SUMMER MATH+II.doc - LICENSURE EXAMINATION FOR TEACHERS(LET...

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LICENSURE EXAMINATION FOR TEACHERS (LET) Refresher Course Content Area: MATHEMATICS Focus: ADVANCED ALGEBRA Competencies : Show mastery of the basic terms, concepts and equations in Advanced Algebra involving radicals, rational exponents and functions. Solve, evaluate and manipulate symbolic and numerical problems in above areas by applying fundamental principles and processes. KEY IDEAS Some Helpful Tips in Answering the LET 1 Read the question/s or the items carefully and understand what they say. 2 Determine what is/are wanted or what is/are asked for. 3 Find out what is/are given and which data are needed to solve the problem. 4 Reason out what processes (operations) to apply and the order in which they are to be applied. 5 Summarize the problem by means of an open number sentence. 6 Compute carefully . Check each step in the computations. 7 Decide the reasonableness of the result. 8 Check the result by seeing to it that the result satisfies all the conditions of the problem. RATIONAL EXPONENTS If a is a real number and n is any positive integer, the symbol n a denotes the n th power of a . The real number a is called the base and n is called the exponent . In symbols, a a a a a n ... . n factors Examples: a)    4 3 3 3 3 3 or 81. b)   . 2 2 2 2 3 m m m m c) . 2 1 2 1 2 1 2 1 2 1 4 d)  . 3 . 1 3 . 1 3 . 1 2 e)  math math math 2 . e)  . 2 2 2 m m m Note that any base raised to the power of 1, is just the base. Moreover, any base raised to the power of 0 is 1, while 0 0 is indeterminate. Examples: a) . 1 9 0 b) . 4 4 1 c) (- m ) 1 = - m. d) z 0 = 1. e) 1 0 3 2 e op h . f) 1 23 . 38 0 . g) 5 3 2 1 5 3 2 y o j y o j . h) a a m 4 1 4 1 1 0 . Laws of Exponents If a and b are real numbers and m and n are positive real numbers, then the following are true. n m n m a a a . nm m n a a . If n m and 0 a , then n m n m a a a . n n n b a ab . If m n and 0 a , then m n n m a a a 1 . If 0 b , then n n n b a b a .  If 0 a , then 1 0 a a a n n . Examples: a) . 4 4 6 3 2 b)  . 32 2 2 2 2 5 2 3 2 3 c) (3 x 4 ) 2 = 3 2 x 4 2 . d) . 1 3 3 2 2 e) . 27 3 3 3 3 3 2 5 2 5 f). . 27 1 3 1 3 3 3 3 3 3 5 2 5 2 Exercises 1. In the expression 8 m 5 , 5 is called the ________. A. base B. coefficient C. constant D. exponent 1
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2. Evaluate 0 10 8 6 0 14 3 9 0 2 0 10 20 5 25 m n s s n m m m . A. 5 B. 23 m 12 n 4 s -2 C. 20 2 m D. undefined 3. Anthony wrote 4 1 4 3 b a = ( ) 4 1 3 a + 4 1 4 b . Which of the following is his misconception ?
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