Grade 6 Mathematics Midterm Study Guide PDF

MODERN KNOWLEDGE SCHOOLS MIDDLE SCHOOL MATHEMATICS MIDTERM STUDY GUIDE GRADE 6 Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools  SECTION A:...

MODERN KNOWLEDGE SCHOOLS MIDDLE SCHOOL MATHEMATICS MIDTERM STUDY GUIDE GRADE 6 Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools  SECTION A: OPERATIONS WITH INTEGERS MULTIPLE CHOICE QUESTIONS 1. Compare: which integer is greater? a) -5 b) -3 c) equal 2. What is the absolute value of -7? a) 0 b) 7 c) 1 3. Which of the following integers is the smallest? a) 2 b) 0 c) -5 4. What is the value of ( |6| - |4 | )? a) 10 b) -2 c) 2 5. Which statement is true about the temperature 21’C? a) The absolute value is -21∘C. b) 21∘C away from the freezing point. c) −21∘C away from the freezing point. 6. What is the opposite of the opposite of -1? a) 2 b) 0 c) 1  Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 7. What is the absolute value of 0? a) 0 b) -1 c) 1 8. Arrange integers from least to greatest. a) -9, 12, -14, -10 b) -9, -10, 12, -14 c) -14, -10, -9, 12 TRUE OR FALSE QUESTION SET 1. The absolute value of any integer is always positive. True or False 2. Zero is considered an integer. True or False 3. The absolute value of a number is always positive. True or False 4. The absolute value of 0 is 0. True or False 5. The absolute value of a number represents its distance from zero on the number line. True or False.  Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools CONTENT QUESTIONS 1. The temperature dropped from 5 degrees to -3 degrees. What is the change in temperature? 2. A diver is 15 feet below sea level. If he ascends 10 feet, what is his new position relative to sea level? 3. A bank account has a balance of -$50. If $30 is deposited into the account, what is the new balance? 4. A mountain climber is at an elevation of -200 meters. If he climbs 150 meters, what is his new elevation?  5. A football team lost 7 yards on one play and gained 10 yards on the next play. What is the net change in yards for the team? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools SECTION B: CLASSIFY RATIONAL NUMBERS MULTIPLE CHOICE QUESTIONS 1. What is the product of ⅔ and ⅘ ? b) 6/15 c) 8/5 d) 6/5 2. Which of the following fractions is equivalent to 6/8? b) ⅔ c) 4/6 d) ⅝ 3. What is the least common multiple (LCM) of 6 and 8? a) 12 b) 2 c) 18 4. What are the four categories of numbers? a) Rational Number, Repeating number, Multiples, Factors. b) Natural numbers, Whole Numbers, Integers, Rational Numbers. c) Parenthesis, Exponents, multiplication, division. 5. Two bells ring at intervals of 12 and 18 minutes, respectively. If they ring together at 10:00 AM, at what time will they ring together again? a) 10:18 AM  b) 10:36 AM c) 11:12 AM 6. The elevation of New Orleans is on average 8 feet below sea level. Which correctly describes the opposite of New Orleans Elevation? a) On average 8 feet below sea level. b) At sea level c) On average 8 feet above sea level. 7. Which of the following is the simplest form of 12/16? a) 4/3 b) ⅔ c) ½ Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 8. To which set or sets of numbers does 4 belong? a) Integer, Rational Numbers b) Whole number, Integer, Rational Number c) Integers TRUE OR FALSE QUESTION SET 1. Every integer is a rational number. True or False 2. The decimal representation of a rational number is always terminating. True or False 3. A rational number can be expressed as the ratio of two integers. True or False 4. The sum of two rational numbers is always irrational.  True or False 5. 0/5 is a rational number. True or False CONTENT QUESTIONS 1. The value of a bank account is -98 BD. The amount of 28 BD is then deposited into the account. How much is left in the account? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 2. A pizza is cut into 8 equal slices. If Emily eats 3 slices and her friend Tom eats 2 slices, what fraction of the pizza is left? 3. A recipe calls for ⅔ cup of sugar. If you want to make half of the recipe, how much sugar will you need? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools SECTION C: OPERATIONS WITH FRACTIONS MULTIPLE CHOICE QUESTIONS 1. Which picture shows ½ ? a) Green b) Blue  c) Purple 2. What is ⅖ times 3/7? a) 5/14 b) 1/12 c) 1/10 3. Divide 4/9 by ⅔ a) 6/9 b) 4/6 c) 2/3 4. Which of the following is equivalent to 10/15? a) ⅗ b) 5/7 c) ½ 5. Find the sum: a) 32/14 b) 47/12 c) 13/12 Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 6. What do you call a fraction that is equal? a) Mixed fraction b) Improper fraction c) Equivalent fraction 7. What must you have to add and subtract fractions? a) Different numerators. b) Common denominators. c) Common numerators  8. Are the fractions equivalent? a) Yes b) No 9. Put 15/45 in simplest form. a) 3/6 b) ⅓ c) ⅔ 10. What is the answer to.. a) 4 ⅔ b) 5 ⅓ c) 3 ⅓ TRUE OR FALSE QUESTION SET 1. To add fractions, you must have a common denominator. True or False 2. The product of two fractions is always greater than either of the original fractions. True or False 3. The fraction ¾ is less than ⅔. True or False Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 4. Dividing by a fraction is the same as multiplying by its reciprocal. True or False 5. The sum of two fractions can be greater than 1. True or False CONTENT QUESTIONS 1. Rocky has 50 cookies and 40 brownies to share with 6 friends. How many treats will  each friend receive, if each person receives an equal amount? 