GEAR-UPSAT Prep Workshop

Math SectionClaudette Reep

September 10, 2011

Problems used in this presentation are from “Cracking the SAT 2009 Edition” published by The Princeton Review

A test of “reasoning ability” Not necessarily how “smart” you are 3hrs 45 min 10 sections

◦3 each of Math, Writing, and Critical Reading

◦1 experimental Scored differently than most other tests

What is the SAT?

About the SAT scoring Multiple Choice

◦ Correct = +1 point◦ No answer = 0

points◦ Incorrect = -1/4 point

Grid-Ins◦ Correct = 1 point◦ Incorrect = 0 points

The test is made up of 3 sections◦ Math◦ Writing◦ Critical reading

Scoring range is 200-800 per section of the test.◦ Minimum score is 600◦ Maximum score is

2400

Since it would take 4 incorrect responses to cancel out 1 correct response it makes sense to guess when you can do so reasonably.

There are 5 answer choices for each question. ◦ Consider you can eliminate until you only have 2

choices….◦ Consider you can eliminate until you only have 3

choices….

Ultimately, you must decide what is in your best interest!

To guess or not to guess…..

3 sections, maybe 4 if the experimental is a math◦ 24 multiple choice (25 minutes)◦ 8 multiple choice/10 grid ins (25 minutes)◦ 16 multiple choice (20 minutes)

Four categories◦ Arithmetic◦ Basic Algebra◦ Geometry◦ Basic Algebra II

Math Sections

You may have one, but you don’t have to

One will NOT be provided for you

You may NOT use one with a standard computer keypad◦ Basically any TI83 or TI 84 (pluses, silver edition,

etc.) are ACCEPTABLE◦ TI 90’s are not okay, neither are Voyagers◦ TI Inspires should be fine as long as you have the

84 faceplate

Calculator

You have used one in every math class, please take one to the test!!!!!!

Most teachers will let you check one out the Friday before the test, however you must remember to bring it back first thing Monday morning.

Calculator

Each section of Math on the Sat will begin with the same set of instructions.

The instructions include a few formulas and other information you may need to know to answer some of the questions.

You should learn then instructions before the day of the SAT in order to not wasting valuable time reading/referring to them during the actual test.

Instructions

Integers are numbers that are not fractions or decimals

Even numbers are divisible by 2 (if the last digit is divisible by 2 the entire number is)

Odd numbers are not divisible by 2

The ten digits are:◦ 0,1,2,3,4,5,6,7,8,9

Some basic rules you need to remember:

Factors are numbers that go into a number evenly.

◦ Example: The factors of 6 are 1,2,3, and 6

The number 6 is composite because more than 1 and itself go into it.

The factors of 5 are 1,5 The number 5 is Prime because its only factors are 1 and 5.

Special things about prime numbers◦ 0 and 1 are not prime◦ 2 is the smallest, and only even, prime◦ Not all odd numbers are prime

The most common use of factors is factoring.

Factors

Sum is what you get when you add Difference is what you get when you subtract Product is what you get when you multiply Quotient or Ratio is what you get when you divide Exponents and Powers are the same thing

◦ The number raised to the power is the base Is means = More than can mean + or > depending on the

problem Less than can mean – or < At Least means ≥ No more than means ≤

Key Words

The order of operations matters!

Please Excuse My Dear Aunt Sally is okay to remember, but be careful with the part after the excuse.◦ Parenthesis◦ Exponents◦ Multiply OR Divide from left to right◦ Add OR Subtract from left to right

Order of Operations

You can only add or subtract when you find common denominators

You multiply by doing numerator x numerator OVER denominator x denominator (top x top over bottom x bottom)

You divide by flipping the denominator (bottom) and multiplying the top by this fraction.

Fractions

Multiples are numbers you get when you multiply a number by another number◦Example: Some multiples of 3 are 3,6,9,12,…. Some multiples of 5 are 5,10,15,20,…

The most common use of multiples is in finding least common denominators so that you can add or subtract fractions.

