MAT 106-04

Fall 2005                                  Test 2 Review Sheet

The exam will cover Sections 6.1, 6.2, 6.3, 6.4, and 6.6 in the text. 
 

Be sure to bring your calculator and a pencil to the exam with you.

You are responsible for all material covered in class, the sections that we have covered in the text, and related material covered in the homework.  The main conceptual points of Chapter 6 are summarized in the Chapter 6 Outline on p. 371  in the course text.  Note, however, that we did not discuss simple and compound interest, the material in Section 6.5.  Most of the problems on the exam will be problems similar to those done in class or in the homework (all of the assigned homework, not just the collected homework).  Be sure you are able to communicate your responses to problems with clear written explanations of what you have done.  This includes being sure that you have answered the question asked.  Note that in some cases being able to explain or motivate a method or computation may be more important than actually being able to do the computation.

More specifically, consider the list below.  This list is not an exclusive list; unless I have specifically excluded something from the list, you are responsible for it even if I have not mentioned it here.  However, I am not trying to fool you by leaving some important topic off the list.  If you understand and know how to do everything on the list, you should do fine on the exam.

1.                  Know Simon Stevin’s place in the history of decimal fractions.

2.                  Be able to compare and order fractions and decimals, and be able to find their approximate locations on a number line.

3.                  Given a number written in decimal form, be able to identify the place values, both for the integer and fractional parts.

4.                  Given a number involving decimal fractions expressed in words, be able to write it in terms of numerals.

5.                  Be able to write numbers involving decimal fractions as sums in which powers of ten are used to present place value.

6.                  Given numbers written as sums in which powers of ten are used to present place value. be able to write those numbers as decimal fractions.

7.                  Be able to represent a number as a decimal fraction using base-ten blocks.

8.                  Know what is meant by the term terminating decimal.

9.                  Know which rational numbers can and cannot be expressed as terminating decimals.

10.              Given fractions whose denominators are powers of ten or, more generally, products of powers of 2 and powers of 5, be able to express those fractions as terminating decimals.  Be able to do this both with and without using a calculator.

11.              Be able to multiply or divide by a power of ten by moving the decimal point.

12.              Be able to order terminating decimals.

13.              Be able to explain our algorithm for adding decimals.

14.              Be able to add, subtract, multiply, and divide decimals.

15.              Given a problem in which you are multiplying two decimals, be able to explain where you put the decimal point.

16.              Be able to explain and justify our method of moving the decimal point when dividing decimals.

17.              Know how to express a given number in scientific notation.

18.              Given a number in scientific notation, be able to write the number without using scientific notation.

19.              Know how to interpret on your calculator a number that is expressed in the scientific notation of the calculator.

20.              Given our tools used for mental computations with whole numbers, be able to use them to perform mental computations with decimals.

21.              Know our rules for rounding and be able to round decimal to a specific place value.

22.              Be able to use rounding to help you estimate answers to computational problems involving decimals.

23.              Know what is meant by the terms repeating decimal and repetend.

24.              Know our notation for writing repeating decimals.

25.              Given a rational number expressed as a fraction, be able to express that number as a repeating decimal and be able to justify your choice of repetend.

26.              Be able to use a calculator to help determine a repetend.

27.              Given a repeating decimal, be able to write it in the form a/b, where a and b are integers and b is not 0, both for cases where the repeating block starts immediately after the decimal point and for cases where the repeating block does not start immediately after the decimal point.

28.              Be able to order repeating decimals.

29.              Given any two decimals that either terminate or repeat, be able to find a rational number in decimal form between them.

30.              Know our definition of percent and our notation for writing percents.

31.              Be able to relate fractions, decimals, and percents.

32.              Be able to write a fraction as a decimal and as a percent.

33.              Be able to write a decimal as a fraction and as a percent.

34.              Be able to write a percent as a fraction and as a decimal.

35.              Be able to discuss three ways of explaining how to convert a number to a percent: writing the number as a fraction with 100 as a denominator, solving a proportion, and using the fact that 100%=1.

36.              Be able to motivate and give a meaning to percents greater than 100 and less than 1.

37.              Be able to set up and solve application problems involving finding a percent of a number.

38.              Be able to set up and solve application problems involving finding what percent one number is of another.

39.              Be able to set up and solve application problems involving finding a number when a percent of the number is known.

40.              Be able to do mental math with percents by recognizing fraction equivalents.

41.              Be able to do estimations with percents.

42.              Be able to recognize when it is appropriate to do operations with percents and when it is not.  (For examples, look at page 352.).

43.              Know two ways to characterize irrational numbers: first, as nonterminating and nonrepeating decimals, and second, as numbers that cannot be written in the form a/b, where a and b are integers.

44.              Know the relationships between the following sets of numbers:  real numbers, irrational numbers, rational numbers, integers, whole numbers, natural numbers.

45.              Given that the arithmetic operations of addition, subtraction, multiplication, and division can be extended to all of the real numbers, know and be able to state those properties involving these operations on the rationals that can be extended to these operations on all of the reals. 

46.              Understand the general structure of the nth roots.  Which roots have principal roots and why?   Which roots exist for negative numbers?

47.              Know the difference between saying x^2=b and the square root of b = x.

48.              Know which integers have irrational square roots.

49.              Know that the rationals are closed under our arithmetic operations, except when we try to divide by 0, but that the irrationals are not.

50.              Be able to represent the square root of 2 geometrically.

51.              Be able to estimate a square root using our squeezing method.

52.              Know the basic laws of exponents, that can now be extended to the real numbers.

53.              Be able to work with radicals and rational exponents on your calculators, noting that taking the nth root of a number is the same as raising it to the 1/n power.

54.              Have an understanding of large numbers and be able to recognize and appropriately use exponential, scientific, and calculator notation.

The End!!