COMPASS

HOBET

NET

Top 10 Test Taking Strategies10. Read all directions and questions carefully

9. Attempt every question – it may not be as difficult as it appears

8. Anticipate the answer – if it isn’t there, test the other answers

7. Use logical reasoning –can the answer you came up withbe the correct answer?

Top 10 Test Taking Strategies6. Use the practice tests as a study guide

5. Keep a positive attitude. Don’t go into the test thinking you will fail

4. Keep your tension under control and try to concentrate on points that youwish to remember

3. Make sure you are ready to sit down and concentrate on the test

Top 10 Test Taking Strategies2. Select your answer and then re-read the question to

make sure that you understood it correctly

1. Relax! Keep calm. And do your best!

Structure of the COMPASS Test The test is not timed

The computer will generate the questions individually

The English essays contain many errors in punctuation, grammar, and style.

Carefully read the essays

When you locate an error, choosethe best option for rewriting the essay.

Structure of NET/HOBET Test Evaluates

Reading Comprehension

Written Expression

Basic Math

Learning Styles

Multiple Choice Questions

Look for the “best” answer

Structure of NET/HOBET Test Number of Questions 25 to 35 reading comprehension

30 math problems

45 decisions statements

30 test taking skills

Time Limits COMPASS is not timed

NET/HOBET is a 2.5 hour timed test

Purpose of the Entrance Test There are minimum requirements for entrance in to

Southeast – do your best!

The entrance test will establish your needs in a collegiate setting.

The test is designed to identify needs so that they may be addressed before they become an issue.

The learning style assessment willbe used only for counseling.

Mathematics ASSUMPTION: This class assumes that you know how

to add, subtract, multiple and divide whole numbers

If you need additional help in this area, drill with the multiplication tables and division facts!

COMPASS

HOBET

NET

Numerator & Denominator

Numerator – top part of the fraction & indicates how many parts are being counted

Denominator – bottom part of a fraction & indicates how many parts the whole is divided

Each slice = 1/8 Each slice = 1/4 Each slice = 1/2

Fractions

The denominator indicates how many parts a whole thing is divided into

Slice two pizzas, one into 8 slices and one into 4 slices. Which pizza would have the larger slices?

A larger denominator indicates that there are more pieces of the whole. Hence each piece must be smaller.

Proper & Improper Fractions

If the numerator is less than the denominator, the fraction is a proper fraction and is less than 1

1/3 < 1 7/20 < 1

If the numerator is greater than the denominator, the fraction is an improper fraction and is greater than 1

3/2 > 1 8/3 > 1

If the numerator and denominator are the same,the fraction is equal to 1

5/5 = 1 10/10 = 1

Simplify an Improper Fraction

Divide the numerator by the denominator

• The quotient is the whole number part.

• The remainder is the numerator of the fractional part.

• The denominator is the same as one in the original fraction.

COMPASS

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NET

Change a Mixed Number to an Improper Fraction

A mixed number is the sum of an integer and a properfraction

2 3/5 is the sum of 2 and 3/5 1 + 1 + 3/5 or 5/5 + 5/5 + 3/5 or (5 + 5 + 3)/5 or 13/5

Change a Mixed Number to an Improper Fraction (Cont.)

To change 2 3/5 to an improper fraction, multiply the whole number by the denominator

Then add the numerator. Place the result over the denominator.

COMPASS

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NET

Equivalent Fractions

Equivalent Fractions have the same value

Equivalent Fractions

You can multiply or divide the numerator and denominator of a fraction by the same number to get an equivalent fraction

Find the Equivalent Fractions

Ratio & ProportionsA ratio is a comparison of one number

to another

A proportion is an equality of two ratios

The expression “2 is to 4 as 10 is to 20” is the same as the following2:4::10:20

2/4 = 10/20

Equivalent Fractions, Ratios, & Proportions

Which fractions are equivalent?

