SAT II 数学-Level 1

PART I. ABOUT THE SAT MATH LEVEL 1 TEST 1 Chapter 1 Test Basics / 3 About the Math Level 1 Test / 3 The Level 1 vs. Level 2 Test / 4 Chapter 2 Calculator Tips / 7 On the Day of the Test / 8 Chapter 3 Diagnostic Test / 9 Answer Key / 25 Answers and Solutions / 25 PART II. MATH REVIEW 37 Chapter 4 Algebra / 39 Evaluating Expressions / 41 Order of Operations / 41 Fractions / 41 Simplifying Fractions / 41 Least Common Denominator / 42 Multiplying Fractions / 44 Using Mixed Numbers and Improper Fractions / 44 Variables in the Denominator / 45 Percents / 46 Converting Percents to Decimals / 46 Converting Fractions to Percents / 47 Percent Problems / 47 Exponents / 48 Properties of Exponents / 48 Common Mistakes with Exponents / 49 Rational Exponents / 50 Negative Exponents / 51 Variables in an Exponent / 51 Real Numbers / 52 Vocabulary / 52 Properties of Real Numbers / 53 Absolute Value / 56 Radical Expressions / 57 Roots of Real Numbers / 57 Simplest Radical Form / 58 Rationalizing the Denominator / 58 Conjugates / 60 Polynomials / 60 Vocabulary / 60 Adding and Subtracting Polynomials / 61 Multiplying Polynomials / 61 Factoring / 62 Quadratic Equations / 64 Quadratic Formula / 65 Solving by Substitution / 66 The Discriminant / 67 Equations with Radicals / 67 Inequalities / 68 Transitive Property of Inequality / 69 Addition and Multiplication Properties / 69 “And” vs. “Or” / 69 Inequalities with Absolute Value / 70 Rational Expressions / 71 Simplifying Rational Expressions / 71 Multiplying and Dividing Rational Expressions / 71 Adding and Subtracting Rational Expressions /72 Solving Equations with Rational Expressions / 73 Systems / 74 Solving by Substitution / 74 Solving by Linear Combination / 75 No Solution vs. Infinite Solutions / 76 Word Problems with Systems / 78 Chapter 5 Plane Geometry / 80 Undefined Terms / 81 Lines, Segments, Rays / 83 Angles / 85 Measures of Angles / 85 Supplementary and Complementary Angles / 86 Vertical Angles / 87 Linear Pairs of Angles / 88 Triangles / 89 Types of Triangles / 89 Sum of Interior Angles and Exterior Angles / 90 Medians, Altitudes, and Angle Bisectors / 92 Congruent Triangles / 93 Isosceles Triangles / 95 Triangle Inequality / 96 Pythagorean Theorem / 97 Special Right Triangles / 98 Parallel Lines / 100 Polygons / 101 Types of Polygons / 102 Perimeter / 103 Sum of the Interior Angles / 103 Sum of the Exterior Angles / 104 Special Quadrilaterals / 105 Similarity / 106 Ratio and Proportion / 106 Similar Triangles / 107 Circles / 109 Chords / 109 Tangents / 110 Arcs and Angles / 111 Circumference / 113 Arc Length / 114 Area / 116 Area Formulas / 116 Area vs. Perimeter / 118 Area Ratio of Similar Figures / 119 Figures That Combine Numerous Shapes / 119 Chapter 6 Solid Geometry / 122 Vocabulary for Polyhedra / 123 Prisms / 124 Distance Between Opposite Vertices of a Rectangular Prism / 126 Cylinders / 127 Pyramids / 129 Cones / 130 Spheres / 133 Volume Ratio of Similar Figures / 134 Chapter 7 Coordinate Geometry / 135 Plotting Points / 136 Midpoint / 138 Distance / 138 Slope / 140 Slope of Parallel and Perpendicular Lines / 141 Equations of Lines / 141 Horizontal and Vertical Lines / 142 Standard Form / 142 Point-Slope Form / 143 Slope-Intercept Form / 143 Determining x- and y-Intercepts / 145 Circles / 145 Parabolas / 147 Graphing Inequalities / 150 Graphing Absolute Value / 151 Chapter 8 Trigonometry / 153 Right Triangle Trigonometry / 153 Relationships Among Trigonometric Ratios / 156 Secant, Cosecant, Cotangent / 156 Cofunction Identities / 158 Inverse Functions / 159 Special Right Triangles / 160 Trigonometric Identities / 161 Chapter 9 Functions / 163 Functional Notation / 164 Functions vs. Relations / 167 Graphing Functions / 169 Composition of Functions / 169 Identity, Zero, and Constant Functions / 170 Determining the Maximum or Minimum / 170 The Roots of a Quadratic Function / 172 Inverse Functions / 173 Rational Functions / 175 Higher-Degree Polynomial Functions / 176 Exponential Functions / 178 Chapter 10 Data Analysis, Statistics, and Probability / 180 Counting Problems / 181 Probability / 183 Mean, Median, Mode / 184 Data Interpretation / 186 Chapter 11 Number and Operations / 188 Invented Operations / 189 “In Terms Of” Problems / 190 Sequences / 190 Arithmetic Sequences / 191 Geometric Sequences / 192 Logic / 194 Number Theory / 196 PART III. SIX PRACTICE TESTS 199 Practice Test 1 / 201 Answer Key / 216 Answers and Solutions / 216 Diagnose Your Strengths and Weaknesses / 222 Practice Test 2 / 225 Answer Key / 240 Answers and Solutions / 240 Diagnose Your Strengths and Weaknesses / 246 Practice Test 3 / 249 Answer Key / 264 Answers and Solutions / 264 Diagnose Your Strengths and Weaknesses / 270 Practice Test 4 / 273 Answer Key / 288 Answers and Solutions / 288 Diagnose Your Strengths and Weaknesses / 295 Practice Test 5 / 297 Answer Key / 312 Answers and Solutions / 312 Diagnose Your Strengths and Weaknesses / 319 Practice Test 6 / 321 Answer Key / 338 Answers and Solutions / 338 Diagnose Your Strengths and Weaknesses / 345