Multiples

Consecutive means one after another◦ Examples of consecutive integers are:

1,2,3 150,151,152 x, x+1,x+2

Consecutive even integers would look like:◦ 2,4,6◦ 10,12,14◦ x, x+2, x+4

Consecutive odd integers would look like:◦ 3,5,7◦ x, x+2, x+4

Consecutive Integers

When you multiply bases you add powers

When you divide bases you subtract powers. (Any negative powers need to go across the fraction bar to become positive)

Exponent Rules

2 3 5( )x x x ( )a b a bx x x

129

3

xx

x

aa b

b

xx

x

46

10 6

1xx

x x

When you have a power to a power you multiply

Special Rules◦ Anything to the zero power is 1.

Exponent Rules (2)

3 5 15( )x x ( )a b abx x

0 1x

These are the favorite quadratic equations on the SAT, according to “The Princeton Review”

Factoring

2 2

2 2 2

2 2 2

( )( )

( ) 2

( ) 2

x y x y x y

x y x xy y

x y x xy y

Example:◦ If 4x + 2 = 4, what is the value of 4x – 6?A. -6B. -4C. 4D. 8

Solving Equations Strategies

Options:

Actually solve by algebra methods and plug into 4x-6

Solve by graphing and then plug into 4x-6

Make the left side look like the 4x-6

Ans= B

Factoring Example 1

1. In the expression k is an integer and k<0. Which of the following is a possible value of k?

A. -13B. -12 C. -6D. 7E. It cannot be determined

from the information given

Is there any number you can eliminate?

What are the possible factors of the quadratic?

Foil these out, what are the possible k values?

2 12x kx

Page 216, correct answer is A

Factoring Example 2 If 2x – 3y = 5, what is

the value of

A. B. 5C. 12D. 25E. 100

Factor the trinomial, think about what one of the factors must be….

5

2 24 12 9x xy y

Page 217, D

Solving Quadratics- Example 1 If , which of

the following is a possible value for x?

A. -7B. -1C. 1D. 3E. 7

The traditional way to solve is to multiply by x and turn into a quadratic.

One possibility is substituting in the answers….

Another is solving by graphing on the calculator….

33 7xx

Absolute Value

For the equations shown above, which of the following is a possible value of x-y?

A. -14B. -4C. -2D. 1E. 14

Solve the top equations (could do so graphically)

Try different combinations

3 8

2 7

x

y

P220 B

Zoe won the raffle at a fair. She will receive the prize money in 5 monthly payments. If each payment is half as much as the previous month’s payment and the total of the payments is $496, what is the amount of the first payment?

A. $256B. $96C. $84D. $16E. $4

Specific Amounts: Guess and Check Method

Is there a good place to start with a guess and check method?

P222, A

The units digit of a two digit number is 3 times the tens digit. If the digits are reversed the resulting number is 36 more than the original number. What is the original number?

A. 26B. 36C. 39D. 54E. 93

Guess and check #2

Page 226, A

If Jayme will be J years old in 3 years, then in terms of J, how old was Jayme 5 years ago?

A. J-8B. J-5C. J-3D. J+5E. J+8

Plugging in numbers to guess and check

Pick any number you want for J. I suggest something larger than 3+5 which is 8; so maybe 10?

Page 227, A

The sum of four consecutive positive even integers is x. In terms of x, what is the sum of the second and third integers?

A. (x-12)/4B. (x-6)/2C. 2x+6D. x/2E. (x^2 – 3x)/4

Plugging in continued

P228, D

If a-b is a multiple of 7, which of the following must also be a multiple of 7?A. abB. a + bC. (a + b)/2D. (b - a)/2E. b - a

One more plug in

p232E

If x#y = 1/(x-y), what is the value of ½ # 1/3

A. 6B. 6/5C. 1/6D. -1E. -6

Strange operations….

