Prep Street

SAT Study Guide 2011

SAT Math

!Concepts Explained

!Detailed Solutions to The Official SAT Study Guide with Commentary

www.PrepSt.com Your Fast Track to Success

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© 2011 Prep Street Education Services. All rights reserved.

This publication was written by Clement Yip and Jupiter Yue.

Book design, compilation, editing, and formatting by Jupiter Yue.

No part of this publication may be reproduced, stored, or transmitted in any form or by any means (electronic or mechanical, including but not limited to photocopying, recording, or by any information

storage and retrieval system) without prior written permission of the copyright holder.

Although reasonable effort has been taken to ensure the accuracy of the contents of this book, neither the

publisher nor the author assumes any responsibility for any error or omission. Furthermore, neither the

publisher nor the author assumes any liability for any damages resulting from the use of information

contained herein.

All information contained herein is provided for information purposes only. Neither the publisher nor the

author makes any warranties or guarantees either expressed or implied that the information contained

herein will be accurate, complete or current in content, or that the information contained herein will serve

any particular purpose(s).

Prep Street, the street sign logo and the shield logo are trademarks of Prep Street Education Services.

College Board and SAT are registered trademarks of the College Board. SAT Subject Tests, The Official

SAT Online Course, The Official SAT Question of the Day and The Official SAT Study Guide are

trademarks owned by the College Board. College Board has not endorsed and is in no way affiliated with

this publication or Prep Street Education Services.

Published and Distributed by:

Prep Street Education Services

Email: info@prepst.com

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CHAPTER 1

Introduction

! Prep Street SAT Study Guide

Topics covered

Welcome to Prep Street SAT Study Guide. Our SAT Math Study Guide is written by a team of college graduates that have obtained a perfect score on the math portion of the SAT. Because of their SAT scores, they have gone into the nation most prestigious universities. A stellar SAT score can take you really far! The strategy guide consists of two portions. The first portion covers the math concepts that will be tested on the SAT. It contains detailed examples will full color illustrations. We want to make sure that you understand each and every concept and be able to apply them in any situation. In this chapter, we will give you an overview of the SAT and some of our test taking tips.

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CHAPTER 2

Math Concept Review I

! Numbers

Topics covered

This is the first chapter of our math concept review. Take this as a chance to review what you learned from high school. You should be familiar with the following concepts: ! Integers

! Squares and Square Roots

! Fractions and Rational Numbers

! Ratios, Proportions and Percentages

! Sequences

! Word Problems

! Number Lines

! Number Theory – Factors, Multiples and Prime Numbers

! Sets

! Permutations & Combinations

! Logical Reasoning

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CHAPTER 3

Math Concept Review II

! Graphs, Statistics, Probability

Topics covered

In this chapter, we have included a lot of sample questions and answers that you can expect to see on the SAT. You should be familiar with the following concepts: ! Data Interpretation

" Circle Graphs (Pie Charts)

" Line Graphs

" Bar Graphs

" Pictographs

! Statistics

" Arithmetic Mean

" Median

" Mode

" Weighted Average

! Probability

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Data Interpretation You should be familiar with the following different types of graphs:

Circle Graphs (Pie Charts)

You can expect to see the following different types of questions: Q. In Muller High School, every student studies one and only one foreign language.

If there are 8 students studying Latin, what is the total number of students of Muller High

School? A. 4% of the students studying Latin, therefore we can set up an equation regarding the total number of students.

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4%x = 8

4

100x = 8

4x = 800

x = 200

Therefore, there are 200 students in Muller High School.

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Q. How many students study either French or Chinese?

A. 20% of students study French and 4% of students study Chinese, therefore, 24% (20% + 4%) of students study either French of Chinese. Since the total number of students is 200, the number of students who study either French or Chinese is:

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24% " 200

= 48

Line Graphs

Number of Sunny Days in Three Different Cities

You can expect to see the following different types of questions: Q. In that months did each city have the greatest number of sunny days?

A. You can answer this question by looking at the highest point of each curve. Jupster – August Clementi – August Rogera – May

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CHAPTER 4

Math Concept Review III

! Algebra, Functions

Topics covered

Algebra and functions deal with the manipulation of variables and solving of equations.

In this chapter, you should be familiar with the following concepts:

! Algebraic Operations

! Solving Equations

! Inequalities

! Direct and Inverse Proportion

! Functions

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CHAPTER 5

Math Concept Review IV

! Geometry

Topics covered

Geometry deals with different points, lines, and shapes. In this chapter, you should be

familiar with the following concepts:

! Geometric notations

! Points and Lines

! Angles

! Triangles and Special Triangles

! Quadrilaterals

! Areas and Perimeters

! Circles

! Solid Geometry

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CHAPTER 6

Real Problems in Action

! Selected Answers Explained with Commentary

Topics covered

In this chapter, we provide you with detailed answers from 54 selected problems from

CollegeBoard’s The Official SAT Study Guide, Second Edition. The page and question

numbers of each question are marked clearly to facilitate your revision. We have also

labeled the concept tested for each question.

There are 54 math questions on the SAT test, which are arranged in increasing difficulty

in each section. In this chapter, however, we have chosen mostly “medium” and “hard”

questions. We hope that by practicing harder questions, you can consolidate and reinforce

your understanding of the nuances of different concepts.

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The page and question numbers in the section refer to The Official SAT Study Guide,

Second Edition published by CollegeBoard.

Page 398, Question 8 Concept tested: Circles

The radius of the largest circle = radius of A + diameter of C (or diameter of B)

We know that the diameter of a circle is always two times the length of its radius.

The answer is (C).

Page 399, Question 11 Concept tested: Numbers

We can express the integer in terms of n

where 6 is the remainder. We also see that = , and is divisible by 7

Then, we can add 2 on each side

We see that the 1 is the remainder.

The answer is (B).

The Sneaky Method

Another method that works almost every time is to plug in some arbitrary number that

satisfies the conditions set out by the question.

From the question, can be any number that has a remainder of 6 when divided by 7.

It can be 55, 62, 69 etc, which all now we add 2 to all three numbers and find the remainder when divided by 7.

! 57 64 69

! Remainder 1 1 1

All three numbers arrive at the same answer.

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Page 585, Question 16 Concept tested: Linear Equations and their Graphs (A) does not have to be true.

Line k can pass through any point on line l (not necessarily the origin) and still be perpendicular to line l. In the graph below, k does not pass through the origin but is still

perpendicular to l.

(B) is false.

It is impossible for line k to be positive and be perpendicular to line l. To be perpendicular to l, k must have a negative slope.

(C) must be true.

For line k to be perpendicular to line l, it must be negative.

(D) does not have to be true. Line k can have positive or negative x-intercept. In the diagram below, k has a negative x-

intercept but is still perpendicular to l.

x

y

l

k

x

y

l

k

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(E) does not have to be true.

Line k can have positive or negative y-intercept. In the diagram below, k has a positive y-intercept but is still perpendicular to l.

The answer is (C).

Page 585, Question 18 Concept tested: Sequences

The total costs of all shirts:

The total cost of all shirts

= the cost of the first shirt the cost of the shirt at price times number of shirts bought at a price

The number of shirts bought at price is because the first shirt is at price .

The answer is (A).

Price of 2nd shirt

Price of 1st

shirt

Price of 3rd shirt

Price of nth

shirt

x

y

l

k