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COMPASS
HOBET
NET
Top 10 Test Taking Strategies
10. 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 with
be the correct answer?
Top 10 Test Taking Strategies
6. 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 you
wish to remember
3. Make sure you are ready to sit
down and concentrate on the test
Top 10 Test Taking Strategies
2. 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, choose
the 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 will
be 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
HOBET
NET
Change a Mixed Number to an Improper Fraction
 A mixed number is the sum of an integer and a proper
fraction
 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
HOBET
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 & Proportions
 A 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 following
 2:4::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
HOBET
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 10
 Move 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
HOBET
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
HOBET
NET
Percentages
 Percent means ‘per 100’ and is written with the symbol %
A Percent Can Be Expressed
as 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 Decimal
20% = 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 point
two 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
HOBET
NET
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 ml
100 mg * X ml = 75 mg * 1 ml
100 X = 75
X 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
HOBET
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 positive
number 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 Subtracting
Algebraic 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 left
to 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
http://www.testprepreview.com/hobet_practice.htm
http://www.testprepreview.com/compass_practice.htm
 Self Assessment Modules
 Basic Algebra
 Advanced Algebra
 Averages & Rounding
 Arithmetic
 Commas
 Estimation & Sequences
 Fractions & Square Roots
 Geometry
 Basic Grammar
 Intermediate Grammar
 Advanced Grammar
Mixture Problem
Suppose 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 Variables
Liters
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
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?
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)
What equation(s) can you set up?
Mixture problem
Distance Problem
Practice Hobbit or Compass Test
http://www.testprepreview.com/hobet_practice.htm
http://www.testprepreview.com/compass_practice.htm
 Self Assessment Modules
 Basic Algebra
 Advanced Algebra
 Averages & Rounding
 Arithmetic
 Commas
 Estimation & Sequences
 Fractions & Square Roots
 Geometry
 Basic Grammar
 Intermediate Grammar
 Advanced Grammar
Slope = Rise/Run =
y 2  y1
x 2  x1
 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
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