SAT MATH PREP. Introduction Danny Pham [email protected] Graduated from California State University in Los Angeles Hobbies include watching Professional.

SAT MATH PREP

Introduction

• Danny Pham• [email protected]• Graduated from California State University in Los Angeles

• Hobbies include watching Professional League of Legends, reading Japanese Comics, and Cooking

Class Schedule• Weekly

Week 1 – Numbers and OperationWeek 2 – Algebra and Geometry IWeek 3 – Algebra and Geometry IIWeek 4 – Statistics and ProbabilityWeek 5 – Review

• Daily Class BreakdownReview Homework and Quiz (25 minutes)Lecture (65 minutes)Quiz (30 minutes)[Everything here is tentative]

Class Set Up• Power Points, Homework and Quiz Answers will all be

posted online• Email will be sent out how to access all of these on

Monday• Homework and Quizzes will be graded and there will be a

Final Grade at the end• The more effort you put in, the more successful you’ll be

SAT Math Format• 3 sections broken down into 20/18/16 questions to be

done in 25/25/20 minutes• Total of 54 questions with only 44 having the ¼ penalty for

being incorrect• 10 Student Response (Grid-in) Problems

Today’s Topic – Numbers and Operations

1. Basic Strategies

2. Definitions

3. Translating Word Problems

4. Basic Math

5. Logic

6. Sets

7. Counting Techniques

8. Sequence and Series

Basic Strategies I• Read each Question Carefully

• Circle the Question and Underline Clues

• Example: In a class of 78 students 41 are taking French, 22

are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

Basic Strategies II• Use Calculator whenever possible• Process of Elimination/Brute Force• Example:

Of the following, which is greater than ½ ?A. 2/5 B. 4/7 C. 4/9 D. 5/11 E. 6/13

Definitions I• Numbers

Definition II• Prime numbers – 2,3,5,7,11,13,…• Even numbers – 0, 2, 4, 6, …. , 2k, ….• Odd numbers – 1, 3, 5, 7, ….. , 2k + 1, ….• Consecutive Numbers –

1,2,3,4 or 7,8,9,10 or 2,4,6,8 or 5,10,15,20• Factors – Numbers that can be divided into another

number; Factors of 12 : 1,2,3,4,6,12• Multiples – Multiples of a given number are numbers that

can be divided by that number with remainder;Multiple of 7: 7, 14, 21, 28, 35, …

• Numerator/Denominator – Top and Bottom of a FractionReciprocal – Flip the Top and Bottom of a Fraction.

Division Algorithm• When “a” is divided by “b”, it can be written as

where x is the quotient, r is the remainder and 0• Example:

If k is divided by 7, the remainder is 6. What is the remainder if k+2 is divided by 7?

• • • •

Translating Word ProblemsAdd Subtract Multiply Division Equal

Sum Difference Product Quotient Is

Increased by Decreased by Times Each Was

More Than Less Than Double/Twice Share Equally Has

Total Fewer Than Each Every Are

Together How Many More

In all Per Will Be

Combined How Much is Left

Of Out of Gives

Change Percent Yields

Basic Math I• Fractions?• Ratio – Relationship between two entities expressed

using “to”, :, and as a fraction• Example:

3 dogs to 4 cats, 6 dimes : 1 marble, $3/lbs• Unit Conversion Example:

Michael is making wind chimes for a fundraiser. He can make one wind chime every 10 minutes. How many wind chimes can he make from now until the fundraiser starts in 3 hours?

Basic Math II• Proportion – Equation relating two Fractions/Ratios• Example:

The ratio between the length of a box to its width is 5:2. If the length of the box is 15 inches, what is its width?

• • Use Cross Multiplication•

•

Basic Math III• Decimal – Decimals can be obtained by dividing the

numerator by denominator in fractions• Percent – Per hundred which means divide by hundred• Example: 30% means 30/100 or .30• Scientific Notation – A way to write big numbers as a

multiple of 10Example: 12345 could be written as

• When re-writing from Scientific Notation to Standard, positive exponent means move the decimal that many times to the right and negative means move that many times to the left.

Basic Math IV• Exponents – The number of times by which a number

multiplies itselfExample

• Rules for Multiplying and Dividing numbers with the same base and different exponent

• Multiply – Add the exponentDivide – Subtract the exponent

• Example:

Basic Math V• Zero exponent for any base except 0 is equal to 1

Example:

• When a number with an exponent is raised to another exponent, the two exponent are multiplied

• Example:

• Use Calculator

Sets I• Sets – Sets are list of numbers that are primarily

organized in brackets• Example : A{2, 4, 6, 8} , B{4, 8, 12, 16}• Union – A set collecting all units of each set

Example : {2, 4 , 6, 8, 12, 16}• Intersection – A set collecting only the common units

Example : {4, 8}• Subset – A smaller set made from a bigger set

Example C{4, 8} C is a subset of A• Complement – If a subset contains some units from a

bigger set, the complement would be a set that contains the rest.

Sets II• Example:

In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

A. 6 B. 15 C. 24 D. 33 E. 54

Logic• Definitions:• And – Must meet both Conditions• Or – Must have at least one Condition• Exclusive Or – One or the other• Counter-Example – One example to prove any statement

to be false• If—Then Statements – Includes a Hypothesis and

Conclusion: If P then Q.• Converse – If Q then P• Inverse – If not P then not Q• Contrapositive – If not Q then not P.

Logic II• Example:

All of Kay’s brothers can swim.

If the statement above is true, which of the following must also be true?

(A) If Fred cannot swim, then he is not Kay’s brother.

(B) If Dave can swim, then he is not Kay’s brother.

(C) If Walt can swim, then he is Kay’s brother.

(D) If Pete is Kay’s brother, then he cannot swim.

(E) If Mark is not Kay’s brother, then he cannot swim.

Logic III• Example:

The set  consists of all multiples of 6. Which of the following sets are contained within ?

I.The set of all multiples of 3

II.The set of all multiples of 9

III.The set of all multiples of 12

(A) I only

(B) II only

(C) III only

(D) I and III only

(E) II and III only

Counting Techniques I• Permutation – A way by which a set of things can be

arranged. Order matters so the number of thing in each set is decreased by 1 upon selection.

• Example 1:Five people are running in a race. How many different ways can the people be placed at the end of the race?

• Example 2:• Five people are running in a race. How many different

ways can first, second, and third be placed?

Counting Techniques II• Combination – A way to select things out of another group

and order doesn’t matter.• Example – • 12 kids are working on a project. 2 kids are designated to

buy materials for the project. How many different pairs of kids can be chosen to buy the materials?

• , • Calculator

Sequence and Series I• A Sequence is an Ordered List of Numbers defined by a

Function with Domain in Natural Numbers• Example: 5,12,19,26,….

• Arithmetic Sequence – Sequence that have a common difference “d” between each term

• General Formula: • Geometric Sequence – Sequence that have a common

ratio “r” between each term• Example: 4,16,64,256,…• General Formula:

Sequence and Series II• Example Problem:

-20, -16, -12, -8…

In the sequence above, each term after the first

is 4 greater than the previous term. Which of the

following could NOT be a term in the sequence?

(A) 0

(B) 200

(C) 440

(D) 668

(E) 762

Sequence and Series III• Series – Summation of all terms in a Sequence or up until

a certain point• Arithmetic Series : • Example – Add 1 – 100• Finite Geometric Series: • Infinite Geometric Series: