)

Simplifying √(5xy7) √(10x3y3);
Simplifying  3√(2r-s)3;
Simplifying 4√(x-y)4

Ch 1.3 Algebraic Expressions

Polynomial Vocabulary of g(x) = -7x-3x2+2x3

Is 5x+2=7 Expression or Equation ?
Is 5x2-7x=(2x-5) Expression or Equation ?
Identifying Polynomial Vocabulary for 5x3-7x+2 ;
Classify 1 / x+1  as Either a Polynomial or not ;
Classify 3x2+7x7/2 as Either a Polynomial or not ;
Classify 3√x2+7x as  Either a Polynomial or not ;
Classify as √3x5-5/2x6+56 Either a Polynomial or not ;
Simplifying (6x3-2x2+x-2)-(8x2-x-2) ;
Simplifying (3u-1)(u+2)+7u(u+1)(u-1);
Simplifying  6x2yz3-xy2z /xyz;
Simplifying  (√x + √y)2 (√x-√y)2;
Simplifying (x2+x+1)2

Factoring  a2-b2;
Factoring  a3-b3;
Factoring  a3+b3;
Factoring  4u2-2uv;
Factoring  7x2+10x-8;
Factoring  12x2-x-6;
Factoring  x3-25x;
Factoring  125x3-8;
Factoring  2ay2-axy+6xy-3x2

Factoring x4-3x3+8x-24 by Grouping ;
Factoring 8c6+19c3-27

Simplifying  2x2+9x-5 / 3x2+17x+10;
Simplifying  9x2-4 / 3x2-5x+2 ÷ 27x4+8x / 9x4-6x3+4x2 ;
Simplifying  15/x2-9 – 5x/x2-9;
Simplifying  x-4-x;
Simplifying  x2+4x-6 / √x;
Simplifying 7/24 + 5/18

Simplifying  2x+6/x26x+9 + 5x/x2-9 +7/x-3;
Simplifying  y-2 – x-2/ y-2+x-2;
Does 3-2-4-1/ 5-1 = 5/ 32-4 ?
Simplifying Complex Fraction 1/x+h -1/x / h

Simplifying Complex Fraction 2/x+3 / 1+ 3/x

Simplifying Complex Fraction 3/x2+5x / -2/x+5 + 1/x

Simplifying Complex Fraction (1/ m2-m-12 + 1/m+5) / (1/m+3 – 1/m2+m-20)

Rationalizing the Numerator of √t – 4 /  √t + 4;
Rationalizing the Numerator of  √2(x+h)+1  -  √2x+1  /  h;
Simplifying (1-x²)½(2x)-x²(1/2)(1-x²)(-2x)  /  ((1-x²)½

Ch 1.4 Equations

Solving  6(2y+3)-3(y-5)=0;
Solving  -5/3x-9 + 4/x-3 = 5/6;
Solving  6/2x+11 +5 = 5;
Solving 4/5x+2 – 12/15x+6 =0

Solving 2/2x+3 + 4/2x-3 = 5x+6 / 4x2-9 ;
Showing that (3x-4)(2x+1)+5x=6x2-4 is an Identity ;
Are 8x/x-7 = 72/x-7 and x=9 Equivalent Equations ?
Solving C=2πr for r ;
Solving  A=P+Prt for r ;
Solving  for S=2(lw+hw+hl) for h

Solving  x(3x+10)=77 ;
Solving  5x/x-2 + 3/x +2 = -6/x²-2x;
Solving  16x²=49;
Solving  9(x-1)² =7;
Solving  x²-8x+11=0 by Completing the Square
http://www.youtube.com/watch?v=ixonUroW7Gc&list=PL554F9F460401DF50&index=16&feature=plpp_video (Part 2 of the Video)

Solving   4x²+20x+13=0 by Completing the Square;
Solving  x+1/3x+2 = x-2/2x-3 by Cross Multiplying and by using Quadratic Formula ;
Solving  2x²-xy=3y²+1 by using Quadratic Formula ;
Solving  5(x+2)² – 4(x+2)-7 = 0 by using Quadratic Formula

Solving the following Rational Equations
2/x+3 = 1/x
1/2x+6 – 4/x2-4 = 7/x-3
Solving Rational Equation 6/x-3 – 6/x = 18/x2-3x with Infinite Solutions
√(4x-9) =1
-x+√x-4 +6=0
Solving Quadratic Equation f(x)=x2-10x+9 using Factoring and using the Quadratic Formula -b±√b²-4ac / 2a
Using the Discriminant √b²-4ac to Determine the Type of Solutions in Quadratic Equation 3x²-3x+6=0
Solving Equation 5(x-1)+2x=10 using the TI-89 Calculator

Ch 1.5 Complex Numbers

Introduction to Complex Numbers
Solving x²=-16 ;
Simplifying (-5+7i)+(4+9i) ;
Simplifying  (-5+7i)-(2+3i);
Simplifying  (-5+7i)(2+3i);
Simplifying (-5+7i)² ;
Dividing  -5+7i / 2+3i;
Dividing  5+2i / -3+5i;
Simplifying   i5 , i9  , i(4n+1)  , i6  , i10  , i(4n+2)  , i7  , i11  ,  i(4n+3) ,  i4 , i8  , i12  , i4n  ,  i37 ,  i43 ,   ,  i33 ;
Simplifying (-3+√-25)(8-√-36) ;
Finding x and y for 8+(3x+y)i=2x-4i ;
Solving x4=81
Dividing Complex Numbers 2+6i / 6-i
Simplifying i623
Solving 27x4+21x2+4=0

Ch 1.6 Inequalities

Showing Inequalities in Inequality Notation and Interval and Graphing them ;
Solving, Expressing the following Solutions as an Inequality, Graphing and Interval Notation for x+4≥7 ;
-2x>8;
x/2>-1;
x-9≥-12;
7x>-7;
x-9≤-12
Graphing Inequalities x>-3, and Expressing using Interval Notation ;
Graphing Inequalities x≥-3 , and Expressing using Interval Notation ;
Graphing Inequalities x<-3, and Expressing using Interval Notation ;
Graphing Inequalities x≤-3, and Expressing using Interval Notation
Solving and Graphing the following Inequalities, and then Expressing using Interval Notation
x+5>3;
x-7≤-3;
Definition of Absolute Value Inequalities ;
Solving Absolute Value Inequalities ;
Solving and Graphing |x-2|<6 ;
Solving and Graphing |2x-1|≥7 ;
Solving and Graphing 3|2x|-4≤5
Solving |x|<4, Expressing the Solutions as an Inequality, a Graph, and Using Interval Notation ;
Solving |x|>4, Expressing the Solutions as an Inequality, a Graph, and Using Interval Notation
Solving |x-3  / 2|≤ 1, Expressing the Solution as a Compound Inequality, a Graph, and Using Interval Notation
Graphing 5≤x<8 ;
Graphing 2<x<7 ;
Graphing  -1≤x≤2;
Graphing  x≤2;
Solving  x-8>5x+3;
Solving  -2<3+ 1/4 x≤5;
Solving  (6x+5)<(3x-2)(4x+1);
Solving  | 2 / x+8 |<-2;
Solving  | 2 / x+8 |>-2;
Solving  3/ 2x+5≤0;
What does |x|<4 mean ?
What does |x|>4 mean ?
Solving  |3x-7|≥5;
Solving |2x+5 / 3 |<1