3) The lower quartile is 8, 10, 11 and the upper quartile is 15, 16, 18. Q1 is 10 and Q3 is 16.

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1 Strategy for Benchmark Questions: 1. Asking for the interquartile range. The formula is IQ Range = Q3 - Q1. Q3 (42) - Q1 (7) = Asking for the interquartile range. Formula: IQ Range = Q3 - Q1 1) First, put the numbers in order. 8, 10, 11, 15, 16, 18 (be sure to count the number on the paper against what you have put on your worksheet. 2) Take the two numbers in the center (11 and 15), add them together and then divide by 2 to get the median (Q2). 3) The lower quartile is 8, 10, 11 and the upper quartile is 15, 16, 18. Q1 is 10 and Q3 is 16. 4) The interquartile is Q3 (16) - Q1 (10) = 6 3. This question is a proportion question. You can look at the first sentence. 10 out of 50 would be set up as 10/50. How many people in the total would be x/350? You will set it up as a proportion. Cross multiply and then solve for x. 10 x 350 and 50x = 50x = 3500 divide 50 into 3500 x = This question is a proportion question. 2 out of 5 is 2/5. How many students in all is x/450. Cross multiply and then solve for x. 2 x 450 and 5x. 5x = 900 divide 5 into 900. x = This is a cross section of a 3D shape. The clue word here is rectangular. Because the base is a rectangle, when you make a cross section parallel to base, the cross section will be a rectangle. 6. The sum of a triangle. Remember, the sum of a triangle measures is 180. Since you have two of the three angle measures, you can add those two measures together and subtract that from 180. The second part of the question wants to know what type of angle the third angle is based on it's measure. Since the angle is 60 degrees, it would be acute. Definition of angles: Acute - less than 90; Obtuse - more than 90; Right equal Reading a quartile chart. The first notch is the minimum, the left side of the box is Q1, the center notch is Q2 and the right side of the box is Q3; the last notch is the maximum. A. Median (Q2) for Friday: 480 Saturday 450 B. Range for Friday: = 60 Saturday = 70 C. Interquartile Friday: = 90 Saturday = 100

2 D. What percent of Saturday's attendance is below the 3rd quartile? This is a trick question. Each quartile is 25%. No matter where the numbers fall in the set, each quartile represents 25%. 1st - 25%, 2nd - 25% and 3rd - 25%. So there is 75% of the attendance below the 3rd quartile. 8. Cross Section of 3-D shapes. Because we spent limited time on this concept. Just know, you cannot get an octagon or circle from the cross section cutting of a square. 9. Sum of a Triangle. Again, you will use the sum of a triangle (180), to solve. Add 69 and 57. Subtract the sum from Determining if a triangle exist with 3 given sides. 9, 4, 6 Take the two short side (4,6) and add. If the sum of those two numbers is greater than the third, the answer is yes. If the sum is equal or less than the third, it is no = 10, since 10 is greater than 9, the answer is yes. 11. Determining if a triangle exist with 3 given sides. 10, 7, 3. Since the sum of is 10 and the third number is 10, the answer is no. 12. Sum of a Triangle. This problem involves the solving of x. Since you know that the sum of a triangle is 180, you will set up the equation x = x = 180 x = (be sure to put the 180 in first x = Cross Section of a 3D Shape: A circle cone cut parallel to the base will be a circle.

