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For help with the math
section,complete the following review sheets (MATD 0370,
MATD 0390, and MATH 1314) at: http://www.austincc.edu/math/prereqreviews.html.
Then follow up with any math tutor in one of the Learning
Labs. Obtain a blue Assessment Referral
form from the Assessments Center (CYP 2116) before coming to
the Learning Lab. Contact Assessment at Cypress at
512.223.2020. The Mathematics Test assesses
students’ knowledge in three levels of math skills:
pre-algebra/numerical skills, algebra, and college algebra
and results in placement into the appropriate skill building
mathematical course or approval for enrollment into a
college-level mathematical course. Pre-algebra/numerical
skills items range from basic math concepts and skills
(integers, fractions, and decimals) to the knowledge and
skills that are required in an entry-level algebra course
(absolute values, percentages, and exponents). The algebra
items are essentially questions from elementary and
intermediate algebra (equations, polynomials, formula
manipulations, and algebraic expressions). The college
algebra test items measure algebra knowledge and skill in
operations with matrices, functions, and
factorials. You will be permitted a calculator,
scratch paper, and pencil. You will not be allowed to return
to previous questions in order to change your answers. You
must answer each question presented to you. You will not be
penalized for guessing. Multiple-choice items in each of
the five mathematics placement areas test the
following: Students are permitted to use
approved calculators when completing the COMPASS®
mathematics placement or diagnostic tests. Your test scores determine which
course you are to be placed in at Austin Community
College: Click here for Basic
Math Review. Click
here for Basic Math Tutorial. Click
here for lectures on EXPONENTS &
ROOTS. Rule 2: A-m = 1/
Am Rule 3: Am +
An = A m + A
n Rule 4: Am x A
n= Am+n Rule 5: (Am
)n = Amn Rule 6: Am /An
= Am-n Rule 7: Any quantity except
zero, raised to the zero power is 1." That is, zero to
the zero power doesn't equal one; it equals
zero. This shouldn't be a problem for you
since you can use your calculator. For example: 4 x 105 =
400,000; 7 x 104 = 70,000. Just count the number
of zeros to the right of the number. 1. The product (or quotient) of
positive numbers is positive. When you have an absolute value,
perform the operation within the brackets just like it was a
parenthesis before you apply that absolute value.
The absolute value of a number is
its distance on the number line from 0. Since distance is a
positive number, absolute value of a number is
positive. If the number is negative, simply
make it positive; and if it is already positive, leave it as
is. For example, since -2.4 is negative, | -2.4 | = 2.4 and
since 5.01 is positive, | 5.01 | = 5.01. If the variable is positive, simply
drop the absolute value symbol. For example, If x > 0,
then | x | = x. If x < 0, then | x | = -(x).
Probability is the number of
desired or looked for outcomes divided by the number of
possible outcomes. Two examples follow: You have 8 blue shirts, 6 red
shirts, and 4 white shirts. After you take a blue shirt out,
what's the probability you will take a blue shirt out again?
The key here is to remember to
subtract from your total. In this case, we have 7 blue
shirts left and a total of 17 shirts in the closet. So you
have a 7 in 17 chance of pulling out a blue shirt.
