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Potpourri Grade 4 1. What is the greatest common factor of the numbers 72, 102, and 120? 2. What is the sum of the next two numbers in the following sequence? 1, 2, 4, 8, 16... 3. What is the sum of the integers from zero to 50, inclusively? 4. An envelope contains a sheet listing a three-digit mystery number. On the outside are three clues: • The mystery number is prime • My tens digit is equal to my hundreds digit • My ones digit is equal to one less than the sum of the tens and hundreds digit What is the mystery number? 5. If you were to list the numbers from 1 to 271, inclusively, how many times would you write the digit ‘2’? 6. If 15 objects are to be placed into four different piles, each with a different number of objects, what is the largest number of objects any of the piles can have? 7. What is the fraction equivalent of the repeating decimal 0.24 ? Express your answer as a reduced fraction. 8. If the first term of a sequence is 2, the second term of the sequence is 7, and each of the following terms is equal to the sum of the previous two terms, what is the tenth term in the sequence? 9. If each of the operators, “+”, “-”, and “x” must be used exactly once in each of the blanks below, what is the largest value that the expression can have? 2 __ 4 __ 3 __ 3 10. In chess, a queen can move in any one linear direction any number of spaces each move. If the queen is placed on one of the 64 squares, what is the greatest number of possible moves you can have? Potpourri Grade 5 1. What is the sum of the integers from zero to 50, inclusively? 2. An envelope contains a sheet listing a three-digit mystery number. On the outside are three clues: • The mystery number is prime • My tens digit is equal to my hundreds digit • My ones digit is equal to one less than the sum of the tens and hundreds digit What is the mystery number? 3. If you were to list the numbers from 1 to 271, inclusively, how many times would you write the digit ‘2’? 4. If 15 objects are to be placed into four different piles, each with a different number of objects, what is the largest number of objects any of the piles can have? 5. What is the fraction equivalent of the repeating decimal 0.24 ? Express your answer as a reduced fraction. 6. If the first term of a sequence is 2, the second term of the sequence is 7, and each of the following terms is equal to the sum of the previous two terms, what is the tenth term in the sequence? 7. If each of the operators, “+”, “-”, and “x” must be used exactly once in each of the blanks below, what is the largest value that the expression can have? 2 __ 4 __ 3 __ 3 8. In chess, a queen can move in any one linear direction any number of spaces each move. If the queen is placed on one of the 64 squares, what is the greatest number of possible moves you can have? 9. Suppose that a spelling test ends after a student gets ten consecutive words incorrect. If a student spelled 10 words correctly, what is the largest number of words the student could have been given? 10. When two numbers are multiplied together, the product is 120. When the numbers are added together, the sum is 29. What is the positive difference of the two numbers? Potpourri Grade 6 1. If you were to list the numbers from 1 to 271, inclusively, how many times would you write the digit ‘2’? 2. If 15 objects are to be placed into four different piles, each with a different number of objects, what is the largest number of objects any of the piles can have? 3. What is the fraction equivalent of the repeating decimal 0.24 ? Express your answer as a reduced fraction. 4. If the first term of a sequence is 2, the second term of the sequence is 7, and each of the following terms is equal to the sum of the previous two terms, what is the tenth term in the sequence? 5. If each of the operators, “+”, “-”, and “x” must be used exactly once in each of the blanks below, what is the largest value that the expression can have? 2 __ 4 __ 3 __ 3 6. In chess, a queen can move in any one linear direction any number of spaces each move. If the queen is placed on one of the 64 squares, what is the greatest number of possible moves you can have? 7. Suppose that a spelling test ends after a student gets ten consecutive words incorrect. If a student spelled 10 words correctly, what is the largest number of words the student could have been given? 8. When two numbers are multiplied together, the product is 120. When the numbers are added together, the sum is 29. What is the positive difference of the two numbers? 9. Assuming n < 50 , how many bases n will not make the base-n number 121n a square number when converted into a base ten number? 10. Two numbers, neither of which contains the digit zero, have a product of five billion. What is the smaller of the two numbers? Potpourri Grade 7 1. What is the fraction equivalent of the repeating decimal 0.24 ? Express your answer as a reduced fraction. 2. If the first term of a sequence is 2, the second term of the sequence is 7, and each of the following terms is equal to the sum of the previous two terms, what is the tenth term in the sequence? 3. If each of the operators, “+”, “-”, and “x” must be used exactly once in each of the blanks below, what is the largest value that the expression can have? 2 __ 4 __ 3 __ 3 4. In chess, a queen can move in any one linear direction any number of spaces each move. If the queen is placed on one of the 64 squares, what is the greatest number of possible moves you can have? 5. Suppose that a spelling test ends after a student gets ten consecutive words incorrect. If a student spelled 10 words correctly, what is the largest number of words the student could have been given? 6. When two numbers are multiplied together, the product is 120. When the numbers are added together, the sum is 29. What is the positive difference of the two numbers? 7. Assuming n < 50 , how many bases n will not make the base-n number 121n a square number when converted into a base ten number? 8. Two numbers, neither of which contains the digit zero, have a product of five billion. What is the smaller of the two numbers? 9. What is the sum of the following arithmetic series? 55 + 51 + 47 + ... + (!37) + (!41) 10. If each letter represents a different number between 0 and 9 inclusively, what is the five-digit number that is represented by “AEIOU”? AEIOU ! 4 = UOIEA Potpourri Grade 8 1. If each of the operators, “+”, “-”, and “x” must be used exactly once in each of the blanks below, what is the largest value that the expression can have? 2 __ 4 __ 3 __ 3 2. In chess, a queen can move in any one linear direction any number of spaces each move. If the queen is placed on one of the 64 squares, what is the greatest number of possible moves you can have? 3. Suppose that a spelling test ends after a student gets ten consecutive words incorrect. If a student spelled 10 words correctly, what is the largest number of words the student could have been given? 4. When two numbers are multiplied together, the product is 120. When the numbers are added together, the sum is 29. What is the positive difference of the two numbers? 5. Assuming n < 50 , how many bases n will not make the base-n number 121n a square number when converted into a base ten number? 6. Two numbers, neither of which contains the digit zero, have a product of five billion. What is the smaller of the two numbers? 7. What is the sum of the following arithmetic series? 55 + 51 + 47 + ... + (!37) + (!41) 8. If each letter represents a different number between 0 and 9 inclusively, what is the five-digit number that is represented by “AEIOU”? AEIOU ! 4 = UOIEA 9. How many squares of any size can be found in the eight-by-eight chess board as seen below? 10. What is the smallest number that can be multiplied by 1080 to make it a perfect square?