CBEST Math

Whole numbers

The counting numbers beginning with zero: 0,1,2,3,4...

Natural numbers

The counting numbers: 1,2,3,4...

Translating percent word questions into actual equations to solve

- "What" = x -"Is" = equal sign - "Of" = multiplication Example: 18 is what percent of 90? 18 = x (90) >>. Then you just solve the equation like regular where you divide by 90 to both sides. And then simplify. Change percents to decimals or fractions if that's easier to solve the equation. Example: 10 is 50% of what number? 10 = 50% (x) 10 = .50 (x) 10/.50 = x 20 = x

Changing percents to decimals

-Eliminate the percent sign -Move the decimal point two places to the left (sometimes adding zeros will be necessary) Example: 5% = .05 23% = .23 .2% = .002 75% = .75 5% = .05

Changing decimals to percents

-Move the decimal point two places to the right -Insert a percent sign Example: .75 = 75%

Changing percents to fractions

1. Eliminate the percent sign 2. Place the number without the percent sign over 100 3. Reduce if necessary Example: 60% = 60/100 = 6/10 = 3/5 Example: 13% = 13/100

Changing fractions to percents

1. Multiply by 100 2. Divide by the denominator 3. Insert a percent sign Example: 1/2 > 1/2 x 100 = 100/2 = 50% Example: 2/5 > 2/5 x 100 = 200/5 = 40%

Order of operations

1. Parentheses 2. Exponents 3. Multiplication or division 4. Addition or subtraction

How do you add mixed fractions?

1. Take the big numbers and add them, separate from the fraction parts. 2. Take the fraction parts and add them. But first you need to change the denominators to match if they don't. Then add. 3. Then put together the whole number in front of the final fraction added.

How do you multiply mixed fractions?

1. Turn each mixed fraction into improper fractions. 2. Multiply the improper fractions straight across top and bottom. 3. Reduce final fraction or turn back into mixed number if need be.

Ratio

A comparison of two quantities by division. Take the two numbers and divide them or simplify them down by each other. Make sure to put them in the right place either numerator or denominator- numerator is the number that comes first in the word problem and denominator is the number that comes second in the word problem.

What is the name of a quadrilateral with two sets of parallel sides?

A parallelogram, square, rectangle, or rhombus.

What is the name of a polygon with four equal sides and four equal angles?

A square

What is the name of a polygon with three sides?

A triangle

Identity element for addition is 0

Adding any number to 0 gives the original number. 3 + 0 =3.

Multiplicative inverse is the reciprocal of the number

Any number multiplied by its reciprocal equals 1. 2 x 1/2 = 1 because both 2's cancel out by cross multiplication.

Stanine score

Are based on a simple method that compares a student's performance to other students at the same grade level. Stanine score convert percentile scores into a single digit number from 1 to 9. The lowest score is 1 and highest score is 9. Example: So if you have a 96-99% then you top at a stanine score of 9. If you have a 60-76% then you are a stanine score of 6.

Finding a percent of a number

Change the percent to a fraction or decimal. Then multiply together. Example: What is 20% of 80? 1. Turn 20% into fraction or decimal. Move the invisible decimal point over two spaces to get me .20. 2. Then take .20 and multiply by 80 : .20 x 80 3. Final answer : .20 x 80 = 16. Example: What is 12% of 50? 1. Turn 12% into fraction or decimal. So it can be .12 OR 12/100 (there are two decimal spaces going right to left so you add two zeros) 2. Then take .12 and multiply by 50 : .12 x 50 3. Final answer: .12 x 50 = 6.

What is the equation needed to find Discount Price in word problem?

Discount Price = ( 1 - % discount/100) x (Original Price) Example: Nearly new motocross motorcycle is selling at a 30% discount off it sticker price. Its sticker price is $8000. What is its new selling price? Answer: (1-30%/100) x ($8000) > (1-.30) x (8000) > (.7) x (8000) > $5600.

Word Problem Example

Example: In a school of 280, only 35 students did not attend graduation. What percent of the school population did not attend gradation? Answer: Divide! 35/280. = .125 = 12.5% Moved the decimal two places to the right to turn into percent.

How to read stanine test scores

Example: Lydia's scores: Raw score = 55 Percentile = 45 Stanine = 5 Which of the following is a true statement regarding Lydia's stanine test scores? Answer: Lydia's performance was at the same level as other students who took the test. A stanine test score of 4,5,6 shows that her score is average and that she performed at the same level of other students who took the test.

Mean

How to calculate mean: 1. Add all numbers together 2. Divide by the number of data values given in set Also known as the average.

Permutations

If there are a number of successive choices to make and the choices are affected by the pervious choice or choices (dependent upon order), then permutations are involved. Example: How many ways can you arrange the letters STOP in a row? 4 x 3 x 2 x 1 = 24 different ways

Counting principles

If there are a number of successive choices to make and the choices are independent of each other, the total number of possible choices is the product of each of the choices at each stage. Example: How many possible arrangements of shirts and ties are there if there are five different color shirts and three different color ties? Multiply them to find the total: 5 x 3 = 15

Range

Is the difference between the largest data value and the smallest data value. To calculate the range, subtract the smallest number from the largest number.