Simplify (Reduce) Fractions

Divide the numerator and the denominator by a common factor or the largest number that evenly divides both the numerator and the denominator

Combine “Like” Fractions “Like” fractions have the same denominator

Add or subtract the numerators and place the sum or difference over the denominator

Reduce the fraction, if possible

Combining “Unlike” Fractions “Unlike” fractions have different denominators

Find a common denominator or the Least Common Multiple of the denominators

Express each fraction as an equivalent fraction with a common denominator

A common denominator is the product of the denominators, although it may not be the smallest common denominator

Add or subtract the numerators and place the sum or difference over the denominator

Reduce the fraction

Combine “Unlike” Fractions

Another Example

Another Example

Combine Mixed Numbers Find the Least Common Denominator (LCD)

Find the equivalent fractions

Add or subtract the fractions and add or subtract the whole numbers

Simplify your answer

COMPASS

HOBET

NET

Multiply Fractions Simplify the fractions if not in lowest terms

Multiply the numerators of the fractions to get the new numerator

Multiply the denominators of the fractions to get the new denominator

Simplify the resulting fraction

Problem: Solution:

Example – 2 Different Methods

Multiplying with Mixed Numbers

Change each number to an improper fraction

Simplify if possible

Multiply the numerators and then the denominators

Put the answer in lowest terms

COMPASS

HOBET

NET

Decimal Place Values Numbers to the right of the decimal point have a value less than 1

Numbers to the left of the decimal point have a value greater than 1

Rounding Decimals

Look at the digit to the right of the place you wish to round to.

When the digit is 5, 6, 7, 8, or 9, round up

When the digit is 0, 1, 2, 3, or 4, round down

COMPASS

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NET

Add or Subtract Decimal Numbers

Put the numbers in a vertical column aligning the decimal points and adding O’s at the end of any number as needed

Add or subtract the numbers

Place the decimal point in the answer directly below the decimal points in the column

Decimals Line up the numbers on the right – do not align the

decimal points

Multiply the numbers just as if they were whole numbers

Place the decimal point in the answer by starting at the right and moving a number of places equal to the sum of the decimal places in both numbers

Multiply a Decimal by a Power of 10Move the decimal point to the right as many places as

there are zeros in the multiplier

Dividing Decimal Numbers If the divisor is not a whole number, move the decimal

point to the right to make it a whole number

Move the decimal point in the dividend the same number of places

Dividing Decimal Numbers (Cont.)

Divide as usual until the answer terminates or repeats

Dividing Decimal Numbers (Cont.)

Put the decimal point in the answer directly above the decimal point in the dividend

Check your answer by multiplying the quotient by the divisor. Do you get the dividend?

Examples of Division with Decimals

Divide a Decimal Number by a Power of 10

Move the decimal point to the left as there are zeros in the divisor

COMPASS

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NET

Convert a Fraction into a Decimal Number

Divide the numerator (top number) by the denominator (bottom number)

Convert a Decimal Number to a Fraction

Read the numerical decimal, paying close attention to the ending

Place the number in the decimal, written as a whole number, in the numerator of the fraction

Take the ‘ths’ off the ending read in step 1 and place the numeric value of the number in the denominator

COMPASS

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NET

Percentages Percent means ‘per 100’ and is written with the symbol %

A Percent Can Be Expressedas a Fraction or a Decimal

Convert a Percent to a Fraction

Drop the % symbol

Divide the number by 100

Simplify the fraction

Another Example

Convert a Percent to a Decimal20% = 20/100 = .20 = .2

½% = .5/100 = .005

20 ½% = 20.5/100 = .205

2.4% = 2.4/100 = .024

Convert a Fraction to a Percent

Multiply both numerator and denominator by a number to make the denominator equal to 100

Write down the numerator followed by ‘%’

