Competitive Math for Middle School

Competitive Math for Middle School

Algebra, Probability, and Number Theory

Contents

1 Algebra 1
Part 1 Linear Equations 1
Part 2 Cross Multiplication 6
Part 3 Systems of Equations 8
Part 4 Exponents and Roots 13
Part 5 Simplifying Radical Expressions 21
Part 6 Proportions 23
Part 7 Inequalities 28
Part 8 Counting Numbers 31
Part 9 Sequences and Series 32
Part 10 Distance, Rate, and Time 36
Part 11 Rates 38
Part 12 Unit Conversion and Analysis 42
Part 13 Percentages 45
Part 14 Mixtures 48
Part 15 Polynomial Expansions 50
Part 16 Equivalent Expressions 53
Part 17 Factoring 54
Part 18 Special Factorizations 59
Part 19 The Quadratic Formula 60
Part 20 Solving for Whole Expressions 65
Part 21 Infinite Series 66
Part 22 Sets 70
Part 23 Mean, Median, Mode, and Range 74

Solutions Manual 76
Part 1 Linear Equations 76
Part 2 Cross Multiplication 82
Part 3 Systems of Equations 84
Part 4 Roots and Exponents 89
Part 5 Simplifying Radical Expressions 94
Part 6 Proportions 95
Part 7 Inequalities 100
Part 8 Counting Numbers 104
Part 9 Sequences and Series 105
Part 10 Distance, Rate, and Time 110
Part 11 Rates 113
Part 12 Unit Conversion and Analysis 119
Part 13 Percentages 120
Part 14 Mixtures 123
Part 15 Polynomial Expansions 124
Part 16 Equivalent Expressions 129
Part 17 Factoring 130
Part 18 Special Factorizations 135
Part 19 The Quadratic Formula 137
Part 20 Solving for Whole Expressions 142
Part 21 Infinite Series 144
Part 22 Sets 146
Part 23 Mean, Median, Mode and Range 147

2 Counting and Probability 151
Part 1 Basic Probability 151
Part 2 Basic Counting 155
Part 3 Multiple Events 157
Part 4 Orderings 160
Part 5 Dependent Events 162
Part 6 Subsets 168
Part 7 Organized Counting 169
Part 8 Permutations and Combinations 171
Part 9 Expected Value 176
Part 10 Weighted Average 178
Part 11 Generality 180

Solutions Manual 183
Part 1 Basic Probability 183
Part 2 Basic Counting 185
Part 3 Multiple Events 187
Part 4 Orderings 189
Part 5 Dependent Events 192
Part 6 Subsets 200
Part 7 Organized Counting 202
Part 8 Permutations and Combinations 206
Part 9 Expected Value 211
Part 10 Weighted Average 212
Part 11 Generality 214

3 Number Theory 219
Part 1 Basic Number Theory 219
Part 2 Counting Factors, GCF, LCM 224
Part 3 Bases 229
Part 4 Modular Arithmetic 231
Part 5 Divisibility Tricks 235

Solutions Manual 237
Part 1 Basic Number Theory 237
Part 2 Counting Factors, GCF, LCM 239
Part 3 Bases 243
Part 4 Modular Arithmetic 247
Part 5 Divisibility Tricks 252

Index 255