Bell Ringer

1. 60 50 40 30 20 10 02 03 05 01 04 Bell Ringer seconds remaining Your bell ringer will begin in 1 minute. Be ready. It won’t wait for you. You can’t go back. If you have seen this before, do NOT talk until everyone is finished working and I say it’s ok to discuss your answers. You won’t need a calculator for this. Be ready.

2. Bell Ringer Three men get a room together at a hotel. They each pay $10.00 for a room costing $30.00. After they settle in, the desk clerk knocks on their door and says that he overcharged them; the room only costs $25.00… so he handed them $5 refund. Since they could not divide the $5 evenly among themselves, they each took $1 and gave the hotel clerk a $2 tip. Now, each man is out $9 for the room; and they gave the hotel clerk a $2 tip. 3 times $9 is $27; plus the $2 tip equals $29. but they started with $30. Where’s the missing dollar?

3. Bell Ringer This is a trick question. The total money paid is $9 * 3 = $27. The total money received is $25 for the room and $2 to the bellboy = $27. There simply is no extra dollar. The $2 to the bellboy is included in the $27 the three men paid. By adding it to the $27 it is being counted twice.

4. Chapter 7 Powers Radicals and

5. But First… Let’s Review! Sets The Intersection of two sets X and Y is the set of elements common to X and Y. An element has to be in both sets to be in the intersection. Intersection is written X ∩ Y. The Union of two sets X and Y is the set of all elements in either set X or set Y, with no element repeated twice. An element that is in one set or both sets is in the union. Union is written X U Y.

6. Let Set X = even integers and Set Y = odd integers. Therefore X ∩ Y. A. prime numbers B. integers C. empty set D. composite numbers E. whole numbers The two sets have nothing in common so it is an empty set.

7. Sequences Arithmetic Sequence – a sequence in which each term is a constant difference d from the previous term. The formula can be used to find the nth term of an arithmetic sequence. Example: 3, 6, 9… and d = 3 Fourth term: Geometric Sequence – a sequence such that each term is given by a constant multiple r of the previous one. Find the next three terms in the sequence: 3, 6, 12,… In this sequence r = 2. Therefore, the next three terms in the sequence are 24, 48, 96 The formula can also be used to find the nth term of the Sequence. In this problem a1 = 3 and r = 2. Sixth term:

8. Sequences Arithmetic Sequence – Geometric Sequence – The first term in a geometric sequence is 3 and the 4th term is 81. What is the 10th term of the sequence? A. 177,147 B. 59,049 C. 19,683 D. 6,561 E. 2,187 Answer: B First find the common multiplier needed to get from 3 to 81 in 3 steps. This number is 3. Six more steps gets us to the 10th term. Therefore 81 x 36 = 59,049.

9. GCF and LCM The GREATEST COMMON FACTOR (GCF) of two numbers is the largest factor the two numbers have in common. The LEAST COMMON MULTIPLE (LCM) of two numbers is the smallest multiple two numbers have in common.

10. What is the LCM of the numbers that satisfy these conditions? factor of 48 multiple of 8 Answer: 8 The factors of 48 are {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}. Of these numbers {8, 16, 24, 48} are also multiples of 8. 8 is the LCM of these numbers

11. Ratio and Proportion

12. Jordan swam 4 laps. Each lap is 100 meters. Jordan’s average speed for the first ¾ of his swim was 40 meters per minute, and for the rest of his swim he averaged 35 meters per minute. What is Jordan’s average rate for the entire 4 laps, rounded to the nearest whole number? Answer: 39 meters per minute Therefore, the 400 meters took approximately 10.357 minutes to complete. Don’t round yet. Jordan’s average rate of speed was That’s 39 meters.

13. Percent Increase and Percent Decrease

14. Percent Increase and Percent Decrease During last year’s baseball season, a certain player has 625 at bats and gets a hit 32% of the time. This season the player increased the at bats by 12%, and got a hit 34% of the time. What is the percent increase in the number of hits? Answer: 19 Part = Percent x Whole => last season hits = 0.32 x 625 = 200 New Amount = (1 + Percent Increase) x Original Amount this season at bats = (1 + 0.12) x 625 = 1.12 x 625 = 700 Part = Percent x Whole => this season hits = 0.34 x 700 = 238

15. Chapter 6: Mean, Median, Mode The Arithmetic Mean (average) is the sum of the items divided by the number of items. The Median is the middle number when the list is placed in order if there is an odd number of items. If there is an even number of items, the median is the mean of the two middle numbers. The Mode is the item that occurs most frequently. If every item appears the same number of times, then there is no mode in the set.

16. Homework Review:

17. Homework Review:

19. 6. Say that Ed scored 16 points in the fourth game. What should be added to Jay’s median score to equal the median of Ed’s scores?

31. Chapter 7 Powers Radicals and

32. The secret to solving powers and radical problems is to know the root algebraic rules. The best way to do this is to apply the rules to problems. This section gives you practice with these algebraic techniques. Basic rules for exponents:

38. Practice SAT Problems:

39. Practice SAT Problems:

40. Homework: Chapter 7: 19 Practice Problems More time? Play Millionaire!