Additive inverse property of addition

Is the opposite (negative) of the number. Any number plus its additive inverse equals 0. 3 + (-3) = 0.

Probability

It is the likelihood that a particular event will occur. It is probability = number of favorable outcomes/ number of possible total outcomes You use multiplication when calculating.

Changing fractions to decimals

Just take the fraction and turn it on its side to the right to straight divide it through.

Median

Median is simply the middle number of a list of numbers after it has been written in order. Arrange them in order from greatest to least. If the number of data values is even, you add the two middle values and divide the total by two and you have your median.

Mode

Mode is simply the number most frequently listed in a group of numbers.

Multiplying Decimals

Multiply regularly. For the decimal points: You count how many decimal places there are from right to left on each individual number and add the totals together. Ex: 40.012 (3 decimal places) 3.1 (1 decimal place) , add together 3 + 1 = 4 decimal places to add to the final number after doing the multiplying.

Identity element for multiplication is 1

Multiplying any number by 1 gives the original number. 3 x 1 = 3

Composite number

Number divisible by more than just 1 and itself: 4,6,8,9,10,12,14,15...

Even numbers

Numbers divisible by two: 2,4,6,8...

Prime numbers

Numbers divisible only by 1 and itself: 2,3,5,7,11,13...

Odd numbers

Numbers not divisible by two: 1,3,5,7...

Commutative property of multiplication

Order does not make a difference. a x b = b x a

Perimeter of a rectangle

P = 2L + 2W

Integers

Positive and negative whole numbers and zero.

Measurements

Pounds: It's about medium like if you were measuring a human being. Ounces: This can be liquids or solids but on the smaller side. Quarts and Pints: Measuring water/liquids Tons: Measuring huge things like cars and buildings. Example: What would you use to measure a pencil? Answer: Ounces!

Solving inequality equations

REMEMBER: If you multiply or divide both sides by a negative number, you must reverse the direction of the sign in the end.

What is the name of a quadrilateral with two sets of parallel sides and all right angles?

Rectangle or square

Associative property of multiplication

The grouping does not make any difference. (a x b) x c = a x (b x c)

Associative property of addition

The grouping of the numbers does not make any difference. (a + b) + c = a + (b + c)

Commutative property of addition

The order does not make any difference. a + b = b + a

Percent score

The percent score is the number of questions answered correctly compared to the total number of questions. Example: If a student answers 80 questions correctly out of a possible 100 questions, the percent score is 80%; you calculate 80 divided by 100. Example: If a student answers 80 questions correct out of 85 possible questions, the percent score is 94%; you calculate 80 divided by 85.

How to read percentile scores

The percentile associated with a score represents how many whole percent of all scores lie below that score. Therefore, if a score is in the 89th percentile, this means that 89% of all other scores are below that score. Example 1: Kelsey took a standardized math test, and her grade report showed that her score was in the 89th percentile. Which of the following is the best interpretation of the meaning of this percentile? Answer: Eighty-nine percent of all those taking the exam had scores below Kelsey's score. Example 2: Kim scores - Raw score : 72 Percentile score : 88 Stanine score : 8 Grade Equivalent Kim's test scores indicate that: Answer: He scored as well as or better than 88% of the test takers. Example 3: Daniel's scores - Raw score: 55 Percentile score: 82 Stanine score : 8 Daniel's scores indicate: Answer: Daniel scored as high as or higher than 82% of the other test takers.

Raw score

The raw score is simply the number of correct answers on a given test.

Sum, total, plus

The result of using addition. Example: The sum of 5,6, and 8, 5+6+8 = 19.

Quotient, divided by, divided into, ratio, half, each

The result of using division.

Product, of, times, at, twice

The result of using multiplication. Example: The product of 3 and 6 is 18, 3x6 = 18.

Difference

The result of using subtraction.

Cubes

The result when numbers are multiplied by themselves, and again by the original number, raised to the third power. (2x2x2 = 8), (3x3x3 = 27) ; 1,8,27

Squares

The result when the numbers are multiplied by themselves: (2x2 = 4), (3x3 =9): 1,4,9,16,25,36

Problems with distance, time, and speed

Use the equation: d = rt

Finding percentage increase or decrease

Use this formula: Change/starting point x 100 = percentage change Example: What is the percentage decrease of a $500 item on sale for $400? Change : 500 - 400 = 100 100/500 x 100 = 0.2 x 100 = 20% decrease

Turing decimals into fractions

You look at the decimal and move it over to the right until you get to the end of the entire number. You count the amount of times you moved over places and that is how many zeros you will add to 1 when making the number of the denominator in the fraction. Ex: 12.5 % - Turn into a decimal first : Move decimal place over two times to the left to get .125. Next: Turn that decimal into a fraction. You move the decimal over 3 times to the right to get to the end of the number. Then you put 125/ 1000. There are three zeros because you counted three spaces to the right when in decimal form.