You have two dice, each numbered
from 1 - 6. What is the probability that you will roll a
combination that totals 2? When you look at this analytically,
you realize that you have only one combination that will
result in a 2. Both dice need to turn up with 1's. How many
total combinations are possible? If you roll a 1 on one
cube, how many other possible numbers can come up on the
other cube? Six! So, you have six combinations of six each
--or 36 total combinations. So the answer is
1/36. Click
here for more on Probability. Click
here for Plane Geometry Review. Click
here for an extensive Formula
Guide. Click
here for lectures on COORDINATE
GEOMETRY. Learn the basic rules below:
1. There are 180 degrees in a
straight angle. 2. Two angles are supplementary if
their angle sum is 180 degrees. 3. Two angles are complementary if
their angle sum is 90 degrees. 4. Perpendicular lines meet at
right angles. 5. A triangle with two equal sides
is called isosceles. The angles opposite the equal sides are
called the base angles. 6. The angle sum of a triangle is
180 degrees. 7. In an equilateral triangle all
three sides are equal, and each angle is 60
degrees. 8. The area of a triangle is bh/2,
where b is the base and h is the height. 9. In a triangle, the longer side
is opposite the larger angle, and vice versa. 10. Pythagorean Theorem: In a
right triangle, the square of the two sides that form a
right angle is equal to the square of the longest
side. 11. Two triangles are similar (same
shape and usually different size) if their corresponding
angles are equal. If two triangles are similar, their
corresponding sides are proportional. 12. Two triangles are congruent
(identical) if they have the same size and
shape. 13. In a triangle, an exterior
angle is equal to the sum of its remote interior angles and
is therefore greater than either of them. 14. Opposite sides of a
parallelogram are both parallel and congruent. Area of a
parallelogram: A = bh (b = base and h =
height) 15. The diagonals of a
parallelogram bisect each other. 16. If w is the width and l is the
length of a rectangle, then its area is A = lw and its
perimeter is P = 2w + 2l. 17. The volume of a rectangular
solid (a box) is the product of the length, width, and
height. The surface area is the sum of the area of the six
faces. V = bhw (b = base, h = height, w =
width) 18. If the length, width, and
height of a rectangular solid (a box) are the same, it is a
cube. Its volume is the cube of one of its sides, and its
surface area is the sum of the areas of the six
faces. 19. An angle inscribed in a
semicircle is a right angle. 21. Area of a circle: A = pi times
the radius squared. (Note: Pi = approximately 3.14. Pi is an
infinite, non-repeating decimal.) 22. Circumference of a Circle: C =
pi x d (pi = 3.14 and d = diameter) 23. Volume of a Cylinder: V = pi
times the radius squared times the height The slope of a line measures the
inclination of the line. By definition, it is the ratio of
the vertical change to the horizontal change. The vertical
change is called the rise, and the horizontal change is
called the run. Thus, the slope is the rise over the
run. M = (y - b)/(x -
a) The y-coordinate of the point where
a line crosses the y-axis is called the
y-intercept. Click
here for more on Slope-Intercept
Form. The length of the line segment, d,
is "the square root of the sum of the squares of the other
two sides": Click
here to review the Distance
Formula.
M = ([x + a]/2, [y +
b]/2) In other words, to find the
midpoint, simply average the corresponding coordinates of
the two points. Click
here to review the Midpoint
Formula. Click
here for Algebra Modules from Brazosport
ISD. Click
here for tips on Solving Simple
Equations. Click
here for Algebra Tutorial. Click
here for Algebra I Review. Click
here for lecture on the Quadratic
Formula. Click
here for lecture on Polynomials. 1. Only like terms may be added or
subtracted. To add or subtract like terms, merely add or
subtract their coefficients: 2. You may add or multiply
algebraic expressions in any order. This is called the
commutative property: xy = yx Caution: the commutative
property does not apply to division or
subtraction. 3. When adding or multiplying
algebraic expressions, you may regroup the terms. This is
called the associative property: x(yz) =
(xy)z Caution: the associative property
doesn't apply to division or subtraction. 4. Parentheses When simplifying expressions with
nested parentheses, work from the inner most parentheses
out: 5. Order of Operations:
(PEMDAS) When simplifying algebraic
expressions, perform operations within parentheses first and
then exponents and then multiplication and then division and
then addition and then subtraction. This can be remembered
by the mnemonic: Inequalities are manipulated
algebraically the same way as equations with one
exception: Multiplying or dividing both sides
of an inequality by a negative number reverses the
inequality. That is, if x > y and c < 0, then cx <
cy. As with equations, our goal is to
isolate x on one side: Click
here for lecture on solving Word
Problems. Substitution is a very useful
technique for solving math problems. It often reduces hard
problems to routine ones. In the substitution method, we
choose numbers that have the properties given in the problem
and plug them into the answer-choices. When using the substitution method,
be sure to check every answer-choice because the number you
choose may work for more than one answer-choice. If this
does occur, then choose another number and plug it in, and
so on, until you have eliminated all but the answer. This
may sound like a lot of computing, but the calculations can
usually be done in a few seconds. When substituting in quantitative
comparison problems, don't rely on only positive whole
numbers. You must also check negative numbers, fractions, 0,
and 1 because they often give results different from those
of positive whole numbers. Plug in the numbers 0, 1, 2, -2,
and 1/2, in that order. Sometimes instead of making up
numbers to substitute into the problem, we can use the
actual answer-choices. This is called Plugging In. It is a
very effective technique, but not as common as
Substitution. At first, students often struggle
with these problems since they have forgotten many of the
basic properties of arithmetic. So before we begin solving
these problems, let's review some of these basic
properties. A number n is odd if the remainder
is one when n is divided by 2:
n = 2z + 1. Consecutive integers are written as
x, x + 1, x + 2, . . . Consecutive even or odd integers
are written as , x + 2, x + 4, . . . The integer zero is neither
positive nor negative, but it is even:
0 = 2(0). A prime number is an integer that
is divisible only by itself and 1. The prime numbers are 2, 3, 5, 7,
11, 13, 17, 19, 23, 29, 31, 37, 41, . . . A number is divisible by 3 if the
sum of its digits is divisible by 3. For example, 135 is
divisible by 3 because the sum of its digits (1 + 3 + 5 = 9)
is divisible by 3. 1. A recipe for 60 cookies uses 3
cups of flour. How many cups of flour will be needed to make
150 cookies? When you can, set proportion
problems up as ratio as in this case: 60/3 = 150/X. By
setting this problem up as a ratio, you can solve it by
cross multiplying and it allows you to be able to check to
make certain your ratio is set up to compare like entities.
