CEOE OSAT Advanced Mathematics Field 11 Teacher by Xamonline

By Xamonline

Get the consultant that will get effects! This CEOE OSAT complex arithmetic examine consultant from XAMonline offers an summary of the middle advantage and talents assessed at the  certification examination for the sub-areas of challenge fixing and Reasoning: Mathematical platforms and quantity conception; Algebra, capabilities and Analytic Geometry; Geometry and dimension; Trigonometry and Calculus; and chance, data, and Discrete arithmetic. flip your wisdom into perform with eighty multiple-choice attempt questions and complete resolution rationales.

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Additional info for CEOE OSAT Advanced Mathematics Field 11 Teacher Certification Test Prep Study Guide (XAM OSAT)

Sample text

Electronics and engineering are two disciplines that use applications of complex numbers. When graphing complex numbers, we plot the real number a on the x-axis (labeled R for real) and b on the y-axis (labeled I for imaginary). The modulus is the length of the vector from the origin to the position of the complex number on the graph. The argument is the angle the vector makes with the horizontal axis R. ADVANCED MATHEMATICS 29 TEACHER CERTIFICATION STUDY GUIDE 5 I (3 + 2i) θ R -5 5 Argument = θ Modulus = (32 ) + (22 ) = 13 -5 An alternative representation of a complex number is the polar form.

4)(60) = (15)( x ) 240 = 15 x 16 = x Example: x +3 2 is a proportion. = 3x + 4 5 To solve, cross multiply. 5( x + 3)= 2(3 x + 4) 5 x + 15 = 6 x + 8 7=x x+2 2 = 8 x−4 Example: is another proportion. To solve, cross multiply. 8(2) ( x + 2 )( x − 4 ) = x 2 − 2x − 8 = 16 x 2 − 2 x − 24 = 0 ( x − 6)( x + 4) = 0 = x 6= or x − 4 Both answers work. ADVANCED MATHEMATICS 21 TEACHER CERTIFICATION STUDY GUIDE Fractions, decimals, and percents can be used interchangeably within problems. → To change a percent into a decimal, move the decimal point two places to the left and drop off the percent sign.

Sample problems: Determine if the given function is even, odd, or neither even nor odd. 1. Find f ( − x ) . 1. f( x ) =x 4 − 2 x 2 + 7 f( − x ) =( − x )4 − 2( − x )2 + 7 2. Replace x with − x . f( − x ) =x 4 − 2 x 2 + 7 f(x) is an even function. 3. Since f ( − x ) = f( x ) , f(x) is an even function. 1. Find f ( − x ) . 2. f (= x ) 3 x 3 + 2x = f( − x ) 3( − x )3 + 2( − x ) − f(= x) − = f( x ) − − 2. Replace x with − x . 3 x 3 − 2x 3. Since f ( x ) is not equal (3 x 3 + 2 x ) to f ( − x ) , f(x) is not an even function.

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