3. Look at the volume formulas provided on the OAT reference sheet… Volume of Cone =  r 2 h 1 3 Volume of Cylinder =  r 2 h Since the cone only has 1/3 as much volume, it will take 3 cones to fill up the cylinder.

4. Together, these two angles form a straight line. Therefore, their measures need to add up to 180 o. 180 -133 47 Be careful. Don’t get tricked here. The question asks for the sum of angles K & L. Angles K & L have the same measure. They are both 47 o. 47 o + 47 o = 94 o

5. Favorite Subjects Circle graphs always work best when comparing percentages.

6. slope = y 2 – y 1 x 2 – x 1 xyxy #2#1 slope = 0 – 3 5 – 1 slope = -3 4

7. $20 full price Always convert percentages into decimals when doing word problems. 15% =.15 x.15 discount $3.00 savings Rob originally thought he would be saving at least $4.00. Since his actual savings will only be $3.00, Rob’s estimate is not reasonable.

8. When shapes are similar, the corresponding angles have equal measures. Since L and X occupy the same position in each pentagon, they will have the equal measures.

9. (2 3 ) (3 -2 ) 2 x 2 x 2 8 9 1 3232 1 9 8

10. Volume = (length)(width)(height) Volume = (10)(5)(0.1) Volume = 5 cm 3 Density = 13.5 g 5 cm 3 Density = 2.7 g/cm 3

11. The numbers in the 2 nd column are 30 times larger than the numbers in the first column. F = 30 * R F = flow rate R = # of revolutions This blockage would cause the slope to be cut in half as well. It would change from 30 to 15. # of rotations Flow rate 0 246 60 120 180

12. Discrete data comes from a measurement scale where intermediate values are not allowed. Often times in word problems, this means no fractions or decimals can be used—just whole numbers. In these first 3 examples, any values can be used--including fractions & decimals. data, because you can’t collect partial butterflies. This data must be expressed using whole numbers. This is an example of discrete

13. The circles will end up being the top & bottom bases of the cylinder. In order for this to happen, the circles need to be on opposite sides of the rectangle.

14. 248 miles  55 MPH 4.509 hours This is very close to 4 hours and 30 minutes of driving time. (Don’t get fooled into picking this answer!) Jason started at 10:30 AM and drove for 4 hours and 30 minutes. He should arrive at his destination at 3:00 PM.

15. The easiest way to solve this problem is to simply type it into your calculator. 300 ≈ 17.32050808 By the way, if you didn’t have a calculator, you could still get the answer by squaring the answer choices. 15 2 = 225 16 2 = 256 17 2 = 289 18 2 = 324 As you can see, 300 fits in right here!

16. The median will give people a better idea about what’s going on here. The owner’s salary is much higher than everyone else’s. This will inflate the mean, making it seem like everyone is richer than they actually are. The median isn’t affected nearly as much by extremely high or extremely low values.

17. Mean:$140,000 $50,000 $45,000 $32,000 $30,000 + $327,000  6 people $54,500 = mean salary Median: Eliminate the highest & lowest salaries. Repeat this process until 1 or 2 salaries are left. If two salaries remain, average them together. $77,000  2 2 $38,500 = median salary The median would be a better choice in this situation, because the mean was higher than 5 out of the 6 salaries.

18. 3x < -2x + 15 +2x < +2x + 15 5x < 15 55 x < 3

19. $3.5 x 10 4 = $35,000 $4.51 x 10 5 = $451,000 $416,000 3.5000000 The 10 4 tells us that the decimal point needs to be moved 4 places to the right. Simply repeat this process to evaluate $4.51 x 10 5. (subtract)

20. $3.5 x 10 4 = $35,000 $4.51 x 10 5 = $451,000 $416,000 $ 4 1 6 0 0 0 When converting a number into scientific notation, you slip the decimal point in so that you’ve got a number between 1 and 10. Next, you see how far the decimal point needs to be moved in order to get it back to where it’s supposed to be. (Since we’re moving it to the RIGHT, the exponent will be POSITIVE.)

21. The product CAN be less than 4. (3 x 1, for example) Also, the product CAN be greater than 18. (4 x 6, for example) The most likely product is 10, since the 1 st spinner has a pair of twos, and the 2 nd spinner has a pair of fives.

22. y x For those who may have trouble drawing figures accurately, here’s a method that might help… Start at the origin and draw a straight line out to a point on the figure. Measure the length of your segment, then go the same distance in the opposite direction. Repeat this process until you have enough points to form a good drawing.

23. This green rectangle will cover the side of the cylinder perfectly. 6 in. 4  in. C = 2  r= 4  in. The height is the same in both shapes. The top of the rectangle will be the same length as the circumference of the circle. The area of the green rectangle is 24  in 2, or ≈ 75.398 in 2.

24. 6 in. 4  in. The area of the green rectangle is 24  in 2, or ≈ 75.398 in 2. r = 2” The bottom of the glass is a circle with diameter = 4”. The area of the circle is 4  in 2, or ≈ 12.566 in 2. A =  r 2 A = 4  in 2 Adding the areas gives us 87.964 in 2.

25. This PowerPoint presentation brought to you by Mr. Jeff Luce Beachwood Middle School Enjoy and good luck!