NES Elementary Education Subtest 2 Exam Questions With 100% Correct Answers

NES Elementary Education Subtest 2 Exam Questions With 100% Correct Answers Natural Numbers - answerN = {1, 2, 3, 4, 5, 6, . . . } Whole natural numbers together with zero. - answerW = {0, 1, 2, 3, 4, 5, 6, . . . } Every whole number has a unique opposite or negative whose sum with it is 0. For example, - answer2 + (-2) = 0 The set of integers consists of the whole numbers and their opposites. - answerZ = {. . ., -3, - 2, -1, 0, 1, 2, 3, . . . } Every nonzero integer has a unique reciprocal whose product with it is one. For example, - answer2 × 1/2 = 1 The ratio or fraction of one integer to a nonzero integer is the product of the first integer with the reciprocal of the second. For example, the ratio of 2 to 3 is - answer2/3 = 2 × 1/3 not every rational number is an integer. For example, 1/2 is a rational number that is not an integer. - answer1/2 = 0.5 There are three basic properties of addition: - answercommutativity, associativity and identity. Commutative property. - answerWhen adding two numbers, the sum is the same regardless of the order in which the numbers are added. 2 + 3 = 3 + 2 Associative property. - answerWhen adding three or more numbers, the sum is the same regardless of the way in which the numbers are grouped. 2 + (3 + 5) = (2 + 3) + 5 Identity property. - answerAdding zero to a number does not change it. 2 + 0 = 2 There are three basic properties of multiplication: - answercommutativity, associativity and identity. Distributive property. - answerThe product of a number with a sum equals the sum of the products of the number with each term of the sum. 2 × (3 + 5) = (2 × 3) + (2 × 5) Exponentiation - answerExponentiation is repeated multiplication. An exponent is often called a power. For example, the third power of 2 is 2³ = 2 × 2 × 2 = 8 We define the zero power of any nonzero number to be 1. For example, - answer(-3)0 = 1 A negative exponent indicates a reciprocal. For example, - answer2 (-3rd power) =1 / 2 (3rd power) = 1 / 8 The first power of any number is itself. For example, - answer2 (to the 1st power) = 2 To multiply like bases with exponents, add the exponents. For example, - answer2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth) To exponentiate a power, multiply the exponents. For example, - answer(2 to the 3rd) to the 5th = 2 to the 15th 10 to the 0 power - answer1 10 to the 1 power - answer10 10 to the -2 power - answer1 / 10 to the 2 power or 1 / 100 10 to the 2 power x 10 to the 3 power - answer10 to the 5 power Identifying Place Value in Numbers 2045 - answer2045 = (2 x 10 to the 3 power) + (0 x 10 to the 2 power) + (4 x 10 to the 1 power) + 5 x 10 to the 0 power) Digits to the right of a decimal point correspond to negative powers of ten. For example, 23.405 - answer23.405 = (2 x 10 to the 1 power) + (3 x 10 to the 0 power) + (4 x 10 to the -1 power) + (0 x 10 to the -2 power) + (5 x 10 to the -3 power) Converting a fraction to a decimal. For example 3/8 - answer3 divided by 8 = 0.375 convert 0.45 to a fraction. - answer45/100 convert 3.208 to a mixed number. - answer3 + 208/1000 Converting a fraction to a percentage. Convert the fraction to a decimal and then convert the decimal to a percentage. For example, 2/5 - answer2/5 = .4 = 40% Converting a percentage to a fraction. Convert the percentage to fraction with a denominator of 100. For example, 65% - answer65/100 A fundamental concept of mathematics is that the set of real numbers is in one-to-one correspondence with the set of points on a line. That is, each real number corresponds to exactly one point on a line, and each point on a line corresponds to exactly one real number, called the _____ of the point - answercoordinate It is worthwhile to memorize the first several prime numbers. - answer2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ... A natural number is _____ if it is greater than 1 and not prime. - answercomposite Divisibility Tests - answerTo find the prime factorization of a number, it is helpful to know a few tests for divisibility. Divisibility by 2. - answerIf the last digit is even, then the number is divisible by 2. For example, 158 is divisible by 2 since its last digit is 8. Divisibility by 3. - answerIf the sum of the digits is divisible by 3, then the number is also. For example, 177 is divisible by 3 since the sum of its digits is 15 (1 + 7 + 7 = 15), and 15 is divisible by 3. Divisibility by 4. - answerIf the last two digits form a number divisible by 4, then the number is divisible by 4. For example, 316 is divisible by 4 since 16 is divisible by 4. Divisibility by 5. - answerIf the last digit is a 5 or a 0, then the number is divisible by 5. For example, 1995 is divisible by 5 since its last digit is 5. Divisibility by 6. - answerIf the number is divisible by both 3 and 2, then it is also divisible by 6. For example, 168 is divisible by 6 since it is divisible by 2, and it is divisible by 3. Divisibility by 8. - answerIf the last three digits form a number divisible by 8, then the number itself is also divisible by 8. For example, 1,120 is divisible by 8 since 120 is divisible by 8.