College Panda The College SAT SAT Math Advanced Guide Advanced Guide and Workbook and Workbook 2nd Edition 2nd Edition Copyright © 2020 The Copyright College Panda The College Panda All rights reserved A l l rights reserved. 978-1-7331927-2-9 ISBN: 978-1-7331927-2-9 part of this No part book may this book be reproduced may be reproduced without without written permission from the written permission the author. ‘SAT is aa registered *SAT registered trademark trademark of the College Board, the College which does Board, which n o t endorse does not product. endorse this product.
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/ Introduction Introduction best way The best The to do way to do well on any well on any test is to test is to be be experienced experienced with with the material. Nowhere the material. Nowhere is is this this more than on true than more true on the which is standardized SAT, which the SAT, standardized toto repeat repeat the the same question types same question types again again. The and again.
again and purpose of this The purpose book is this book to teach you the teach you concepts and the concepts and battle-tested approaches you battle‐tested approaches need to know you need know for all these these questions types. If questions types it's If it's n in this o t in not book, it's this book, it’s not on the not on the test. goal is The goal test. The is for every question to be every SAT question be a simple reflex, a simple reflex, something something youyou know know how to handle how to instinctively because handle instinctively because you've seen it so you’ve seen so many many times before.
won’t find any You won't cheap tricks any cheap in this tricks in this book, simply because book, simply because there aren't any there aren’t any that consistently. Don't work consistently. that work Don’t buy buy into idea that the idea into the you can that you improve your can improve your score significantly without score significantly without hard work. hard work Format of the Test Format There are There t w o math are two on the sections on math sections the SAT.
The contains 20 questions The first contains questions to be be done 25 minutes done in 25 without aa minutes without calculator. second contains The second contains 38 questions to be 38 questions be done done in 55 55 minutes and a minutes and permitted. calculator is permitted a calculator Some topics Some only show topics only up in the show up calculator section. the calculator I’ve made section.
I've sure to accurately made sure the practice divide the accurately divide questions practice questions non-calculator and into non-calculator into and calculator components. Read this How to Read How Book this Book For complete understanding, For aa complete understanding, this book is best this book best read from beginning read from beginning to end. That being said, That being each chapter said, each chapter was was be independent written to be written independent of the others as much others as much asaspossible. After all, possible.
After all, you may already you may already be proficient in some be proficient some topics weak in others. topics yet weak to jump others. If so, feel free to jump around, focusing on around, focusing the chapters on the that are chapters that are most relevant to most relevant improvement. your chapters come All chapters with exercises.
come with them. You won’t exercises. Do them won't master the material master the until you material until think through you think the through the questions yourself. que stions yourself.
If you you get stuck on a question, give yourself stuck on a question, give yourself a a few minutes minutes to figure it out. If you’re figure out. If you're still stuck, still stuck, then then look at the look at solution and the solution take the and take time to fully understand the time Then circle understand it. Then the question circle the number question number or make make aa note somewhere so note of it somewhere so that that you you can the question redo the can redo question later.
Revisiting questions later. Revisiting questions you’ve missed is you've missed best way the best improve your way to improve your score. the Author About the About Nielson Phu Nielson graduated from New Phu graduated University, where New York University, where hehe studied studied actuarial He has science. He actuarial science.
perfect obtained perfect has obtained scores on the SAT and scores and on the subject test. math subject the SAT math test. As aa teacher, he has teacher, he helped hundreds has helped students hundreds of students throughout Boston throughout Boston and Hong Kong and Hong perform better Kong perform better on on standardized standardized tests. Although he tests.
Although he continues pursue continues to pursue his interests his education, he interests in education, he is now n o w an engineer in the an engineer Boston area. the Boston area. THE COLLEGE PANDA COLLEGE PAND A Contents Table of Contents 1 Exponents & Radicals Exponents Radicals 7 .r exponents Laws of exponents Laws Evaluating Evalua expressions with ting expressions exponents with expo nen ts Solving equations with exponents Solving equations with exponents Simplifying square roots Simplifying square roots 2 Percent Percent 15 15 change Percent change Percent Compound interest Compound interest Percent word problems Percent word problems 33 Exponential vs Exponential Linear Growth vs. Linear Growth 23 Linear growth and Linear growth decay and decay Exponentiall growth Exponentia growth and decay and decay Positive negative associa and negative Positive and association tion 4 Rates Rates 32 factors Conversion factors Conversion 5 Ratio Proportion Ratio & Proportion 38 38 6 6 Expressions Expressions 44 44 Combining like terms Combining like terms Expansion Expans and factoring ion