Convert a Percent to a Decimal Drop the % symbol

Divide by 100 by moving the decimal point two places to the left

Add zeros as needed

Convert a Decimal Number to a Percent

Multiple by 100 by moving the decimal pointtwo places to the right

Add zeros as needed

Add percent symbol

Ratios and Proportions A ratio is a relationship between two quantities expressed

as a fraction or with a colon The ratio of 1 to 2 can be written as ½ or 1:2

A proportion is the equality of two ratios 1:3 :: 2:6 1/3 : 2/6

Solve for X in a Proportion

4x = 12

x = 3

Product of the Means

equals the product of the

Extremes

Percentage Problems ‘Of’ means multiply and ‘Is’ means equals

COMPASS

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Solve for the Unknown 75 milligrams of Demerol is prescribed for a patient following

surgery. The medication is available as a liquid solution, with 1 milliliter of solution containing 100 milligrams of Demerol. To administer the prescribed dose of 75 milligrams, X milliliters of the solution would be given.

100 mg Demerol: 1 ml Solution :: 75 mg Demerol: X ml

solution

100 mg/1 ml = 75 mg/X ml100 mg * X ml = 75 mg * 1 ml100 X = 75X ml= 75/100 = ¾

Addition Axiom (Truth)

You add or subtract the same number or expression to each side of an equation

X – 15 = 30

X – 15 + 15 = 30 + 15

X = 45

Practice: W – 4 = 8

M – 12 = 14

Y – 9 = 21

Subtraction Axiom (Truth) You can subtract the same number or expression from each

side of an equation

3 + x = 12

3 – 3 + x = 12 – 3

x = 9

Practice

5 + g = 20

21 + w = 45

S + 3 = 19

Multiplication Axiom (Truth) You can multiply each side of an equation by the same

number or expression x/3 = 12

x/3 * 3 = 12 * 3

x = 36

Practice x/4 = 5

x/3 = 3

x/2 = 50

Division Axiom (Truth) You can divide each side of an equation by the same

number or expression 3x = 12

3x/3 = 12/3

x = 4

Practice 5x = 20

2w = 16

4y = 28

COMPASS

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NET

Multiplying Signed Numbers

A negative number times a negative number equals a positive number -3 * -4 = +12

A positive number times a positive number equals a positive number +9 * +11 = +99

A negative number times a positivenumber equals a negative number +6 * - 5 = -30

Dividing Signed Numbers

A negative number divided by a negative number equals a positive number -8/-2 = 4

A positive number divided by a positive number equals a positive number +18/+9 = +2

A negative number divided by a positive number equals a negative number -14/7 = -2

A positive number divided by a negative number equals a negative number +24/-3 = -8

Adding Two Numbers with ‘Like’ Signs

Add the numbers and give the answer the same sign

(+10) + (+15) = +25

(-10) + (-15) = -25

Adding Two Numbers with ‘Unlike’ Signs

Subtract the two numbers and give the sign of the number with the larger absolute value

(-10) + (+6) = -4

(+10) + (-6) = +4

(-10) +(+7) = -3

(+10) + (-7) = +3

Subtracting Signed Numbers Change the sign of the second number then follow the

rules for addition -14 – (-9) = -14 + (+9) = -5

-15 – (+8) = -15 + (-8) = -23

+22 - +12 = +22 + (-12) = 10

-14 – (-20) = -14 + (+20) = +6

Order of Operations If there are roots or powers in any term, you may be able

to simplify the term by using the laws of exponents 5xy(3x2y)=15x3y2

Perform operations in parentheses

Perform multiplication and division in order from left to right before addition or subtraction

Commutative Property The order in which you multiply does not matter 6xy is the same as 6yx

The order in which you add terms does not matter a + b is the same as b + a

Distributive Property 2(a + b) = 2a + 2b

3(2 + c) = 3 * 2 + 3c = 6 + 3c

2x(y+3) = 2xy+ 2x(3)= 2xy + 6x

Simplifying Algebraic Expressions Combine like (similar) terms

Like terms would be –x, 2x, 5x

6x – 2x + x + y

(6-2+1)x +y

5x + y

Simplifying Algebraic Expressions If an expression has more than one set of parentheses,

work on the inner parentheses first and then work out through the rest of the parentheses 2x – (x+6(x-3)) + y

