2015 ARML Local Problems and Solutions Team Round Solutions
... I-1 The graph of y = ax2 + bx + c passes through (−1, −3), (1, 3), and (2, 12). Compute abc. I-1 Solution Substituting x− and y−coordinates of the three points into the general equation gives us three equations: a − b + c = −3, a + b + c = 3, and 4a + 2b + c = 12. Subtracting the first two equations ...
... I-1 The graph of y = ax2 + bx + c passes through (−1, −3), (1, 3), and (2, 12). Compute abc. I-1 Solution Substituting x− and y−coordinates of the three points into the general equation gives us three equations: a − b + c = −3, a + b + c = 3, and 4a + 2b + c = 12. Subtracting the first two equations ...
Doc - UCF CS
... compute the gcd of three integers, and use this method to find gcd(26, 78, 117). gcd(a,b,c) = gcd(gcd(a,b),c). Thus, we can use Euclid's algorithm to compute the gcd of a and b. Let this value be d. Then, reuse Euclid's algorithm to calculate the gcd of c and d. (Let this be e.) This value, is the d ...
... compute the gcd of three integers, and use this method to find gcd(26, 78, 117). gcd(a,b,c) = gcd(gcd(a,b),c). Thus, we can use Euclid's algorithm to compute the gcd of a and b. Let this value be d. Then, reuse Euclid's algorithm to calculate the gcd of c and d. (Let this be e.) This value, is the d ...
Algebra 1- Midterm review
... The championship basketball game at North High School was this past Friday night. The school raised $600 in ticket sales. The tickets sold for $5.50 in advance and $8.00 at the door. If 100 tickets were sold, what was the number of tickets sold at the door? Only and algebraic solution will be accept ...
... The championship basketball game at North High School was this past Friday night. The school raised $600 in ticket sales. The tickets sold for $5.50 in advance and $8.00 at the door. If 100 tickets were sold, what was the number of tickets sold at the door? Only and algebraic solution will be accept ...
Standard 1 - Briar Cliff University
... 7.1.3.14. Finds % of a number (ITBS) 7.1.3.15. Adds, subtracts, multiples, and divides percents 7.1.3.16. Applies fractions, decimals, and percents to problem solving 7.1.3.17. Uses appropriate methods to compute with integers (ITBS)* 7.1.3.18. Locates integers on the number line 7.1.3.19. Knows the ...
... 7.1.3.14. Finds % of a number (ITBS) 7.1.3.15. Adds, subtracts, multiples, and divides percents 7.1.3.16. Applies fractions, decimals, and percents to problem solving 7.1.3.17. Uses appropriate methods to compute with integers (ITBS)* 7.1.3.18. Locates integers on the number line 7.1.3.19. Knows the ...
Draft 12
... Larger numbers with missing factor reasoning. Example: 317 ÷ 7 = ? Restate as a missing factor: ? × 7 = 317 Think: How many groups of 7 are in 317? Explain your reasoning, similar to above for smaller numbers, using the language of “groups of,” “left over,” “too high,” and “too small.” Connect y ...
... Larger numbers with missing factor reasoning. Example: 317 ÷ 7 = ? Restate as a missing factor: ? × 7 = 317 Think: How many groups of 7 are in 317? Explain your reasoning, similar to above for smaller numbers, using the language of “groups of,” “left over,” “too high,” and “too small.” Connect y ...
Measuring and Scientific Notation
... Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is a useful technique. Unit factors may be made from any two terms that describe the s ...
... Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is a useful technique. Unit factors may be made from any two terms that describe the s ...
Lesson 3
... Since the coefficients of the x terms, 4 and 4, are the same, you can eliminate the x terms by subtracting the equations. Write the equation in column form and subtract. Notice that the x value is eliminated. Divide each side by 5. ...
... Since the coefficients of the x terms, 4 and 4, are the same, you can eliminate the x terms by subtracting the equations. Write the equation in column form and subtract. Notice that the x value is eliminated. Divide each side by 5. ...
6.037, IAP 2016—Streams 1 MASSACHVSETTS INSTITVTE OF TECHNOLOGY
... Since the stream represents a function, we can write operations which work on functions and try to implement them in terms of the coefficients of the series. One such operation is integration. The integral of an infinite polynomial is also an infinite polynomial, but the coefficients will be differe ...
... Since the stream represents a function, we can write operations which work on functions and try to implement them in terms of the coefficients of the series. One such operation is integration. The integral of an infinite polynomial is also an infinite polynomial, but the coefficients will be differe ...
Vocabulary for Exponents: Exponent
... "I AM NOT AFRAID OF EXPONENTS, I AM SMARTER THAN EXPONENTS!!! ...
... "I AM NOT AFRAID OF EXPONENTS, I AM SMARTER THAN EXPONENTS!!! ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.