KCIS Gr.12 College Algebra
Terms in this set (68)
If a=b, then a can be replaced by b in any expression involving a.
The four basic arithmetic operations are addition, multiplication, subtraction and division
If a, b, and c are integers such that ab=c, the a and b are factors or divisors of c.
A prime number is a positive integer that has exactly two factors: itself and 1.
Integers such as 1, 3, 9, 16 and 49 are called perfect squares.
leading coefficient, constant term
Let an,...a2,a1,a0 be real numbers and let n be a nonnegative inter.
A polynomial in x is an expression of the form anxn+...+a2x2+a1x+a0 where an . The polynomial is of degree of n, and the number of an is the leading coefficient. The number a0 is the constant term.
A polynomial that has all zero coefficients.
A linear equation in one variable x in an equation that can be written in the standard form ax+b=0 where a and b are real numbers with a ≠0
Many common types of geometric, scientific, and investment problems use ready-made equations, called formulas.
A quadratic equation in x is an equation that can be written in general form ax²+bx+c=0 where a, b, and c are real numbers with
Zero -factor property
If ab=0, then a=0 or b=0.
Two inequalities that have the same solution set are equivalent.
The midpoint of the line segment joining the points (x1, y1) and (x2, y2) in the coordinate plane is ((x1+x2)/2, (y1+y2)/2)
For an equation in variable x and y , a point (a, b) is a solution if the substitutions x = a and y = b satisfy the equation.
x - intercept
The x-intercept of a graph are the points at which the graph intersects the x-axis.
y - intercept
The y-intercept of a graph are the points at which the graph intersects the y-axis.
slope of a line
The slope m of tough the nonvertical line passing the points (x1, y1) and (x2, y2) is m = (y2-y1)/(x2-x1) where x1≠x2
The point slope form of the equation of the line that passes through the point (x1, y1) has a slope of m is (y - y1) = m (x - x1).
The statistical method of fitting a line to a collection of points is called linear regression.
The collection of points is called a scatter plot.
A function defined by two or more equations over a specified domain is called a piece-wise-defined function.
zeros of a function
A zeros of a functions are the x -values for which the function is zero.
Let a and b be real numbers. The number a+bi is called a complex number.
Factors of a polynomial
Every polynomial of degree n>0 with real coefficients can be written as the product of linear and quadratic factors with real coefficients, where the quadratic factors have no real zeros.
slant (oblique) asymptote
If the degree of the numerator is exactly one more than the degree of the denominator, then the graph of the function has a slant (or oblique) asymptotic.
The exponential function f with base a is denoted by f(x) = a∧x where a > 0, a≠0, and x is any real number.
natural exponential function
The function given by f(x) = e∧x is called the natural exponential function.
logarithmic function with base
The function given by f(x) = log_a(x) is called the logarithmic function with base a
common logarithmic function
The logarithmic function with base 10 is called the common logarithmic function.
natural logarithmic function
The function defined by f(x) = log_e(x) = ln(x), x>0 is called the natural logarithmic function
When enough units have been sold so that the total revenue R equals to the total cost C, the sales are said to have reach the break-even point.
To solve a system that is not in row-echelon form, first convert it to an equivalent system that is in row-echelon form by using one or more of the elementary operations. This process is called Gaussian elimination.
solution of an inequality
An order pair (x,y) is a solution of an inequality in and if the inequality is true when a and b are substituted for x and y, respectively.
Many applications in business and economics involve a process called optimization, in which you are asked to find the minimum cost, the maximum profit, or the minimum use of resources.
A matrix that has only one row is called a row matrix.
A matrix that has only one column is called a column matrix.
A matrix derived from a system of linear equations (each written in standard form with the constant term on the right) is the augmented matrix.
The matrix derived from the coefficients of the system (but that does not include constant terms is the coefficient matrix of the system.
Two matrices are row-equivalent
A curve formed by the intersection of a plane and a double-napped cone. Conic sections are also called conics.
co-vertices of an ellipse
The points of intersection of an ellipse and the line perpendicular to the major axis at the center.
discriminant of a general second -degree equation
The expression B² - 4AC for the equation Ax² + Bxy +Cy² + Dx +Ey +F = 0 . Used for identify which type of conic the equation represents.
The set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci, is a constant.
The set of all points P in a plane such that the difference of the distances from P to two fixed points, called the foci, is a constant.
line of symmetry of a parabola
The line perpendicular to the parabola's directrix and passing through its focus and vertex.
major axis of an ellipse
The line segment joining the vertices of an ellipse
minor axis of an ellipse
The line segment joining the co-vertices of an ellipse.
The set of all points equidistant from a point called the focus and a line called the directrix. The graph of a quadratic function y = ax² + bx + c is a parabola.
A system of equations that includes one or more equations of conics.
transverse axis of a hyperbola
The line segment joining the vertices of a hyperbola.
A selection of r objects from a group of C objects where the order is not important, denoted nCr where nCr = (n!)/((n-r)!*r!)
complement of a set
The complement of a set A, written A, is the set of all elements in the universal set U that is not in A .
The union or intersection of two events.
The conditional probability of B given A, written P(B|A) , is the probability that even B will occur that event A has occurred.
Two events such that the occurrence of one event affects the occurrence other event.
Event A and B are disjoint if they have no outcomes in common; also called mutually exclusive events.
element of a set
Each object in a set; also called a member of the set.
The set with no elements, denoted .∅
A group that undergoes some procedure or treatment when an experiment is conducted.
For any positive integer n, the expression n!, read "n factorial", is the product of all the integers form 1 to n. Also 0! is defined to be 1.
A probability found by calculating a ratio of two lengths, areas, or volumes.
intersection of sets
The intersections of two events A and B written A ∩B, is the set of all elements in both A and B .
When all outcomes are equally likely,
A = (number of outcomes not in A)/(number of outcomes in A)
An arrangement of the values nCrof in a triangular pattern in which each row corresponds to a value of n.
An ordering of objects. The number of permutation of r objects taken from a group of n distinct objects is denoted nPr where nPr = (n!)/(n-r)!
probability of an event
A number from 0 to 1 that indicates the likelihood that the event will occur.
If every element of a set A is also an element of a set B, then A is a subset of B . This is written as A⊆B .
union of sets
The union of two sets A and B , written A∪B , is the set of all elements in either A or B .