2. Lori has 7 ⅓ inches of red string and 6 2/3 inches of blue string. How many inches of string does she have in total? 3. A recipe requires ⅔ cup of sugar. If you want to double the recipe, how much sugar is needed? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools SECTION D: DECIMALS MULTIPLE CHOICE QUESTIONS 1. Order these decimals from least to greatest. a) 1.56, 0.64, 0.94, 0.34 b) 0.34, 1.56, 0.64, 0.94 c) 0.34, 0.64, 0.94, 1.56 2. What is 6.0 ÷ 0.5? a) 10 b) 8 c) 6 3. If the remainder is 0 we call the decimal ….. a) Repeating b) Non-repeating c) Terminating 4. If you subtract 4.5 from 10.1, what is the result? a) 6.6 b) 5.6 c) 4.6 5. What is 15.75 ÷ 3? a) 4.75 b) 6.25 c) 7.25 6. What is the product of 4.2 and 3.5? a) 15.2 b) 13.5 c) 14.7 7. What is the sum of 3.5 and 4.75? a) 8.25 b) 7.75 c) 8.05 Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 8. Compare these decimals a) < b) > c) = 9. Which of the following decimals is the largest? a) 0.75 b) 0.72 c) 0.8 10. Convert the fraction to a decimal: 35/100. a) 0.35  b) 3.5 c) 0.035 TRUE OR FALSE QUESTION SET 1. The decimal 0.5 is equivalent to the fraction ½. True or False 2. The sum of two decimal numbers is always a decimal number. True or False 3. 1.25 - 0.75 = 0.5. True or False 4. A bar notation above a decimal indicates it is repeating. True or False 5. The decimal 0.333... is a terminating decimal. True or False CONTENT QUESTIONS 1. Sarah bought 3.5 pounds of grapes for $7.35. How much did she pay per pound of grapes? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 2. Sarah went to the grocery store and bought milk for $3.29, 2 bread for $2.45, and $1.56 cereal. How much did she spend? 3. If a pencil costs $0.85 and you buy 4 pencils, how much do you spend in total? 4. A board is 10.5 feet long. If you cut off 2.75 feet, how long is the remaining piece?  5. A recipe calls for 2.25 cups of flour. If you only have 1.5 cups, how much more flour do you need to complete the recipe? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools SECTION E: FINDING UNIT RATES MULTIPLE CHOICE QUESTIONS 1. Solve the proportion: a) k = 5 b) k = 45 c) k = 6 2. A store sells 4 apples for $2. What is the unit rate in dollars per apple? b) $0.75 c) $1.00 d) $1.25 3. If a runner completes 5 kilometers in 20 minutes, what is the unit rate in kilometers per hour? a) 12 km/h b) 15 km/h c) 18 km/h 4. A recipe requires 3 cups of flour to make 12 cookies. What is the unit rate in cups of flour per cookie? a) 0.25 cups per cookie b) 0.5 cups per cookie c) 0.75 cups per cookie d) 1 cup per cookie  5. The pet shop has 2 dogs, 4 cats, and 5 hamsters. What is the ratio of dogs to all pets? a) 4 : 5 b) 2 : 11 c) 2 : 9 6. A unit rate is a ratio in fraction form that has a _____________ of 1 a) Numerator b) Fraction c) Denominator Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 7. If a person can read 150 pages in 5 days, what is the unit rate in pages per day? a) 30 pages per day b) 35 pages per day c) 40 pages per day 8. Which of the following is not a unit rate? a) b) c) 9. If a cyclist rides 60 miles in 4 hours, what is the unit rate in miles per hour? a) 12 mph b) 14 mph c) 15 mph 10. In an animal shelter, there are 5 dogs for every 20 cats. Which rate best represents the relationship between dogs and cats? a) 10 dogs for every 40 cats b) 2 dogs for every 10 cats c) 1 dog for every 5 cats. TRUE OR FALSE QUESTION SET 1. A unit rate compares two different quantities with different units. True or False 2. A unit rate can be expressed as a fraction. True or False  3. A unit rate is a rate that has a denominator of one found by dividing the numerator by the denominator. True or False 4. If the ratio of boys to girls in a class is 3:4, there are more girls than boys. True or False 5. The unit rate is always a whole number. True or False CONTENT QUESTIONS 1. A school has a ratio of 5 teachers for every 30 students. If the number of students increases to 60, how many teachers are needed to maintain the same ratio? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 2. If a painter can paint 4 rooms in 8 hours, how many rooms can he paint in 1 hour? 3. A cyclist rides 45 miles in 3 hours. What is the cyclist's speed in miles per hour? 4. Hamburger sells for 3 pounds for $6. If Alicia buys 10 pounds of hamburger, how much will she pay? 5. A car rental company charges $120 for 6 days. What is the cost per day to rent the car?  Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools SECTION F: RATIOS WITH CIRCLE GRAPHS MULTIPLE CHOICE QUESTIONS 1. What is the ratio of 12 to 16 in simplest form? a) 4/3 b) ¾ c) ⅔ 2. If a circle graph shows that 25% of students prefer basketball, what fraction of students prefer basketball? a) ¼ b) ½ c) ⅓ 3. A recipe requires a ratio of 2 cups of flour to 5 cups of sugar. If you use 10 cups of flour, how much sugar do you need? a) 25 cups b) 15 cups c) 30 cups 4. In a circle graph representing favorite desserts, if 25% of the graph is for cake, what angle does that represent in degrees? a) 90° b) 144° c) 150° 5. What percentage does a whole circle graph represent? a) 50% b) 100% c) 360%  Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 6. To make a cleaning solution, George mixes 3 cups of water to 4 drops of cleaner. Which table best represents the ratio of the cleaning solution? a) b) c) 7. If 30% of the students chose French, what percent did not choose French? a) 70% b) 55% c) 15% 8. A circle graph shows that 15% of the respondents prefer tea. If 200 people were surveyed, how many prefer tea? a) 30 b) 35 c) 40 9. A circle graph shows the distribution of time spent on activities in a day. If 30% of the time is spent sleeping, how many degrees does that represent? a) 108° b) 120° c) 180°  Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 10. What percent is spent on savings, food and other things? a) 10% b) 40% c) 25% TRUE OR FALSE QUESTION SET 1. A ratio can be expressed as a fraction. True or False 2. A circle graph can show parts of a whole. True or False 3. The total of all the percentages in a circle graph must equal 100%. True or False 4. Ratios can only compare two quantities. True or False 5. A circle graph is also known as a pie chart. True or False CONTENT QUESTIONS 1. A survey shows that 50% of people prefer coffee, 30% prefer tea, and 20% prefer juice. If 400 people were surveyed, how many prefer tea?  Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 2. A circle graph shows how Sarah spends her time each day. If she spends 8 hours sleeping, which represents 360 degrees of the circle, how many degrees represent her sleeping time? 3. In a circle graph representing the favorite colors of students, 25% prefer blue. If there are 80 students in total, how many prefer blue? 4. A recipe requires a ratio of 4 cups of flour to 1 cup of sugar. If you want to make a batch using 16 cups of flour, how much sugar will you need? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools SECTION G: MEASUREMENT AND CONVERSION MULTIPLE CHOICE QUESTIONS 1. How many centimeters are in a meter? a) 100 b) 1000 c) 10,000 2. If a recipe calls for 2 liters of water, how many milliliters is that? a) 2000 mL b) 20,000 mL c) 2,000,000 mL 3. 1 yard is _______ inches a) 36 b) 80 c) 92 4. How many grams are in 2.5 kilograms? a) 500 g b) 2500 g c) 25 g 5. A swimming pool is 25 meters long and 10 meters wide. What is the perimeter of the pool? a) 80 m b) 90 m c) 100 m 6. Write an equation that can be used to find how many meters are in 57 kilometers. a) 57 x 1000 = 57,000m b) 57 x 100 = 5,700m c) 57 / 0.57 = 100m 7. A cafeteria manager buys 25 gallons of milk. She wants the milk in quart containers. How many quart containers does she need (1 gallon = 4 quarts)? a) 40 quarts b) 100 quarts c) 400 quarts Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools 8. If a piece of fabric is 3 meters long, how many centimeters long is it? a) 300 b) 30 c) 0.03 9. Place the following metric prefixes in order of smallest to largest:  a) Kilo, hecto, deca, deci, centi, milli. b) Deci, centi, milli, deca, hecto, kilo. c) Milli, centi, deci, deca, hecto, kilo. TRUE OR FALSE QUESTION SET 1. There are 1000 milliliters in a liter. True or False 2. A kilometer is longer than a mile. True or False 3. The perimeter of a square is calculated by adding the lengths of all four sides. True or False 4. 1 meter is equal to 100 centimeters. True or False CONTENT QUESTIONS 1. If a car can travel 300 kilometers on 15 liters of fuel, what is the car's fuel efficiency in kilometers per liter? 2. A recipe requires 250 grams of flour. If you want to make a double batch, how much flour will you need in kilograms? Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools  3. A recipe calls for 2 cups of flour. How many ounces of flour is this, if 1 cup equals 8 ounces? 4. If a runner completes a marathon (42 kilometers) in 3 hours, what is the runner's average speed in kilometers per hour? ANSWER KEY WILL BE PROVIDED WHEN STUDENTS RETURN FROM WINTER BREAK Compiled by Middle School Math Department Not for use outside of Modern Knowledge Schools