# Math Mammoth Grade 6 End of the Year Test Notes

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1 Math Mammoth Grade 6 End of the Year Test Notes This test is very long, because it contains questions on all major topics covered in Math Mammoth Grade 6 Complete Curriculum. Its main purpose is to be a diagnostic test to find out what the student knows and doesn't know. The questions are quite basic and do not involve especially difficult word problems. Because this test is so comprehensive, it can be used as a pre-algebra pre-test to find out if a student is ready for pre-algebra. Since the test is so long, I do not recommend that you have your student to do it in one sitting. Break it into 3-5 parts and administer them on consecutive days, or perhaps on morning/evening/morning/evening. There is no need to impose strict time limits. Use your judgment. A calculator is not allowed. The test is evaluating the student's ability in the following content areas: exponents order of operations the basic concepts of an equation and expression ratios & proportions, including word problems all operations with decimals prime factorization all operations with fractions, including word problems concept of percent basic word problems with percent measuring units (in problems throughout the test) angles understanding basic shapes finding the area of basic shapes circumference and area of circles volume and surface area the four operations with integers simple and compound probability mean, median, and mode histogram and stem-and-leaf plot The score of 80% is considered passing score. A student scoring at least that can confidently go to studying any regular pre-algebra program. A student scoring between 70% and 80% may need just some remediation in problem areas before going on to pre-algebra. A student scoring between 50% and 70% will probably benefit from studying Math Mammoth Grade 6 complete curriculum. A student scoring less than 50% should take the end-of-year test for 5th grade, to check if s/he can pass it, because it is possible that Math Mammoth 6th grade would be too difficult, and s/he might need to go down a level.

2 Grading Question # Max. points Student score The Basic Operations and Place Value 1 6 points 2 4 points 3 8 points 4 3 points 5 2 points 6 2 points 7 4 points subtotal / 29 Ratios and Proportions 8 4 points 9 4 points 10 4 points 11 4 points 12 4 points 13 2 points 14 4 points 15 3 points subtotal / 29 Decimals 16 4 points 17 3 points 18 2 points 19 6 points 20 3 points 21 6 points 22 6 points 23 6 points 24 3 points 25 3 points 26 2 points 27 4 points 28 3 points 29 4 points 30 4 points 31 3 points Question # Max. points Student score Number Theory 33 2 points 34 6 points 35 6 points 36 2 points 37 2 points subtotal / 18 Fractions 38 4 points 39 4 points 40 4 points 41 2 points 42 3 points 43 4 points 44 3 points 45 2 points 46 4 points 47 3 points 48 4 points subtotal / 37 Percent points 50 4 points 51 2 points 52 2 points 53 2 points 54 2 points 55 2 points 56 2 points 57 2 points subtotal / points subtotal /65

3 Question # Max. points Student score Geometry 58 2 points 59 4 points 60 2 points 61 2 points 62 2 points 63 2 points 64 3 points 65 3 points 66 3 points subtotal / 23 Question # Max. points Student score Integers 67 2 points 68 4 points 69 8 points 70 6 points 71 6 points 72 6 points 73 4 points subtotal / 36 Statistics & Probability 74 3 points 75 2 points 76 6 points 77a 1 point 77b 1 point 77c 2 points 78 4 points 79 2 points subtotal / 21 TOTAL /288 The total is 288 points. A score of 230 points is 80%.

4 Math Mammoth End of the Year Test - Grade 6 The Basic Operations and Place Value 1. Solve. a. 5 2 b c. 1 5 d. 2 4 e f a. The area of a square is 100 m 2. What is its perimeter? b. The volume of a cube is 27 cubic inches. How long is its side? 3. Calculate in the correct order. a b c. 40 (2 + 4) 2 d (15 + 5) 4. Write as numbers. a. 5 billion, 80 million, 7 thousand b. 6 trillion, 392 million, five hundred c. 9 trillion, 20 billion, 154 million

5 5. Write in normal form (as a number). a b Evaluate the expressions when the value of the variable is given. a. 3x + 8 when x = 6 b. 40 y 12 when y = 8 7. Solve the equations. You can just think logically! a x = 920 b. x 250 = 250 c. 6x = 420 d. x 9 = 800 Ratios and Proportions 8. Simplify the ratios. a. 2:6 b. 9 balls to 12 triangles c. 200 g to 2 kg d. 15:21 9. Fill in the missing numbers to form equivalent rates. a. 7 km 30 min = 15 min = 45 min b. \$96 8 hr = 2 hr = 10 hr

