Welcome to the Math S.A.T. Enjoyment Hour

Hosted by the B B & S Brothers Bianco, Bianco & Skeels

Quick Drillsky

#1 11 • 12

#2 140 ÷ 5

#3 150 - 63

#4 (12)2

#5 (5)3

#6 (10)5

#7 √ 49

#8 √ (117)2

#9 (35)23 (35)22

#10 (3)12 •(3)-9

LET’S √ EM!

#1 11 • 12

#2 140 ÷ 5

#3 150 - 63

#4 (12)2

#5 (5)3

#6 (10)5

#7 √ 49

#8 √ (117)2

#9 (35)23 (35)22

#10 (3)12 •(3)-9

The Math Portion SAT contains 54 questions with a 75 minute time limit. Two (2) Sections..... Multiple Guess Student Produced Response

Objective: To give you the opportunity to get the highest possible math score on the PSAT/SAT test.

General Stuff 1. You will not be graded for this course. 2. Please write on all materials. 3. You do not need a pass to use the lavatory. (Wow..... pretty weird concept.) 4. Ask questions as soon as possible.

General Strategies...... Know the directions..... do not waste time reading them. Keep track of time. Do not rush or dilly dally. Keep track of your place.(if you skip a question, then skip an answer space.) Never play games on your calculator during the test!

General Look at Mult Choice 44 questions with 5 answer choices. Questions are in a E-M-H category. The questions arranged in order of difficulty.

General Strategies...... Be sure you answer the question!!! Some incorrect answers will be there for something else in the problem. All answers have the same point value. Incorrect answers are not equal in point value.(MC - (-1/4), SPR - (0))

Stuff you should know..... Look at the formula section. These items are on every test for you to use. Learn these so you do not have look for these formulas. Remember, this test mainly requires knowledge of AlgebraI/II and Geometry.

The Reference Sheet Reference Information                                                              The number of degrees of arc in a circle is 360. The sum of the measures in degrees of the angles of a triangle is 180.

General Information...... Be sure you answer the question!!! Some incorrect answers will be there for something else in the problem. Example:

If AC = 17, then BC = ?? x - 3 2x + 5 A B C Note: Figure is not drawn to scale

If AC = 17, then BC = ?? A) 2 B) 3 C) 5 D)13 E) 15 x - 3 2x + 5 A B C Note: Figure is not drawn to scale A) 2 B) 3 C) 5 D)13 E) 15

General Look at Mult Choice Be careful, they have great wrong answers. The most obvious answer is usually wrong, but not far off. If you can eliminate 1 or more answers guessing is a good idea.

MATH CATEGORIES Arithmetic Algebra Geometry Advanced Algebra & Trig Miscellaneous

Today we will......... focus on strategies to solve different types of problems.

STRATEGIES Finding a pattern. Adopting a different perspective. Trial and error.

WARNING Some of the problems presented today may be challenging. These problems help illustrate specific strategies!!!!

Some of the problems presented today may be challenging Some of the problems presented today may be challenging. These problems help illustrate specific strategies!!!!

WARNING Some of the problems presented today may be challenging. These problems help illustrate specific strategies!!!!

Some of the problems presented today may be challenging Some of the problems presented today may be challenging. These problems help illustrate specific strategies!!!!

WARNING Some of the problems presented today may be challenging. These problems help illustrate specific strategies!!!!

Some of the problems presented today may be challenging Some of the problems presented today may be challenging. These problems help illustrate specific strategies!!!!

WARNING Some of the problems presented today may be challenging. These problems help illustrate specific strategies!!!!

Finding a pattern. Many of the problems on the SAT can be solved very efficiently if you can recognize a pattern within the problem. For example:

Finding a pattern. Write down the following sequence: 3, 5, 8, 13, 21, ... , 377

Which of the following pairs of numbers would occur consecutively between 21 and 377 in the sequence: A) 31, 43 B) 144, 233 C)56, 72 D) 171, 296 E) 55, 91

Which of the following represents the cube of 6,456? Finding a pattern. Which of the following represents the cube of 6,456? A) 632,944,312 B) 74,252,334,444 C) 592,866,468,204 D) 269,085,666,816 E) 788,486,666,122

HELPFUL HINT When answers go beyond the capabilities of your calculator, try to find a pattern and eliminate impossible answer choices.

Solution Try a quick calculation. Look at the answer choices to see how they differ. Can you think about what the solution must contain?

Solution Any integer that ends in 6 and is multiplied by itself also ends in 6. Thus only choice D could be correct.

Different Pt. of View Some problems on the SAT can be solved in a traditional straight forward approach.

Different Pt. of View However, this often takes more of your precious time than if you did the problem from a different perspective.

Different Pt. of View Find the sum of x + y, if: 3x + 5y = 11 A) 1/8 B) 9/4 C) 17/8 D)17 E) 18

Solution Normally, the traditional approach would be to solve for x and y and add. This will work, but take 4 to 5 minutes since they are both fractions!!!!!!!

