Solve the simple problem, and then solve the problem with the larger numbers the same way.. Sample Question Solve this problem using the SOLVE steps described above.. Although writing do
Trang 1L Stands for Live
Living the problem means pretending you’re actually
in the situation described in the word problem To do
this effectively, make up details concerning the events
and the people in the problem as if you were part of
the picture This process can be done as you are
read-ing the problem and should take only a few seconds
V Stands for View
View the problem with different numbers while
keep-ing the relationships between the numbers the same
Use the simplest numbers you can think of If a
prob-lem asked how long it would take a rocket to go
1,300,000 miles at 650 MPH, change the numbers to
300 miles at 30 MPH Solve the simple problem, and
then solve the problem with the larger numbers the
same way
E Stands for Eliminate
Eliminate answers you know are wrong You may also
spend a short time checking your answer if there is
time
Sample Question
Solve this problem using the SOLVE steps described above
1 There are 651 children in a school The ratio of
boys to girls is 4:3 How many boys are there in the school?
a 40
b 325
c 372
d 400
e 468
Answer
1 Subject Experience: You know that 4 and 3 are
only one apart and 4 is more You can conclude from this that boys are a little over half the school population Following up on that, you can cut 651
in half and eliminate any answers that are under half Furthermore, since there are three numbers
in the problem and two are paired in a ratio, you can conclude that this is a ratio problem Then you can think about what methods you used for ratio problems in the past
2 Organize: The clue word total means to add In
the context in which it is used, it must mean girls
plus boys equals 651 Also, since boys is written before girls, the ratio should be written Boys:Girls.
3 Live: Picture a group of three girls and four boys.
Now picture more of these groups, so many that the total would equal 651
4 View: If there were only 4 boys and 3 girls in the
school, there would still be a ratio of 4 to 3 Think
of other numbers that have a ratio of 4:3, like 40 and 30 If there were 40 boys and 30 girls, there would be 70 students in total, so the answer has to
be more than 40 boys Move on to 400 boys and
300 girls—700 total students Since the total in the problem is 651, 700 is too large, but it is close, so
H O T T I P
Don’t try to keep a formula in your head as you solve the
problem Although writing does take time and effort,
jot-ting down a formula is well worth it for three reasons: 1) A
formula on paper will clear your head to work with the
numbers; 2) You will have a visual image of the formula
you can refer to and plug numbers into; 3) The formula will
help you see exactly what operations you will need to
per-form to solve the problem.
Trang 2the answer has to be less than 400 This would
narrow your choices to two
5 Eliminate: Since you know from the step above
that the number of students has to be less than
400, you can eliminate d and e Since you know
that the number of boys is more than half the
school population, you can eliminate a and b You
are left with c, the correct answer.
Quick Tips and Tricks
Below is a miscellaneous list of quick tips to help you
solve word problems
Work From the Answers
On some problems, you can plug in given answers to
see which one works in a problem Start with choice c.
Then if you need a larger number, go down, and if you
need a smaller answer, go up That way, you don’t have
to try them all Consider the following problem:
1 One-fifth of what number is 30?
a 6
b 20
c 50
d 120
e 150
Try c:15of 50 is 10 A larger answer is needed
Try d:15of 120 is 24 Not yet, but getting closer
Try e:15of 150 is 30—Bingo!
Problems with Multiple Variables
If there are so many variables in a problem that your
head is spinning, put in your own numbers Make a
chart of the numbers that go with each variable so
there is less chance for you to get mixed up Then write
your answer next to the given answer choices Work
the answers using the numbers in your chart until one
works out to match your original answer In doing this,
avoid the numbers 1 and 2 and using the same num-bers twice There may appear to be two or more right answers if you do
Sample Multi-Variable Question
2 A man drove y miles every hour for z hours If he
gets w miles to the gallon of gas, how many
gal-lons will he need?
