CSET Subtest 2 [Domains 1 and 4: Arithmetic and Statistics Review]

Percentage increase/decrease formula

(change/starting point) x 100% e.g. what is the percentage decrease of a $500 item on sale for $400? (100/500) x 100% (1/5) x 100% 20% decrease

measures of central tendency: mean, median, mode

- Mean: The mean is the average of a set of numbers. - Median: The median is the middle numbers in a set of data. - Mode: The most frequently appearing value in a set of numbers or data points.

Multiplying or Dividing signed numbers

-The product or quotient of two numbers with the same sign will produce a positive answer -The product or quotient of two numbers with the opposite signs will produce a negative answer Example: (-3)(8)(-5)(-1)(-2) = 240

Identity number for addition

0. Any number added to 0 gives that number 0 + a = a + 0 = a Example of using the additive identity: 0 + 3 = 3 + 0 = 3 0 + 3 = 3

x to the 0 power

1

Identity number for multiplication

1. Any number multiplied by 1 gives that number. 1(a) = a(1) = 1 Example of using the multiplicative identity: 1(3) = 3(1) = 3 1(3) = 3

Multiplying mixed numbers

1. Change the mixed number into an improper fraction by multiplying the denominator by the whole number. Then add the numerator in. Your denominator stays the same. 2. Multiply the numerators. 3. Multiply the denominators. 4. Simplify

Simplifying Square Roots

1. Factor the number into two numbers, one (or more) of which is a perfect square 2. Take the square root of the perfect square(s) 3. Leave the others under the √ Example: Simplify √75 √75 = √(25 x 3) = √25 x √3 = 5√3

Multiplying Decimals

1. Multiply numbers as if whole numbers. 2. Then count total number of decimal places in the factors and add them (Ex: 2.2 and 2.33 has three total decimal places) 3. Add the total number of Decimal places to product, counting left to right (Ex: 22*233 = 5126 --> 5.126 final answer)

Decimals to Fractions

1. Read it: 0.8 (eight-tenths) 2. Write it: 8/10 3. Reduce it: 4/5

√2 approx

1.4

√3 approx

1.7

How many ounces are in 1 pound?

16 ounces

How many yards are in a mile?

1760 yards

How many cups are in 1 pint?

2 cups

How many pints are in 1 quart?

2 pints

How many pounds are in a ton?

2,000 pounds

How many pecks are in 1 bushel?

4 pecks

How many quarts are in 1 gallon?

4 quarts

How many feet are in a mile?

5,280 feet

A is what percent of B?

A = x(B) e.g. 4 is what percent of 16? 4 = x(16) 4/16 = x 1/4 = x 25% = x

perfect square

A square of a whole number Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

composite number

A whole number greater than 1 that has more than two factors. e.g. 4,6,8,9

prime number

A whole number that has exactly two factors, 1 and itself. e.g. 2,3,5,7

Rational numbers

Any number that can be expressed as a fraction with integers e.g. 4 1/2, 9/2, 0.3, 0.134134134134...

How is probability calculated?

By dividing the number of favorable outcomes by the total number of possible outcomes.

Associative Property of Addition and Multiplication

Changing the grouping of three or more addends/factors does not change the sum/product. e.g. 8+(4+2) = (8+4)+2 8x(4x2) = (8x4)x2

Commutative Property of Addition and Multiplication

Changing the order of the addends/factors does not change the product. e.g. 2+3 = 3+2 (2)(3) = (3)(2)

Reducing/Simplifying Fractions

Divide by the greatest common factor the numerator and denominator numbers share. Factors of 24 are 1,2,3,4,6,8,12,24

Dividing Decimals

Move the decimal to the right in the divisor, making it a whole number. Move the decimal the same number of places in the dividend and bring to the top in the quotient, then divide normally. (Example: 34/2.5 is 340.0/25.)

Distributive Property

Multiplication outside parentheses distributing over either addition or subtraction inside parentheses does not affect the answer e.g. a(b + c) = ab + ac

Adding fractions with different denominators

Must rewrite with common denominator or least common multiple of denominators 1/2 and 2/3 Lowest common denominator is 6. 6 is a multiple of both 2 and 3. 2 and 3 are factors of 6. 1/2 * 6/6 = 6/12 = 3/6 2/3 * 6/6 = 12/18 = 4/6 3/6 + 4/6 = 7/6

Irrational numbers

Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are never-ending or nonrepeating. e.g. pi (3.14159...), √2 (1.414213)

Approximating square roots

Square roots of nonperfect squares can be approximated. Example: Approximate √83 √81 < √83 < √100 --> 9 < √83 < 10 Since √83 is closer to the √81 than it is to the √100, the √83 will be closer to 9 than it is to 10. The decimal value of the √83 will then be between 9 and 9.5. Therefore, √83 ≈ 9.1

What is probability?

The comparison of the total number of favorable outcomes to the total number of possible outcomes.

Square root rules: addition and subtraction

The numbers must be combined under the radical before any computation of square roots may be done Do the addition/subtraction FIRST, then the √ Example: √(10 + 6) = √16 = 4 √(10 + 6) ≠ √10 + √6

Additive Inverse

The opposite of a number. When added together, the sum is zero.

Multiplicative Inverse

The reciprocal of a number. When multiplied together, the product is 1.

Square root rules: multiplication and division

Two numbers multiplied under a radical (square root) sign equal the product of the two square roots, and likewise with division. Do the √ FIRST, then the multiplication or division Example: √(4)(25) = √4 x √25 = 2 x 5 = 10 or √(4)(25) = √100 = 10

Subtracting Mixed Numbers

You may have to borrow from the whole number, just like you sometimes borrow from the next column when subtracting ordinary numbers. Example: 4 1/6 - 2 5/6 = ? 4 1/6 - 2 5/6 = 3 7/6 - 2 5/6 = 1 2/6 = 1 1/3 To subtract a mixed number from a whole number, you have to borrow from the whole number. Example: 6 - 3 1/5 = ? 6 - 3 1/5 = 5 5/5 - 3 1/5 = 2 4/5

improper fraction

a fraction whose numerator is larger than the denominator

proper fraction

a fraction with a numerator smaller than the denominator

centi

hundredth

if there are parentheses inside other parentheses

start with the INNER most parentheses first and work your way oiut

deci

tenth

milli

thousandth