2. A high school has 700 students.
The ratio of freshmen to sophomores to juniors to seniors is
4:3:2:1. How many juniors are there? The high school has 700 students.
They are in a ratio of freshmen to sophomores to juniors to
seniors of 4 to 3 to 2 to 1. 10x = 700 x = 70 2x = 2(70) = 140
juniors In many word problems, as one
quantity increases (decreases), another quantity also
increases (decreases). This type of problem can be solved by
setting up a direct proportion. (A) 16 (B) 17 (C) 18 (D) 19 (E)
20 As time increases so does the
number of shaped surfboards. Hence, we set up a direct
proportion. First, convert 5 hours into minutes: 5 hours = 5
x 60 minutes = 300 minutes. Next, let x be the number of
surfboards shaped in 5 hours. Finally, forming the
proportion yield The answer is (C). Example: If 7 workers can assemble
a car in 8 hours, how long would it take 12 workers to
assemble the same car? (A) 3 hrs. (B) 3 1/2 hrs. (C) 4 2/3
hrs. (D) 5 hrs. (E) 6 1/3 hrs. As the number of workers increases,
the amount time required to assemble the car decreases.
Hence, we set the products of the terms equal. Let x be the
time it takes the 12 workers to assemble the car. Forming
the equation yields 7(8) = 12x The answer is
(C). To summarize: if one quantity
increases (decreases) as another quantity also increases
(decreases), set ratios equal. If one quantity increases
(decreases) as another quantity decreases (increases), set
products equal. The most basic type of factoring
involves the distributive rule: For example, 3h + 3k = 3(h + k),
and 5xy + 45x = 5xy + 9(5x) = 5x(y + 9). The distributive
rule can be generalized to any number of terms. For three
terms, it looks like ax + ay + az = a(x + y + z). For
example, 2x + 4y + 8 = 2x + 2(2y) + 2(4) = 2(x + 2y +
4). (A) -4 (B) -3 (C) 0 (D) 12 (E)
27 (x - y/3) - (y - x/3) = The answer is
(D). First - Multiply the first term in
each parenthesis. Outer - Multiply the outer term in
each parenthesis. Inner - Multiply the inner term in
each parenthesis. Last - Multiply the last term in
each parenthesis. Click
here for more about the FOIL method Created
by Becky Villarreal
Austin
Community College 2000
Scoring
Basic
Math
EXPONENTS and
ROOTS
Rule 1: Am = A
x A x A
SCIENTIFIC NOTATION
(4 x 106 )(7 x
107 ) = (4 x 7)(1013 ) = 28 x
1013 = 2.8 x 1014
Positive & Negative
Numbers
Miscellaneous Properties of
Positive and Negative Numbers
2. The product (or quotient) of a positive number and a
negative number is negative.
3. The product (or quotient) of an even number of negative
numbers is positive.
4. The product (or quotient) of an odd number of negative
numbers is negative.
5. The sum of negative numbers is negative.ABSOLUTE VALUES
PROBABILITY
GEOMETRY
Slope Formula:
Algebra
Adding & Subtracting Algebraic
Expressions
INEQUALITIES
Subtracting 3 from both sides yields -2x > -11
Dividing both sides by -2 and reversing the inequality
yields x < 11Strategies
SUBSTITUTION
Plugging In
NUMBER THEORY
RATIO AND PROPORTIONS
3(300)/50 = x
18 = x
56/12 = x
4 2/3 = xFactoring using the Distributive
Rule
x - y/3 - y + x/3 =
4x/3 - 4y/3 =
4(x - y)/3 =
4(9)/3 =
12FOIL METHOD
PRACTICE