2008 Cedar Ridge Test Solutions

Transcription

1 2008 Cedar Ridge Test Solutions 1) The value of is Step 1: Line up all of the decimals in the equation: ) Solve: x = Answer: Order of Operations Parenthesis Exponents Multiplication Division Addition Subtraction Step 1: Follow Order of Operations when solving this problem: x =? =? =? =? = 11 3) Your average for the first 4 tests is 88. What must you score on the next test in order for your average on the five tests to be at least 90? Step 1: You need to multiply 88 by 4 to get total score of all four tests: 88 x4 352 Step 2: You need to multiply 90 by 5 to get the total score of all five tests: 90 x5 450 Step 3: You need to minus the total of 4 tests from the total of 5 tests to get the score you will need to make to have a Answer: 11 Answer: 98

2 2008 Cedar Ridge Test Solutions 4) Solve: + + = Step 1: Since the answer needs to be in decimal, you will need to change all of the fractions to decimal. =. =. =. Step 2: Solve the addition problem, by lining up your decimals: Answer:.194 5) Daniel worked 8 hours on Saturday and earned $26. How much did he earn per hour? Step 1: This is a very simple problem, all you need to do is divide $26 by 8 and that will give you the hourly rate: Daniel makes $3.25 per hour Answer: $3.25

3 6) What is the height of a triangle with a base of 6 units and an area of 27 units²? Step 2: Use our Area Formula for a triangle: Step 1: Draw your Triangle: A = 27 = A = = 3h = h h = 9 Answer: 9 7) Which of the following numbers is not divisible by 3(with no remainder)? A) 12,043,821 B) 91,240,615 C) 2,011,785 D) 5,261,001 NOTE: When you need to find out if a large number is divisible by a single digit number, add up all the numbers in the large number and then divide it by the single digit Step 1: Following our rule to the left, lets begin to add: A) = 21 B) = 28 C) = 24 D) = 18 Step 2: See if they are divisible by 3: A) 21 3 = 7 B) 28 3 C) 24 3 = 8 D) 18 3 = 6 Answer: 91,240,615

4 8) If a whole number N is divided by 13, the quotient is 8 and the remainder is 12. What is the sum of the digits of N? Step 1: Write out your equation: N 13 = 8 r12 Step 2: We will need to multiple 13 by 8 and then add the 12 back: 13 x N = 116 Step 3: You must find the sum of the digits of N = 8 Answer: 8 9) What is the sum of the largest number and the smallest number: 0.3, 0.31, 0.305, ? Step 1: List the numbers from smallest to largest:.0309, 0.3, 0.305, 0.31 Step 2: Add the small number to the largest number: Answer:.3409

5 10) How many degrees are in the smaller angle formed by the hands of a clock at exactly 4 o clock? Step 1: Draw the clock to show the angle you are looking for: Step 2: You know that a full circle is 360 degrees, so you the formula of : = 30 degrees for every 5 minutes. Step 3: You now know that for every 5 minutes it s 30 degrees, so now times that by x 4 = 120 degrees. Answer: ) If two-fifths of the 30 math team members are boys, what is the ration of boys to girls? Step 1: You need to find out how many boys there are: x 30 =? Step 2: Find out how many girls there are: = x = 12 Step 3: Put into Ratio Format boys to girls: = Ratio Format: 2:3 Answer: 2:3

6 12) Sarah lives 2.7 miles from school. This year she has made 150 round trips from her home to school and back on her bike. How far is this altogether? Step 1: Find what one round trip would be: 2.7 x miles = one round trip Step 2: Multiply the one round trip by the total round trips: 150 x 5.4 miles miles Answer: 810 Miles 13) Express as a decimal. Step 1: Divide 7 by This will be a repeating decimal. Answer:.63

7 14) Fred phones every 3 days, Barney every 4 days, and Wilma every 8 days. If all three phoned on October 27, on what day will all three phone again? Step 1: Find the LCM of all three numbers: 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 8: 8, 16, 24, 32, 40, 48, 56, 64, 78, 80 Step 2: Add 24 to October 27 th and you will get your day that they all phone on. October 27 th + 4 days October 31 st November 1 st +20 days November 20 th Answer: November 20th 15) What is the sum of all the whole number positive factors of 42? Step 1: List all the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Step 2: Add all the factors together: =? =? = 96 Answer: 96

8 16) Ivy baked brownies for math team practice. She baked them in a 8 in. by 12 in. pan. How many students can she serve if she cuts them into 2 in. x 2 in. squares and serves one per student? Step 1: Find out how many total square inches are in the pan of brownies: 12 inches x 8 inches = 96 inches Step 2: Find the total square inches that Ivy is going to cut them into: 2 inches x 2 inches = 4 inches Step 3: Divide the total square inches for the pan by the total square inches that Ivy is going to cut them into: 96 inches 4 inches = 24 Students Answer: 24 Students