a yzw
b. y w z
c. y w z
d.w zy
e. z y w
Answer
Picture yourself in the situation If you drove 4 (y) miles every hour for 5 (z) hours, you would have driven 20 miles If your car gets 10 (w) miles to the
gal-lon, you would need 2 gallons Since 2 is your answer, plug the numbers you came up with into the answer
choices and see which one is correct Choice b equals
2 and is therefore correct
b. y w z 41×05= 2
c. y w z 41×05≠ 2
d. w zy 105× 4≠ 2
e. z y w 5×410≠ 2
Let the Answers Do the Math
When there is a lot of multiplication or division to do, you can use the answers to help you Suppose you are asked to divide 9,765 by 31 The given answers are as follows:
Trang 3a 324
b 316
c 315
d 314
e 312
You know then that the answer will be a
three-digit number and that the hundreds place will be 3
The tens place will either be 1 or 2, and more likely 1
because most of the answers have 1 in the tens place
Your division problem is practically worked out for
you
Problems with Too Much or Too Little
When you come across a problem that you think you
know how to answer, but there seems to be a number
left over that you just don’t need in your equation,
don’t despair It could very well be that the test writers
threw in an extra number to throw you off The key to
not falling prey to this trick is to know your equations
and check to make sure the answer you came up with
makes sense
When you come across a problem that doesn’t
seem to give enough information to calculate an
answer, don’t skip it Read carefully, because
some-times a question asks you to set up an equation using
variables, and doesn’t ask you to solve the problem at
all If you are expected to actually solve a problem with
what seems like too little information, experiment to
discover how the information works together to lead to
the answer Try the CA tips
More than One Way to Solve a Problem
Some questions ask you to find the only wrong way to
solve a problem Sometimes these are lengthy
ques-tions about children in a classroom who get the right
answer the wrong way and the wrong answer the right
way In this type of question, do the computation
yourself, and work from the answers The choice that
gives an answer different from the others has to be the wrong answer Consider these choices:
a 5% of 60
b. 1500× 60
c 0.05 × 60
d 5 × 60 ÷ 100
e 5 × 60
All of the answers compute to 3 except choice e, which turns out to be 300 Therefore, e must be the
correct answer
M a t h 1 1 : L o g i c a n d
Ve n n D i a g r a m s
You deserve a break after all your hard work on math problems This lesson is shorter than the others; unless logic problems give you a lot of trouble, you can prob-ably spend less than half an hour on this lesson
If Problems
If problems are among the easiest problems on the test
if you know how to work them A genuine if problem begins with the word if and then gives some kind of
rule Generally, these problems mention no numbers
In order for the problem to be valid, the rule has to be
true for any numbers you put in.
Sample If Question
The following is a typical if problem Experiment with
this problem to see how the answer is always the same
no matter what measurements you choose to use
One Success Step for If Problems
Pick some numbers and try it out!
Trang 41 If the length and width of a rectangle are
doubled, the area is
a doubled
b halved
c multiplied by 3
d multiplied by 4
e divided by 4
Answer
First of all, choose a length and width for your
rectan-gle, like 2′ by 3′ The area is 2 × 3, or 6 Now double the
length and the width and find the area: 4 × 6 = 24 24
is 4 times 6, so d must be the answer Try a few
differ-ent numbers for the original length and width to see
how easy these types of questions can be
Practice
Try another one:
2 If a coat was reduced 20% and then further
reduced 20%, what is the total percent of
dis-count off the original price?
a 28%
b 36%
c 40%
d 44%
e 50%
Answer
Since this question concerns percents, make the coat’s
beginning price $100 A 20% discount will reduce the
cost to $80 The second time 20% is taken off, it is
taken off $80, not $100 Twenty percent of 80 is 16
That brings the cost down to $64 (80 – 16 = 64) The
original price of the coat, 100, minus 64 is 36 One
hundred down to 64 is a 36% reduction So two suc-cessive discounts of 20% equal not a 40%, but a 36% total reduction
Venn Diagrams
Venn diagrams provide a way to think about groups in
relationship to each other Words such as some, all, and none commonly appear in these types of questions.