6 10. Eileen mixes juice concentrate and water in the ratio of 2:5, to get diluted juice. She uses 80 ml of juice concentrate. How much water will she need? How much diluted juice will she get? 11. Solve the following proportions. Give your answer as a mixed number. a. x 5 = 7 3 b = 2 M 12. Solve. Show your work. Harry can swim 20 laps in a pool in 18 minutes (swimming at a constant speed). How many laps could he swim in 45 minutes? (Swimming with the same speed.)

7 13. Write a proportion. You do not have to solve it. Just write the proportion To purchase 600 bales of hay costs \$3,300. How may bales would you get with \$2,500? = 14. A car can go 80 km on 7 liters of gasoline (traveling with constant speed). a. How many liters of gasoline would the car need for a trip of 54 km? b. How far can the car travel on 18 liters of gasoline? 15. A rectangle's length and width are in the ratio of 2:5, and its perimeter is 140 cm. What are the rectangle's length and width?

8 Decimals 16. Write as decimals. a. three thousandths b. 12 tenths c millionths d. 27 ten-thousandths 17. Write as fractions or mixed numbers. a b c Write in order from the smallest to the greatest. a b Add mentally. a = = b = = c = = 20. Add or subtract mentally. Give your answers in decimals. a b c Multiply mentally. a = d = b = e = c = f = 22. Divide mentally. a = d = b = e = c = f =

9 23. Round to... three decimals to the nearest tenthousandth Number: Find the value of the expression 6y when a. y = 0.02 b. y = c. y = Calculate. a b c Write as decimals. Round to five decimal digits. a. 3 7 b

10 27. Multiply both the dividend and the divisor so that you get a whole-number divisor. Then divide using long division. Round the answers to the nearest thousandth. a b You are packing books that weigh 14 oz each into a box that must not weigh more than 9 pounds. How many books can you put into the box? 29. Convert to the given unit. You may need the space for calculations. a. 52 oz = lb b. 1.3 lb = oz c. 3.6 ft = in d. 76 in = ft 30. Convert the measurements to the given units. a. 125 cm = m = mm b. 300 g = kg = mg 31. You need 300 ml of flour for a cake. A flour bag has 2 kg of flour, and 1 kg of flour equals 1.6 liters. How many cakes can you make from the bag of flour?

11 32. A laptop weighs 3.3 kg, and its case weighs 650 grams. The airline has an 18-kg limit for your carry-on luggage. If you take the laptop with its case, how much weight is left for the rest of your carry-on luggage? Number Theory 33. Is 283 divisible by 24? Justify your answer. 34. Mark an x if the number is divisible by 2, 3, 4, 5, 6, or 9. Divisible by ,966 9,423 Divisible by , Factor the following numbers to their prime factors. a. 22 / \ b. 65 / \ c. 48 / \ 36. Find the greatest common factor of the given numbers. a. 45 and 36 b. 40 and Find the least common multiple for these pairs of numbers. a. 3 and 7 b. 9 and 12

12 Fractions 38. If you can find an equivalent fraction, write it. If you can not, cross out the whole problem. a. 5 7 = 34 b. 7 = 8 28 c. 9 8 = 56 d = Add and subtract the fractions and mixed numbers. a b c d Compare the fractions, and write <, >, or = in the box. a b c d Is the following multiplication correct? If not, correct it. 2 3 = 42. How many 1 3/4-inch pieces can you cut from a string that is 33 1/2 inches long?

13 43. Solve. Give your answer as a mixed number and in a simplified form. a b c d Dad used 1/7 of his \$1,785 to pay for rent. Of what was left, he used 1/5 to pay a grocery bill. a. How much was the grocery bill? b. How much money does Dad have left now? 45. Of a chess club s members, 2/5 are girls, and the rest are boys. There are 18 boys. How many members does the club have? 46. Mary s vegetable garden is 5 1/2 feet by 5 1/2 feet. a. Find its area in square feet. b. Find its area in square inches.

