OAE Elementary Education Subtest 2 (Math)

We define the zero power of any nonzero number to be 1. For example,

(-3)0 = 1

To exponentiate a power, multiply the exponents. For example,

(2 to the 3rd) to the 5th = 2 to the 15th

The Fibonacci Sequence. The Fibonacci sequence is the sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ... beginning with 0 and 1 so that each term beginning with the third term is the sum of the two preceding terms.

10 to the 0 power

1

10 to the -2 power

1 / 10 to the 2 power or 1 / 100

not every rational number is an integer. For example, 1/2 is a rational number that is not an integer.

1/2 = 0.5

10 to the 1 power

10

10 to the 2 power x 10 to the 3 power

10 to the 5 power

The Sequence of Squares. The sequence of squares of natural numbers is an important sequence.

12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112,... or 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 ...

A negative exponent indicates a reciprocal. For example,

2 (-3rd power) =1 / 2 (3rd power) = 1 / 8

The first power of any number is itself. For example,

2 (to the 1st power) = 2

To multiply like bases with exponents, add the exponents. For example,

2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth)

Every whole number has a unique opposite or negative whose sum with it is 0. For example,

2 + (-2) = 0

Every nonzero integer has a unique reciprocal whose product with it is one. For example,

2 × 1/2 = 1

It is worthwhile to memorize the first several prime numbers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...

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

2/3 = 2 × 1/3

Converting a fraction to a percentage. Convert the fraction to a decimal and then convert the decimal to a percentage. For example, 2/5

2/5 = .4 = 40%

Identifying Place Value in Numbers 2045

2045 = (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

23.405 = (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)

convert 3.208 to a mixed number.

3 + 208/1000

Converting a fraction to a decimal. For example 3/8

3 divided by 8 = 0.375

convert 0.45 to a fraction.

45/100

Converting a percentage to a fraction. Convert the percentage to fraction with a denominator of 100. For example, 65%

65/100

and an area, A, given by

A = πr²

Identity property.

Adding zero to a number does not change it. 2 + 0 = 2

A circle with radius r has circumference, C, given by

C = 2πr

Constants.

Constants are symbols that represent fixed values. In the expression 3x + 7, the constants are 3 and 7.

Exponentiation

Exponentiation is repeated multiplication. An exponent is often called a power. For example, the third power of 2 is 2³ = 2 × 2 × 2 = 8

Grouping symbols.

Grouping symbols are symbols such as parentheses ( ) and brackets [ ] that indicate the order in which we should interpret the operations and the relations in a mathematical expression.

Divisibility by 5.

If 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 2.

If 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 8.

If 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.

Divisibility by 4.

If 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 10.

If the number ends in 0, then it is divisible by 10. For example, 670 is divisible by 10 since its last digit is 0.

Divisibility by 6.

If 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 3.

If 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 9.

If the sum of the digits is divisible by 9, then the number itself is also divisible by 9. For example, 369 is divisible by 9 since the sum of its digits is 18 (3 + 6 + 9 = 18), and 18 is divisible by 9.

Natural Numbers

N = {1, 2, 3, 4, 5, 6, . . . }

Operators.

Operators are symbols such as +, -, × and / that represent operations such as addition, subtraction, multiplication, and division.

Relations.

Relations are symbols that compare expressions. Common relations are =, <, >, ≤, and ≥.

Distributive property.

The 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)

Divisibility Tests

To find the prime factorization of a number, it is helpful to know a few tests for divisibility.

Variables.

Variables are symbols that stand for changing values. Most often we use letters of the alphabet for variables. In the expression 3x + 7, the letter x is a variable. The value of the expression depends on the specific number we substitute for x. For example, if we substitute 2 for x, the value of the expression is 3(2) + 7 = 13.

Whole natural numbers together with zero.

W = {0, 1, 2, 3, 4, 5, 6, . . . }

Associative property.

When 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

Commutative property.

When adding two numbers, the sum is the same regardless of the order in which the numbers are added. 2 + 3 = 3 + 2

The set of integers consists of the whole numbers and their opposites.

Z = {. . ., -3, -2, -1, 0, 1, 2, 3, . . . }

There are three basic properties of addition:

commutativity, associativity and identity.

There are three basic properties of multiplication:

commutativity, associativity and identity.

A natural number is _____ if it is greater than 1 and not prime.

composite

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

coordinate

The diameter of circle, d, is twice the radius. That is,

d = 2r

A _____ is a set of ordered pairs that pairs each element x of one set, called the domain (input) of the function, with a unique element f(x) of another set, called the range (output) of the function.

function