In Venn diagram problems, you are given two or more categories of objects First, draw a circle repre-senting one of the categories Second, draw another circle representing the other category Draw the second circle according to these rules:
1 If the question says that ALL of a category is the
second category, place the second circle around the second category
Example: All pigs (p) are animals (a).
2 If the question says that SOME of a category is
the second category, place the second circle so that it cuts through the first circle
Example: Some parrots (p) are talking birds (t).
3 If the question says NO, meaning that none of
the first category is in the second category, make the second circle completely separate from the first
Example: No cats (c) are fish (f).
H O T T I P
When choosing numbers for if problems, choose small
numbers When working with percents, start with 100.
Trang 5Sample Venn Diagram Question
3 All bipeds (B.) are two headed (T.H.) Which
diagram shows the relationship between bipeds
and two-headed?
a.
b.
c.
d.
e.
Answer
The question says ALL, so the two-headed shape, in
this case, a square, is around the triangle denoting
bipeds The answer is d.
More than Two Categories
Should there be more than two categories, proceed in
the same way
Example: Some candy bars (c) are sweet (s), but no
bananas (b) are candy bars
The sweet circle will cut through the candy bar circle Since the problem did not specify where bananas and sweet intersect, bananas can have several positions The banana circle can be outside both circles completely:
The banana circle can intersect the sweet circle:
Or the banana circle can be completely inside the sweet circle but not touching the candy bar shape:
H O T T I P
Even when there are no pictures of Venn diagrams in the answers, you can often solve this type of problem by drawing the diagram one way and visualizing all the possible positions of the circles given the facts in the problem.
Trang 6W r i t i n g 1 : O u t l i n i n g t h e E s s a y
You will be required to write two essays during your
test time One essay may be a persuasive essay, and the
other a narrative or story essay The persuasive essay
question will ask your opinion, usually on a current or
well-known issue You will need to convince the reader
of your side of the issue The story essay question will
often concern a person or event in your life that has
influenced you in some way You will need to
commu-nicate your experience to the reader in such a way that
the reader will be able to understand and appreciate
your experience The evaluators are not concerned
about whether or not the facts are correct—they are
solely judging your writing ability
Unlike math, writing is flexible There are many
different ways to convey the same meaning You can
pass the test with any logical arrangement of
para-graphs and ideas that are “clearly communicated.”
Most CBEST and English instructors recommend a
five-paragraph essay, which is an easy and acceptable
formula The five-paragraph essay assures that your
ideas are logically and effectively arranged, and gives
you a chance to develop three complete ideas The
longer and richer your essay, the better rating it will
receive
The first step in achieving such an essay is to
come up with a plan or outline You should spend the
first four or five of the 30 minutes allowed in
organiz-ing your essay This first writorganiz-ing lesson will show you
how The rest of the writing lessons will show you
where to go from there
Outlining the Persuasive Essay
Below are some tips on how to use your first four or
five minutes in planning a persuasive essay, based on
an essay topic similar to the one found in the
diagnos-tic exam in Chapter 3
Sample Persuasive Essay Question
1 In your opinion, should public schools require
student uniforms?
Minute 1
During the first minute, read the question carefully and choose your side of the issue If there is a side of the issue you are passionate about, the choice will be easy If you know very little about a subject and do not have an opinion, just quickly choose a side The test scorers don’t care which side you take
Minutes 2 and 3
Quickly answer as many of the following questions as apply to your topic These questions can be adapted to either side of the argument Jot down your ideas in a place on your test booklet that will be easily accessible
as you write Examples of how you might do this for the topic of school uniforms are provided here
1 Do you know anyone who might feel strongly
about the subject?
Parents of school-age children, children, uni-form companies, local children’s clothing shops
2 What reasons might they give for feeling the way
they do?
Pro: Parents will not have to worry about what school clothing to buy for their children Children will not feel peer pressure to dress a certain way Poorer children will not feel that their clothing is shabbier or less fashionable than that of the more affluent children Uni-form companies and fabric shops will receive business for the fine work they are doing
Con: Parents will not be able to dress their children creatively for school Children will not have the opportunity to learn to dress and match their clothes very often They will not
be able to show off or talk about their new