Page 240, A

Remember that % means “out of 100” So 30% is 30/100 If you want to find a percent of a number

you multiply by the decimal version of the % or the percent/100. ◦ For example 20% of 80 is (.20)(80)=16 or

(20/100)(80) = 16 If you want to do some “Plug-ins” to test

100 is a great number because it is so easy to find the %. For example: 15% of 100 is 15.

Percentages

Percent change = Difference/original x 100%

The price of a shirt was raised from $12 to $18. What is the percent of change?◦ (18-12)/12 x100% = 6/12 x 100% = 50%

Percent Change

A number is increased by 25% and then decreased by 20%. The result is what percent of the original number?

A. 80B. 100C. 105D. 120E. 125

Try a percent problem

P257 B

Probability is basically correct/total◦ What is the probability of rolling a 1 on a dice?

There is one 1 and 6 sides, so 1/6

Odds are correct/incorrect◦ What are the odds you will roll a 1 on a dice?

There is one 1 and five non-1s on a dice, so 1/5

Probability and Odds

Probability Example A bag contains 7 blue

marbles and 14 marbles that are not blue. If one marble is drawn at random from the bag, what is the probability that the marble is blue?

A. 1/7B. 1/3C. ½D. 2/3E. 3/7

So how many are “correct”?

How many marbles total?

P267 B

Another Probability

So, what strategy?

A jar contains only red marbles and white marbles. If the probability of selecting a red marble is r/y, which of the following expressions gives the probability of selecting a white marble in terms of r and y?

A. (r-y)/yB. (y-r)/yC. y/(y-r)D. r/yE. y/r

B

Permutations Hal wrote 7 essays in his

English class. He wants to put all 7 essays in his portfolio and is deciding in what order to place the essays. In how many different orders can Hal arrange his essays?

A. 49B. 420C. 5040D. 5670E. 10549

Options:◦ Tree diagrams◦ blanks

C

A triangle contains 180⁰ Equilateral triangles have all 3 angles the

same Isosceles triangles have two angles that are

equal A right triangle has a 90⁰ angle The area of a triangle is 1/2bh The perimeter of a triangle is the sum of the

3 sides If a right triangle then a2 + b2 = c2

Geometry- Triangles

A circle contains 360⁰ r = radius, d = diameter

◦ Area = πr2

◦ Perimeter = 2πr = πd

Squares contain 360⁰ (with each corner being 90⁰) and all sides are equal◦ Perimeter = 4s, where s=length of a side◦ Area = s2

Rectangles contain 360⁰ (with each corner being 90⁰) and have pairs of sides that have equal lengths◦ Perimeter = 2(length) + 2(width)◦ Area = (length)(width)

Geometry- Circles, Squares, and Rectangles

If the area of ∆ABC in the figure below is 30. What is the length of DC?

A. 2B. 4C. 6D. 8E. 12

Basic Triangle Example

B C

A

D

5

4

P298 D

In the figure below, what is the value of x+y+z?

A. 90B. 180C. 270D. 360E. 450

One More Triangle

y

x

z

P304 D

NO DEDUCTIONS FOR WRONG ANSWERS!

If you can come up with an answer; go for it!◦ A wrong answer is no worse than a blank answer.

Start putting answers in from left.

No mixed numbers!◦ Use improper fractions or decimals.

Do not do 3 ½ , you need to put 7/2 or 3.5

You do not need to reduce fractions.

These are usually easier because the answers cannot have variables in them.

Grid Ins

In each section the problems get progressively more difficult.

Make sure your read through practice materials and become familiar with directions and formulas that are given. Do this so you do not have to spend valuable time during the test figuring things out.

Take practice tests (be sure to time yourself) before the test to get a feel for how fast you need to work.

Best wishes in your testing endeavors!!!!

In Conclusion

http://sat.collegeboard.org/home

http://www.majortests.com/sat/problem-solving.php

http://www.testprepreview.com/sat_practice.htm

Internet Resources