9 17) One liter contains 1.8 ounces more than one quart. How many ounces are in a 3 liter bottle of Mountain Dew? Conversion Chart 1 cup = 8 ounces 1 Pint = 16 ounces 1 Quart = 32 ounces 1 Gal. = 128 ounces Step 1: Looking at the chart to the right, determine how many ounces are in one liter, using the Quart plus the 1.8 ounces more: 32 ounces ounces = 33.8 ounces in a liter Step 2: Multiply the 33.8 ounces(1 liter) by 3 liters: 33.8 ounces x 3(liters) = ounces Answer: ounces 18) What is the sum of the prime numbers between and? Step 1: Find the Square Root of 25 and 400 : 25 = 5 x = 20 x 20 The square roots are 5 and 20. Step 2: Find the prime numbers between 5 and 20: 5, 7, 11, 13, 17, 19, 20 Step 3: Add the prime numbers together: =? =? = 67 Answer: 67

10 19) Chris bought one dozen chocolate covered donuts for math team practice. He ate one-third of them on the way to school. Jon ate onefourth of the remaining donuts before practice began. When Bob arrived, he ate all that were left. How many donuts did Bob eat? Step 1: Find how many Chris ate on the way to school. You need to find 1/3 of a dozen: 12 x = 4 donuts So Chris ate 4 donuts on the way to school. Step 2: Find out how many Jon ate. You need to find remaining donuts: of the Chris ate 4 donuts on the way, so minus 4 from a dozen: 12 4 = 8 Now find of 8 donuts: 8 x = 2 donuts Jon ate 2 donuts before practice. Step 3: Find out how many Bob ate. You need to minus what Jon ate from the remaining donuts. Bob ate 6 donuts. 8 donuts 2 donuts = 6 donuts left. Answer: 6 Donuts

11 20) The measure of three angles in a quadrilateral is 90, 130, and 55. What is the measure of the fourth angle? NOTE: All angles in a quadrilateral have to add up to 360 Step 1: add all the angles together: =?? = 275 Step 2: Deduct the total of all of the angles from 360 : = 85 Answer: 85 21) What is the positive difference in the sum of the composite numbers between 10 and 20 and the sum of the prime numbers between 10 and 20? Step 1: Find the Composite Numbers and Prime Numbers between 10 and 20: Composite Numbers: 12, 14, 15, 16, 18 Prime Numbers: 11, 13, 17, 19 Step 2: Find the sum of both Composite Numbers and Prime Numbers: CN: = 75 PN: = 60 Step 3: Find the difference between the total of the Composite Numbers and the total of the Prime Numbers: = 15 Answer: 15

12 22) If 5a = 70 and 8b = 20, what is the value of ab? Step 1: Solve for a and b: 5a = 70 8b = 20 Step 2: Solve ab: (14)(2.5) = 35 23) What is the measure of the supplement of a 50 angle? Supplementary Angles: Two angles that add up to 180 Formula: x Complementary Angles: Two angles that add up to 90 Formula: 90 - X a = = 14 b = = 2.5 Answer: 35 Step 1: Use the formula for finding a Supplementary Angle: = 130 Answer: ) Elisa bought 2 pounds of gummy bears at $2.50 per pound and 3 pounds of gooey bears at $4.00 per pound. What was the average cost per pound? Step 1: Find out how much pounds were bought and how much money was spent: Pounds bought Money Spent 2 pounds of Gummy Bears 2 x $2.50 = $ pound of Gooey Bears 3 x $4.00 = $ pounds of Nuts Total $ Spent = $17.00 Step 2: Use the averaging formula: Total Spent divided by Total Pounds: $ pounds = $3.40 per pound Answer: $3.40

13 25) By how much does the product of 3, 4, and 5 exceed 3² + 4² + 5² Step 1: Find the product of 3, 4, and 5: 3 x 4 x 5 = 60 Step 2: Solve 3² + 4² + 5² (3 x 3) + (4 x 4) + (5 x 5) =? =? = 50 Step 3: Find how much Step 1 exceeds Step 2: = 10 Tiebreaker #1) What is the sum of all the factors of 91? Step 1: You need to find all of the factors of 91: 7 91 Don t forget 1 & Factors of 91: 1, 7, 13, 91 Step 2: Add all the factors together: Answer: =?? = 112 Answer: 112

14 Tiebreaker #2) What is the 12 th number in the following sequence: 1, 4, 9, 16, 25, 36,. Step 1: Find the pattern in the sequence: (1x1), 4(2x2), 9(3x3), 16(4x4), 25(5x5), 36(6x6), As you can see, the pattern is perfect squares of the number in the sequence. Step 2: Find the 12 th number in the sequence: Continuing the sequence from above: (7x7), 64(8x8), 81(9x9), 100(10x10), 121(11x11), 144(12x12) Answer: 144 Tiebreaker #3) The perimeter of a regular octagon and a regular hexagon are equal. If the length of one side of the octagon is 7.5 cm, what is the length of one side of the hexagon? Step 1: Find the Perimeter of the Octagon: P = Measurement of one side times(x) number of sides 7.5 x 8 = 60 Step 2: Find the Perimeter of the Hexagon (Remember: The perimeter of the Hexagon = the perimeter of the Octagon) 60(Perimeter) 6(# of Sides) = 10 cm Answer: 10 cm