Solution Look at the coefficients and notice when you add the 2 equations you produce: 8x + 8y = 18

Solution We want x + y. (÷ by 8) Look at the coefficients and notice when you add the 2 equations you produce: 8x + 8y = 18 We want x + y. (÷ by 8)

Solution We want x + y. (÷ by 8) Look at the coefficients and notice when you add the 2 equations you produce: 8x + 8y = 18 We want x + y. (÷ by 8) x + y = = 4 9 18 8

Different Pt. of View What is the smallest prime number that divides the sum: 35 + 511 + 713 + 1317? A) 2 B) 3 C) 5 D) 7 E) 11

Solution Try a quick calculation. Look at the problem again. Each term will be odd. The sum of 4 odd numbers will be even. Thus be divisible by 2.

Trial and Error. Probably the oldest and still most widely used strategy. Make intelligent guesses and adjust future guesses from the outcome of a previous guess.

Trial and Error. A) 4 B) 4.5 C) 5 D) 6 E) 6.5 Lucy and Linus bought a rectangular rug in Mexico. The rug had an area of 40.5 square feet. The length of the rug is twice the width. What was the width(in feet) of the rug? A) 4 B) 4.5 C) 5 D) 6 E) 6.5

HELPFUL HINT When using Trial & Error, start with choice C since the answers always appear in ascending order. Then you only need to try 3 choices at the most.

Solution w = width A = 40.5 ft2 2w = length

Solution Guess???? w 2w Area

Solution Guess???? w 2w Area 5 10

Solution Guess???? w 2w Area 5 10 50 (too big) 4.5 9

Solution Guess???? w 2w Area 5 10 50 (too big) 4.5 9 40.5

Solution Guess???? w 2w Area 5 10 50 (too big) 4.5 9 40.5 4.5 9 40.5 DONE! Answer:B

Trial and Error. A) 2 B) 4 C) 6 D) 8 E) 10 Mr. Clean gave his daughter $4.05 in dimes and quarters. He gave her 5 more quarters than dimes. How many dimes did Mr. Clean give his daughter? A) 2 B) 4 C) 6 D) 8 E) 10

Solution Guess???? Start in the middle. d q total 6

Solution Guess???? Start in the middle. d q total 6 11

Solution Guess???? Start in the middle. d q total 6 11 .60 + 2.75 = 3.35

Solution Guess???? Start in the middle. d q total 6 11 .60 + 2.75 = 3.35 8

Solution Guess???? Start in the middle. d q total 6 11 .60 + 2.75 = 3.35 8 13

Solution Guess???? Start in the middle. d q total 6 11 .60 + 2.75 = 3.35 8 13 .80 + 3.25 = 4.05 DONE!!!!!

You now have added several strategies to your arsenal to help solve problems. You need to decide when and where these are best used.

Practice Work with your neighbor to complete the 6 practice problems. Try to use some of the strategies presented today to help you. Teachers at this time pass out the 6 practice problems. You have 10 minutes starting now.

10 minutes remaining

5 minutes remaining

1. The sequence 2, 6, 18, 54, ... is created by multiplying every term after 2 by 3. Which terms in this sequence are divisible by 35? A) Only the 5th term B) Only the 6th term C) Every term after the 4th D) Every term after the 5th E) Every term after the 6th

2. The sum of the digits of a two-digit number is 9 2. The sum of the digits of a two-digit number is 9. The new number formed by reversing the digits is larger than the original number by 27. What is the original number?

3. Find the value of x - y, if: A) -1 B) 4 C) 5 D) 9 E) 45

4. How many different angles are formed by 10 distinct rays with a common endpoint,no two of which lie on the same line? A) 10 B) 18 C) 26 D) 35 E)45

5. Barney bought a watchband for $5 5. Barney bought a watchband for $5.00 and then spent half the remaining money on a video game. He then spent $2.00 on a snack. After the snack, he bought Betty a present with half of the remaining money. He was left with $10. How much did he start with? A) 45 B) 49 C) 57 D) 60 E) 85

6. Which of the following represents the units digit of 759? A) 1 B) 3 C) 5 D) 7 E) 9

Finding a pattern. Write down the following sequence: 3, 5, 8, 13, 21, ... , 377

Which of the following pairs of numbers would occur consecutively between 21 and 377 in the sequence: A) 31, 43 B) 144, 233 C)56, 72 D) 171, 296 E) 55, 91

Which of the following represents the cube of 6,456? Finding a pattern. Which of the following represents the cube of 6,456? A) 632,944,312 B) 74,252,334,444 C) 592,866,468,204 D) 269,085,666,816 E) 788,486,666,122

Different Pt. of View Find the sum of x + y, if: 3x + 5y = 11 A) 1/8 B) 9/4 C) 17/8 D)17 E) 18

Different Pt. of View What is the smallest prime number that divides the sum: 35 + 511 + 713 + 1317? A) 2 B) 3 C) 5 D) 7 E) 11

Trial and Error. A) 4 B) 4.5 C) 5 D) 6 E) 6.5 Lucy and Linus bought a rectangular rug in Mexico. The rug had an area of 40.5 square feet. The length of the rug is twice the width. What was the width(in feet) of the rug? A) 4 B) 4.5 C) 5 D) 6 E) 6.5

Trial and Error. A) 2 B) 4 C) 6 D) 8 E) 10 Mr. Clean gave his daughter $4.05 in dimes and quarters. He gave her 5 more quarters than dimes. How many dimes did Mr. Clean give his daughter? A) 2 B) 4 C) 6 D) 8 E) 10