14 47. A 3-ft board was cut into two pieces that were in the ratio of 1:7. How long is each of the pieces? 48. A rectangle with the sides of 2 1/4 in. and 2 in. is enlarged in a ratio of 2:3. a. Find the lengths of the sides of the resulting larger rectangle. (Optionally, you can also draw the rectangles.) b. Find the area of the resulting rectangle. Percent 49. Write as percentages, fractions, and decimals. a. % = = b. 3% = = c. % = = 0.89 d. 270% = = e. % = = f. % = = Write as a percentage. Round your answers to the tenth of a percent. a. 1/7 b. 13/ Jeans cost \$20, but the store increased the price by 20%. What is the new price?

15 52. Tina's book bag contains 12 fiction books and 4 non-fiction books. What percentage of the books are non-fiction? 53. Meredith is 160 cm tall. Jane's height is 90% of Meredith's height. How tall is Jane? 54. How much does a \$5.40 lunch cost if it is discounted by 10%? 55. Arthur and Jim are babies. Arthur is 64 cm long and Jim is 80 cm long. How many percent is Arthur's height of Jim's height? 56. A chess club had 15 members. Next year it has 20 members. How many percent was the increase? 57. The rent was \$200, and then it was lowered to \$190. What percent was the decrease?

16 Geometry 58. The lines l and m are parallel. One angle in the figure is marked as 130. How many degrees are angles A and B? A = ; B = 59. Two angles of a triangle measure 20 and 70. a. Is the triangle acute, right, or obtuse? b. The side between the 20 and 70 angles measures 5 cm. Draw the triangle. 60. Mary is making a quilt using squares like the one on the right. What is the area of one of the small triangles in square centimeters? In square millimeters? 61. The radius of a circle is 6 units. Which of the following expressions will give you the area of the circle? You do not have to calculate the area. a. 6 π b. 6 π 2 c. 36 π d. 12 π e. 6/π f. 6/π 2 g. 36/π h. 12/π 62. The radius of a circle is 10 cm. What is the circumference of the circle, to the nearest millimeter? a. 31 mm b. 314 mm c. 628 mm d. 63 mm 63. The triangles are similar. Calculate the side length marked with x.

17 64. Find the total area of this shape. 65. Find the surface area of a cube with 3-cm sides. 66. Find the volume of this cylinder-shaped can. Use 3.14 for Pi.

18 Integers 67. Order the numbers from the least to the greatest. a b Draw a number line jump for each addition or subtraction sentence. a = b = c. 1 5 = d. 3 8 = 69. Add and subtract. a. b. c. d. 3 + ( 8) = ( 6) + ( 9) = 2 + ( 9) = 4 ( 2) = ( 3) + 8 = 6 9 = 6 5 = 4 ( 2) = 70. Multiply. a. 3 ( 5) = 3 5 = b. ( 7) ( 8) = 7 ( 9) = c. ( 2) 3 ( 2) = 8 ( 2) ( 1) = 71. Divide. a. 20 ( 5) = 33 ( 3) = b. ( 48) ( 4) = 21 ( 7) = c = 150 ( 10) = 72. Find the missing numbers. a. 5 + = 10 b. 2 = 14 c. 3 = 2 d. 48 = 6 e. 4 + = 0 f. 1 = 9

19 73. Plot the points from the function y = 2 x for the values of x listed in the table. x y x y Statistics & Probability 74. You pick randomly one marble from these marbles. Find the probabilities: a. P(yellow) b. P(not red) c. (blue or red) 75. You pick randomly one marble, and put it back. Then you pick another marble. Find the probabilities: a. P(blue; blue) b. P(not yellow; not yellow) 76. If possible, find the mean, median, and mode of the data sets. a. blue, blue, blue, blue, red, red, green, yellow, yellow, yellow mean median mode b. 6, 8, 10, 10, 10, 11, 11, 12, 13, 16 mean median mode

20 77. The line graph shows the number of candles that the candle factory sold in years 2005 to Note the scale is given in thousand candles. a. Estimate from the graph about how many candles were sold in b. About how many more candles were sold in 2010 than in 2005? c. About how many percent was the increase from 2005 to 2010? 78. This data lists the ages of 24 snowboarders (in years). Make a histogram with five bins Age (years) Frequency 79. A factory makes candles and packages them into boxes. The manager chose 15 boxes and counted the number of candles in them. The stem-and-leaf plot shows the data he got. a. What is the median? Stem Leaf b. What is the range? 4 5 means 45

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