and factoring Combining, dividing Combining, dividing,, and splitting fractions and splitting fractions 7 Constructing Models Constructing Models 52 8 Manipulating & Manipulating & Solving Equations Solving Equations 57 Common mistakes to avoid Common mistakes avoid isolating variables Tools for isolating variables Strategies for solving Strategies complicated equations solving complicated equations 9 Equation Solving More Equation More Solving Strategies Strategies 71 Matching coefficients Matching coefficients lnfinitely many Infinitely many solutions solutions solutions No soluti ons Clearing denominators Clearing denominators 10 10 of Equations Systems of Systems Equations 78 Substitution Substitution Elimination Elimination Systems with Systems solutions and with no solutions and infinite solutions infinite solutions problems Word problems More complex More comp systems lex systems Graphs of systems Graphs equations systems of equations 4 THE COLLEGE COLLEGE PANDA PANDA 11 Inequalities Inequalities 91 H o w to solve How solve inequalities inequalities Inequality word problems Inequality word problems Graphs of inequalities Graphs inequalities 12 Word Problems Problems 100 13 13 M i n i m u m 8: Minimum Maximum Word Problems & Maximum Problems 109 14 14 Lines Lines 117 Slope and y-intercept Slope and y-intercept Equations of lines: Equations slope-intercept form lines: slope-intercept and point-slope form and form point-slope form Finding Finding the the intersection intersection of two lines t w o lines Parallel and perpendicular Parallel and perpendicular lineslines Horizontal Horizontal and and vertical lines vertica l lines 15 15 Interpreting Interpreting Linear Models Linear Models 126 16 Functions Functions 132 132 What is a What a function? function? When is a function When function undefined? undefined? Composite Composite functions functions Finding Finding the solutions to a the solutions function a function Identifying function graphs Identifying function graphs Function transformations Function transformations 17 Quadratics Quadratics 146 146 Tactics for finding finding the roots roots Completing Completing the the square square The vertex ver tex and vertex form and vertex form The discriminant The discriminant Quadratic models Quadratic models 18 18 Synthetic Synthetic Division Division 161 Performing synthetic division Performing synthetic division Equivalent expressions Equivalent expressions The remainder remainder theorem theorem 19 Complex Complex Numbers Numbers 170 170 20 Absolute Value Absolute Value 174 21 21 Angles Angles 180 180 Exterior angle Exterior angle theorem theorem Parallel Parallel lines lines Polygons Polygons 5 THE COLLEGE PANDA 22 Triangles 187 lsosceles and equilateral Isosceles and equi lateral triangles triangles Right Right triangles triangles Special right triangles Specia l right triangles triangles Similar triangles Similar Parallel Lines and Parallel Proportionality and Proportionality Radians Radians 23 Circles Circles 207 Area and circumference and circumference Arc length length Area of a sector sector Centra l and Central inscribed angles and inscribed ang les Equations Equa tion s of circles 24 Trigonometry Trigonometry 216 Sine, cosine, and tangent cosine, and tangent Trigonometric Trigonometric identities identities Evaluating trigonometric expressions Evaluating trigonometric expressions 25 Reading Data Reading Data 225 26 Probability Probability 234 27 Statistics II Statistics 244 Mean, median, Mean, and mode median, and mode Range Range and standard and standard deviation deviation Histograms dot plots and dot Histograms and plots Word problems involving averages problems involving averages Boxplots Boxplots 28 Statistics Statistics II II 254 Statistical sampling Statistica l sampling Using and Using interpreting the and interpreting line of best fit the line Margin error Margin of error Confidence intervals Confidence intervals Experimental design Experimental and conclusions design and conclusions 29 Volume Volume 267 30 Answers to the Exercises Answers Exercises 272 6 Exponents Ex Radicals ponents & Ra dicals Here are Here are the laws of exponents the laws exponents you should know: you should know: Law Law Example Example xx1z 1 = Xx 331z 1 = 33 F , L \U_ XO = 11 30_ 3D= 11 A 1 111In I 1 111 xX", m 0n 11 · x" = x + 34 35 Z 39 34.
35 = 39 if: x111 _= : xm‐n XIII -II 7 27 Z 34 37 = 34 x" 33 4 (XVII) (x Z _mn )11= 111 x 11111 (32)-l (32)4 =: 38 38 my)!” =: xlllylll xmym (2 , 3)3 Z 23.33 (xy)"' (2 · 3) 3 = 23 · 33 I "I Xm 2 3 23 (~)m (y) =z ;:: w , (~)3 (g) =z ~: 3‐3 W1 '1 1 xA_,-mIn = 7 - _ 2_ 33 -‐44 = _ g xm 34 1 7 CHAPTER 1 EXPONENTS & RADICALS Many students don 't know the difference between ( - 3) 2 and - 32 Order of operations (PEMDAS) dictates that parentheses take precedence. So, ( - 3) 2 = (- 3) · (- 3) = 9 Without parentheses, exponents take precedence: - 32 = - 3 · 3 = - 9 The negative is not applied until the exponent operation is carried through. Make sure you understand this so you don't make this common mistake. Sometimes, the result turns out to be the same, as in : ( - 2) 3 and - 23 Make sure you see why they yield the same result.
EXERCISE1: Evaluate WITHOUT a calculator. Answers for this chapter start on page 272. 10- 8 THE COLLEGE THE COLLEGE PANDA PANDA EXERCISE 2: Simplify EXERCISE Simplify so that your so that answer contains your answer only positive contains only exponents. Do NOT positive exponents.
use a NOT use The calculator. The first ttwo have been w o have been done done for you. Answers for this chapter start this chapter start on page page 272. (2m 3 )2 (3m3)2 EXAMPLE If3H2 EXAMPLE 1: If 3x+2 = y, then then what what is the the value j r in terms value ooff 33x off y ? terms o ? A )y+9 A)y B ) y-- 9 B)y ql C)% D)% 3 Let's avoid Let’s avoid the trouble of finding the trouble finding what Here we what x is.
