Benchmark 1 Review

Word Problems

100

At Sixth Grade Camp on Palomar Mountain, the temperature was 13 degrees F. That night the temperature dropped to -9 degrees. How many degrees did the temperature drop?

Draw a picture if it helps. You are subtracting -9 from 13 so 13 - (-9) = 22. The temperature dropped 22 degrees.

200

At Sixth Grade Camp on Palomar Mountain, the temperature at night was - 9 degrees F. By noon the next day, the temperature was 68 degrees. How many degrees did the temperature rise?

You want to know how many degrees the temperature rose so you want to know the difference between the end temperature and beginning temperature. 68 - (-9) = 77. The temperature rose 77 degrees.

300

Mardella practiced touch typing a total of 16.1 hours last week. If Mardella had practiced the same amount of time each day last week (7 days), how long did she practice daily?

It's asking you to find the average, so you have to divide the total hours by the number of days. 16.1/7 = 2.3. Mardella practiced an average of 2.3 hours a day.

400

This week, Mardella is averaging 3.25 hours each day. How many hours will she have practiced during the week?

This time it's giving us the average amount per day. We want to know the total that she practiced all week long (7 days). You could add up 3.25 hours 7 times or just multiply 3.25 * 7 to get 22.75. Mardella practiced for 22.75 hours during the week.

500

Osman has to buy 18 pencils and 12 pens. He looked at the prices at two stores shown below: Store A Pencils = $0.25 Pens = $0.75 Store B Pencils (6) = $1 Pens (4) = $1.25 How much will he save if he buys the pens and pencils at Store B?

18 * 0.25 = $4.50 12 * 0.75 = 9 so if he buys at store A, his total will be $13.50. If he buys at store B, 3 * 1 = $3 for pencils & (1.25 * 3 = $3.75) for pens so his total would be $6.75. They want to know how much he will save so subtract that from 13.50 and you get $6.75. He will save $6.75 if he buys at Store B.

Word Problems 2

100

A mountain climber is at an elevation of 1000 ft. After 2 hours, he is at an elevation of 5000 ft. What is the mountain climbers speed?

Speed = distance/time so he went 4000 ft in 2 hours. You can reduce that to 2000 ft/hr

200

The science club has a set of 48 beakers and 20 test tubes. Each set can be divided equally among the club members. What is the greatest possible number of club members?

Find the GCF of 48 and 20. They can only have a maximum of 4 club members if they want to equally divide the test tubes and beakers. Each member would get 12 beakers and 5 test tubes apiece.

300

Wilson has 126 members in DC club while Clarke has 56 DC club members. They want to take a group picture, but the members from each school have to be in separate rows. How can they be arranged so that each row has the same number of players?

Again, you're trying to find the GCF of 126 & 56. Do the upside down birthday cake method, you end up with 14. So for Wilson, there will be 9 rows of 14 students each & Clarke will have 4 rows of 14 students each.

400

What is the GCD (Greatest common divisor) of 36 and 96?

You can using whatever method you'd prefer, but you should end up with 36 as the GCD.

500

Victoria and Daveon both go to pick up their rewards today. Victoria gets a reward every 8 days, while Daveon gets his every 42 days. When will Victoria and Daveon meet up again to redeem their rewards?

The key to this problem is figuring out that it's asking you to find the least common multiple of 8 and 42. Using the upside down birthday cake method, you get 168. Victoria and Daveon will meet up again to get their rewards in 168 days.

Order of Operations

100

(2 + 3) / 15

Parentheses first to get 5/15

Don't get tricked!!! 5/15 is NOT equal to 15/5

Reduce and you get 1/3

200

54 - (4² + 3)

Parentheses first
(Within that do exponents) = 54 - (4*4 +3)
= 54 - (16 +3)
(Within that add) = 54 - 19
Subtract = 54 - 19 = 35

300

(5² + 2) - 67

Parenthesis first
(within that do exponents) = (5*5 +2) - 67
= (25 + 2) - 67
(within that add) = 27 - 67
Subtract (KFC) = 27 + (-67) = -40

400

3 (5 + 3)²

Parentheses first = 3 (8)²
Next Exponents = 3( 8 * 8) = 3 (64)
Last Multiply = 192

500

(15 -25)/5 - 7 (1+2)²

Parentheses and grouping symbols first
(-10)/5 - 7 (1+2)²
-2 - 7 (3)²
Exponents next
-2 - 7(3*3) = -2 - 7(9)
Multiply next -2 - 63 Subtract (KFC) -2 - 63 = -2 + (-63) = -65

Metric System

100

Convert 6.35 kg to _______ g

6350 g

200

Convert 0.574 mg to ________dag

0.0000574 dag

300

The capacity of a beaker is 115 milliliters. How many beakers would have to be used in order to COMPLETELY fill a one-liter container.

1000 mL / 115 mL = 8. 7 but to COMPLETELY fill a one liter container would take 8 COMPLETELY FULL beakers plus 1 more beaker containing 0.7 so it would take 9 beakers total to COMPLETELY fill a one liter container.

400

The capacity of a beaker is 150 mL. How many beakers would have to be used in order to COMPLETELY fill a two-liter container?

2000 / 150 = 13.3 so it would take 14 beakers to complete fill a two liter container.

500

Kevin weighed a worm for a science project. It had a mass of 0.3 g one week ago. In 7 days, it gained 926 milligrams. What is the mass of the worm now?

Change 926 mg to 0.926 g. Add 0.926 + 0.3 = 1.226 g OR change 0.3 g to 300 mg. Add 300 + 926 = 1226 mg

Measures of Central Tendency

100

Find the outlier in the set of data: 34, 31, 35, 33, 38, 41, 35, 78, 36

78 is the outlier, it's the value that stands far away from the other data values.

200

Find the mode of the set of data: Mya, Annette, Annette, Esmeralda, Donte, Giselle, Alonso, Mya

There are two modes (Mya and Annette since they both appear two times)

300

Find the median of the set of data: 6, 4, 1, 5

Ordering becomes 1, 4, 5, 6. Cross out the ends and you're left with 4, 5. To find the median when there's two numbers in the middle, add and divide by 2. So 4 + 5 = 9 /2 = 4.5 The median is 4.5

400

Find the mode of the set of data: 101, 106, 103, 108, 103, 101, 108, 96, 108, 109, 105, 111

108 is the mode because it appears the most (3 times)

500

Find the median in the set of data: 18, 40, 20, 32, 35, 18, 26, 27

Ordering becomes: 18, 18, 20, 26, 27, 32, 35, 40 Crossing the ends leaves you with 26 & 27 in the middle. To find the median when there are two numbers left, you find the mean so add them together and divide by 2. You end up with 26.5. 26.5 is the median.