3 14. The cylinder is just a rectangle that has been folded around. If you cut the cross section, it s a rectangle. 15. A sphere will always cut as a circle. 16. This is an area problem. The formula is provided on the formula sheet. Make sure the measurement you are given is the one you need. You need radius. This problem is giving you the radius. A = 12 2 x x 12 x 3.14 = This is a circumference problem. The formula is provided on the formula sheet. Make sure the measurement you are given is the one you need. You need diameter. This is giving you the diameter. C = 8 x 3.14 = Solving for the unknown angle measure. If it is a right angle, it will be a complementary angle. Look for the square in the corner. Since you already have 61 o, you will need to subtract to get the other measurement = 29 o 19. Solving for the unknown angle measure. If the angles are vertical, then they will be equal. If the known angle is 38 o, then the unknown is 38 o. 20. Solving for the unknown angle measure. If it is a right angle, it will be a complementary angle. Look for the square in the corner. Since you already have 54 o, you will need to subtract to get the other measurement = 36 o 21. Area of a triangle.. The formula is provided on the formula sheet. A= b x h divided by x 8 = 28.8 divided by 2 = 14.4 in Area of a prism. The formula is provided on the formula sheet. 2 x 10 x 6 = x 6 x 10 = x 10 x 10 = km 2 23 Surface area of a triangular prism. The formula is provided. 1) First get the area of the triangles. Since you have two, you only need to multiply the base x height. 9 x 4 = 36 2) Then find the area of the three panels. 8 x 9 = 72 8x 6 = 48 8x 6 = 48 3) Add the numbers together to get 204 ft 2

4 24. Surface area of a rectangular prism. The formula is provided. 2 x 2 x 1 = 4 2 x 1 x 6 = 12 2 x 6 x 2 = km 25. Volume of a triangular prism. The formula is provided. L x W x H divided by 2. Remember, you need only the length, width and height of the prism. Do not use the base as one of the measures. 8 x 9 x 6 = 432 divided by 2 = 216 km Volume of a rectangular prism. The formula is provided. L x W x H. 6 x 2 x 1 = 12 km Find the area of a shaded region. Remember this is cut-out problem. Find the area of the total rectangle and then subtract with cut-out. 30 x 15 = 450 cm 2 is the total rectangle Now, find the area of the cut-out. 22 x 11 = 242 cm 2 is the cut-out area of the rectangle. Subtract = 208 cm Random vs Bias Sampling. Remember in order for the sample to be random, everyone in the population The choice of the Student Council does not allow everyone the chance of being chosen. Therefore, the sample is not random, but bias. 29. Random vs Bias Sampling. Remember in order for the sample to be random, everyone in the population Melanie s system of asking every 4 th person would be considered random. The people walking into the restaurant would be eating at the restaurant and everyone has an equal chance at being the 4 th person. This sample is random. 30. Random vs Bias Sampling. Remember in order for the sample to be random, everyone in the population Mr. Jones pulled his sample from only one grocery store, therefore, anyone who shopped at a different grocery store would not have an equal chance at being chosen. This sample is bias.

5 31. Probability. The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible. favorable outcome/total possible outcomes There are 20 total beads. That is the total possible outcomes. There are 12 red beads. There are 8 white beads. Because there are more red beads than white beads, it is more likely that you will pull a red bead. 32. The range for probability is 0% to 100%. Therefore a 10% chance is not very likely. 33. Probability. 1) First, you need to know how many total possible outcomes you can have. Count the number of chips you have in total = 100 chips 2) The favorable outcome in this problem is pulling a yellow chip. There are 45 yellow chips. 3) The probability of pulling a yellow chip is 45/100 BUT YOU MUST REDUCE THIS. 4) Reduce by dividing the top and bottom number by 5. This gives you 9/20, which cannot be reduced any further. 34. Probability. 1) A die has six side with the number 1-6. Therefore there are six possible outcomes. 2) How many of the numbers 1-6 are odd? There are three 1, 3, and 5. 3) The probability of rolling an odd number is 3/6 BUT YOU MUST REDUCE THIS. 4) Reduce by dividing the top and bottom by 3. This gives you ½, which cannot be reduced any further. 35. Area of a rectangular box with no top. Please label the box with width, length and height. 1 x 20 x 30 = 600 noticed that you only multiply this dimension once, since it represents the bottom panel 2 x 30 x 10 = x 10 x 20 = in Volume of a Compound Shape. You can get the volume of the rectangular prism and then minus out the cutout. Remember, V = L x W x H. 1) If the prism did not have the cut-out, it would be 60 x 80 x 10 = 48,000 2) The cutout measurements are 40 x 60 x 10 = 24,000 48,000 24,000 = 24,000mm 2