2x – (x +6(x) + 6(-3)) + y

2x – (x + 6x -18) + y

2x – (7x - 18) + y

2x + (-1)(7x) + (-1)(-18) + y

2x – 7x + 18 + y

-5x + y + 18

Adding and SubtractingAlgebraic Expressions Like terms in algebraic expressions can be added and

subtracted (3x + 4y – xy) + 2(3x-2y)

(3x + 4y – xy) + 6x - 4y

(3x + 6x) + (4y – 4y) –xy

9x + 0 – xy

9x - xy

Multiplying Binomials Multiply each term of the first expression by each term

of the second expression

FOIL = First times First, Outer times Outer,Inner times Inner, Last times Last

(b-4)(b+a)

b(b+a) -4(b+a)

b2 + ab – 4b – 4a

Equations An equation is a statement that says two algebraic

expressions are equal

Order of operations (MDAS = My Dear Aunt Sally)

Exponentiation

Parentheses

Multiply or Divide in order from left to right

Addition or Subtraction in order from leftto right

Subtraction

Equivalence In Algebraic Expressions Transform a given equation into an equivalent

equation whose solutions are obvious

Group all terms that involve the unknown on one side of the equation and all numbers on the other side (isolating the unknown)

Combine like terms on each side

Divide each side by the coefficient of the unknown

Solve Algebraic Expressions 6x + 2 = 3

6x + 2 – 2 = 3 -2

6x = 1

x = 1/6

5x + 3 = 2x - 9

5x + 3 – 3 = 2x – 9 – 3

5x – 2x = 2x – 2x – 12

3x = -12

x = -12/3 = -4

Algebra - COMPASS Parallel lines have equal slopes

Square roots

Exponents

Mixtures and percentages

Factoring of polynomials

Parabolas

Practice Hobbit or Compass Test

Self Assessment Modules Basic Algebra Advanced Algebra Averages & Rounding Arithmetic Commas Estimation & Sequences Fractions & Square Roots Geometry Basic Grammar Intermediate Grammar Advanced Grammar

http://www.testprepreview.com/hobet_practice.htm

http://www.testprepreview.com/compass_practice.htm

Mixture ProblemSuppose you work in a lab. You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and a 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution, to make your own 15% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use?

Set Up Your VariablesLiters solution

% acid Total liters acid

10% solution X .10 .10 x

30% solution Y .30 .30y

Mixture X+Y= 10 .15 .10 x + .30 y

Since x + y = 10, then x = 10 – y. Using this, we can substitute for x in our grid, and eliminate one of the variables

0.10(10 – y) + 0.30y = 1.5 1 – 0.10y + 0.30y = 1.5 1 + 0.20y = 1.5 0.20y = 0.5 y = 0.5/0.20

y = 2.5

Mixture Problem

Liters solution % alcohol Total liters alccohol

70% solution X .70 .70x

40% solution 50 .40 (.40)(50) = 20

50% mixture 50 + x .50 .50 (50 + x)

How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?

What equation(s) can you set up?

Mixture problem

Distance Problem

Practice Hobbit or Compass Test

Self Assessment Modules Basic Algebra Advanced Algebra Averages & Rounding Arithmetic Commas Estimation & Sequences Fractions & Square Roots Geometry Basic Grammar Intermediate Grammar Advanced Grammar

http://www.testprepreview.com/hobet_practice.htm

http://www.testprepreview.com/compass_practice.htm

Slope = Rise/Run = The slope of a line is

the ratio of the change in the y-coordinates over the change in the x coordinates of 2 points on the line.

Y-change = 2 –(-1) = 3

X-change = 3 – (-1) = 4

Slope = 3/4

12

12

xx

yy

Find the slope of a line

Parallel Lines have the Same Slope

Perpendicular Lines have slopes that are negative reciprocals

Experiment with Perpendicular Lines

http://members.shaw.ca/ron.blond/perp.A

PPLET/index.html