General And Specific Competencies In Mathematics Iv

GENERAL AND SPECIFIC COMPETENCIES IN MATHEMATICS IV (Advanced Algebra, Trigonometry and Statistics) A. Functions 1. Demonstrate knowledge and skill related to functions in general 1.1 define a function 1.2 differentiate a function from a mere relation • real life relationships • set of ordered pairs • graph of a given set of ordered pairs • vertical line test • given equation 1.3 illustrate the meaning of the functional notation f(x); determine the value of f(x) given a value for x B. Linear Functions 1. Demonstrate knowledge and skill related to linear functions and apply in solving problems 1.1 define the linear function f(x) = mx + b 1.2 given a linear function Ax + By = C, rewrite in the form f(x) = mx + b and vice versa 1.3 draw the graph of a linear function given the following: • any two points • x and y intercepts • slope and one point • slope and the y-intercept 1.4 given f(x) = mx + b, determine the following: • slope • trend: increasing or decreasing • x and y intercepts • some points 1.5 determine f(x) = mx + b given: • slope and y-intercept • x and y intercepts • slope and one point • any two points 1.6 solve problems involving linear functions C. Quadratic Functions 1. Demonstrate knowledge and skill related to quadratic functions and apply these in solving problems 1.1 identify quadratic functions' f(x) = 1.2 rewrite a quadratic function ax2 + bx + c in the form f(x) = a(x - h)2 + k and vice versa 1.3 given a quadratic function, determine: • highest or lowest point (vertex) • axis of symmetry • direction of opening of the graph 1.4 draw the graph of a quadratic function using the • vertex • axis of symmetry • direction of opening of the graph • given points 1.5 analyze the effects on the graph of changes in a, h and k in f(x) = a(x-h)2 + k 1.6 determine the "zeros of a quadratic function" by relating this to "roots of a quadratic equation" 1.7 find the roots of a quadratic equation by: • factoring • quadratic formula • completing the square 1.8 derive a quadratic function given: • zeros of the function • table of values • graph 1.9 solve problems involving quadratic functions and equations D. Polynomial Functions 1. Demonstrate knowledge and skill related to polynomial functions 1.1 identify a polynomial function from a given set of relations 1.2 determine the degree of a given polynomial function 1.3 find the quotient of polynomials by: • algorithm

1.4 1.5 1.6

1.7 1.8

• synthetic division find by synthetic division the quotient and the remainder when p(x) is divided by (x-c) state and illustrate the Remainder Theorem find the value of p(x) for x = k by: • synthetic division • Remainder Theorem state and illustrate the Factor Theorem find the zeros of polynomial functions of degree greater than 2 by:

• Factor Theorem • factoring • synthetic division • depressed equations 1.9 draw the graph of polynomial functions of degree greater than 2 (use graphing calculator if available) E. Exponential and Logarithmic Functions 1. Demonstrate knowledge and skill related to exponential functions 1.1 identify certain relationships in real life which are exponential (e.g. population growth over time, growth of bacteria over time, etc.) 1.2 given a table of ordered pairs, state whether the trend is exponential or not 1.3 draw the graph of an exponential function f(x) = ax 1.4 describe some properties of the exponential function, f(x) = ax from its graph • a>1 • o
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900n 1.6 define the six circular functions • sine • cosine • tangent • cotangent • secant • cosecant 1.7 find the six circular functions of angles with special values 1.8 give the angle, - 2 Π ≤  ≤ 2 Π or - 3600 ≤  ≤ 3600 draw the graph of: • sine • cosine • tangent 1.9 describe the properties of the graphs of: • sine • cosine • tangent 1.10 define the six trigonometric functions of an angle in standard position 1.11 find the values of six trigonometric functions of an angle θ, given some conditions 1.12 solve simple trigonometric equations 1.13 state the fundamental trigonometric identities G. Triangle Trigonometry 1. Demonstrate ability to apply trigonometric functions, laws of sine and cosine to solve problems involving: • right triangles • triangles using the Law of Sines • triangles using the Law of Cosines H. Statistics 1. Demonstrate knowledge and skill related to collection and organization of data, sampling techniques, measures of central tendency and variability 1.1 define • statistics • sample • population 1.2 give the history and importance of the study of statistics 1.3 use the rules of summation to find sums 1.4 state and explain the different sampling techniques 1.5 collect statistical data and organize in a table 1.6 construct frequency distribution tables 1.7 find the measures of central tendency using ungrouped data • mean • median • mode 1.8 find the measures of central tendency using grouped data • mean • median • mode 1.9 calculate the different measures of variability relative to a given set of data, grouped or ungrouped • Range • Standard deviation 1.10 give the characteristics of a set of data using the measures of variability 1.11 from a given statistical data: • analyze • interpret • draw conclusions • make predictions • make recommendations/decisions