McGraw-Hill's SAT II: Math Level 1

by Diehl, John J.

• ISBN13: 9780071456715
• ISBN10: 0071456716
• Edition: 1st
• Format: Paperback
• Copyright: 2005-08-22
• Publisher: McGraw-Hill

Summary

Everything students need to ace the SAT II exams As if taking the SAT I weren't traumatic enough, many colleges and universities require applicants to take one or more SAT II tests to demonstrate their mastery of specific high school subjects. The five books in McGraw-Hill's SAT II series cover tests taken by more than 475,000 students each year. Written by experts in their respective fields, these first-rate preparation guides arm students with everything they need to ace the tests, including: Diagnostic exams that pinpoint relative strengths and weaknesses Numerous full-length sample tests Hundreds of problems with complete solutions Step-by-step reviews of all topics covered in each exam Classroom-tested strategies to help students earn top scores

Author Biography

John J. Diehl teaches mathematics at Hinsdale Central High, Hinsdale, Illinois, and is a member of the AP Statistics Development Committee.

Table of Contents

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