Rational Equations and Inequalities in One Variables
... For any x less than 2, the quotient is positive (quotient of two negatives). For any x between 2 and 3, the quotient is negative (quotient of a negative and a positive). For any x greater than 3, the quotient is positive (quotient of two positives). We return to the original inequality x3 ...
... For any x less than 2, the quotient is positive (quotient of two negatives). For any x between 2 and 3, the quotient is negative (quotient of a negative and a positive). For any x greater than 3, the quotient is positive (quotient of two positives). We return to the original inequality x3 ...
Use stratified sampling methods
... Solve a pair of simultaneous equations in two unknowns such as 2x+y=5 and 3x+2y = 4 Know that each equation can be represented by a line on a graph and that the point of intersection of the lines is the solution Complete tables for, and draw graphs of cubic functions Use cubic graphs to solve equati ...
... Solve a pair of simultaneous equations in two unknowns such as 2x+y=5 and 3x+2y = 4 Know that each equation can be represented by a line on a graph and that the point of intersection of the lines is the solution Complete tables for, and draw graphs of cubic functions Use cubic graphs to solve equati ...
The Inclusion Exclusion Principle
... more than the number who solved A and at least one other problem. Of all participants who solved just one problem, half did not solve problem A. How many solved just problem B? 9. How many numbers can be obtained as the product of two or more of the numbers 3, 4, 4, 5, 5, 6, 7, 7, 7? Solution: Solut ...
... more than the number who solved A and at least one other problem. Of all participants who solved just one problem, half did not solve problem A. How many solved just problem B? 9. How many numbers can be obtained as the product of two or more of the numbers 3, 4, 4, 5, 5, 6, 7, 7, 7? Solution: Solut ...
Factors and Multiples
... The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, etc ... Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, etc. What is the "Least Common Multiple"? When you list the multiples of two (or more) numbers, and find the same value in both lists, then that is a common multiple of those numbers. The LCM is s ...
... The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, etc ... Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, etc. What is the "Least Common Multiple"? When you list the multiples of two (or more) numbers, and find the same value in both lists, then that is a common multiple of those numbers. The LCM is s ...
Mathematics, Calculus Year 1 Inverse functions Please solve each
... This is a function of t. But there is no t on the right side. So the function is a constant function. The domain of a constant function is “ all numbers”. d) g(t) = SQRT(1-2^t) Square root of a function is defined only if the value inside the square root is positive. So the function is defined for p ...
... This is a function of t. But there is no t on the right side. So the function is a constant function. The domain of a constant function is “ all numbers”. d) g(t) = SQRT(1-2^t) Square root of a function is defined only if the value inside the square root is positive. So the function is defined for p ...
Group action
... Division with remainder => Euclidean algorithm => unique factorization. Notice, that there are 6 units. Next we come to a question, which circles of radius N have points on integer lattice and how many. It is the same as representing N in the form a2 – ab + b2 (or, which is an equivalent problem, in ...
... Division with remainder => Euclidean algorithm => unique factorization. Notice, that there are 6 units. Next we come to a question, which circles of radius N have points on integer lattice and how many. It is the same as representing N in the form a2 – ab + b2 (or, which is an equivalent problem, in ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.