Success step english 6 doc

Answer Once again, follow the eight Success Steps to solving this problem.. Sample Percent Change Question A change problem is a little bit different than a basic percent problem.. Answe

Sample Question:

Finding Part of a Whole

11 There are 500 flights out of Los Angeles every

hour Five percent are international flights How

many international flights leave Los Angeles

every hour?

Answer

1 You are being asked to find a part of the 500

flights The 500 flights is the whole The percent

is 5 You need to find the part 5% is fairly small,

and considering that 20% of 500 is 100, you

know your answer will be less than 100

2 The second sentence has an implied pronoun.

The sentence can be rephrased “Five percent of

them are international flights.” “Them” refers to

the number 500

3 The question is “How many .” Use the other

sentences to reconstruct the question so it

includes all the necessary information The

problem is asking “5% of 500 (them) are how

many (international flights)?” The question is

now conveniently set up

4 “Are” is the verb 500 and 5% are on the left side

of the verb and “how many” is on the right side

“How many” is all by itself, so it goes on top of

the ratio in the form of a variable 500 is next to

the of so it goes on the bottom At this point,

check to see that the part is over the whole

50x0 =

5 The 5 goes over 100.

50x0 1500

6 The two are equal to each other.

50x0 = 1500

7 Solve.

8 25 international flights leave every hour.

Sample Question: Finding the Whole

12 In a certain laboratory, 60%, or 12, of the mice

worked a maze in less than one minute How many mice were there in the laboratory?

Answer

Once again, follow the eight Success Steps to solving this problem

1 12 is part of the total number of mice in the

lab-oratory 60 is the percent, which is more than half 12 must be more than half of the whole

2 There are no pronouns.

3 The problem is asking, “60% of what number

(total mice) is 12?”

4 “Is” is the verb The 12 is all by itself on the right

of the verb “What number” is next to the of The

12 goes on top, the variable on the bottom

1x2

5 The 60 goes over 100.

16000

6 The two fractions are equal to each other.

1x2= 16000

7 Solve.

8 There were 20 mice in the laboratory.

Sample Percent Question

13 Courtney sold a car for a friend for $6,000 Her

friend gave her a $120 gift for helping with the sale What percent of the sale was the gift?

3

=

12 100

60× 12 100

60×

500 1

5

100 =

500 5

100

1 6,000 is the whole and 120 the part.

2 There are no pronouns, but there are words that

stand for numbers In the question at the end, the

sale is 6,000 and the gift is 120.

3 The question is written out clearly: “What percent

of 6,000 (sale) was 120 (gift)?”

4 “Was” is the verb 120 is by itself on one side It is

the part, so it goes on top 6,000 is near the of and

is the whole, so it goes on the bottom

61,02000

5 There is no percent so x goes over 100.

10x0

6 The two equal each other.

61,02000 = 10x0

7 Solve.

8 The gift was 2% of the sale.

Sample Percent Change Question

A change problem is a little bit different than a basic

percent problem To solve it, just remember change

goes over old:choalndge

14 The Handy Brush company made $500 million

in sales this year Last year, the company made

$400 million What was the percent increase in

sales this year?

Answer

First of all, what was the change in sales? Yes, 100

mil-lion You got that by subtracting the two numbers

Which number is the oldest? Last year is older than this

year, so 400 is the oldest Therefore, 100 goes over 400

140000

The percent is the unknown figure, so a variable

is placed over 100 and the two are made equal to each

other Cross multiply and solve for x.

The answer is 25% Note that if you had put 100 over 500, your answer would have come out differ-ently

Sample Interest Question

15 How much interest will Jill earn if she deposits

$5,000 at 3% interest for six months?

Answer

Interest is a percent problem with time added The

formula for interest is I = PRT I is the interest P is the principal, R is the rate or percent, and T is the time in

years To find the interest, you simply multiply every-thing together Be sure to put the time in years You may change the percent to a decimal, or place it over 100

$5,000 (principal) × 0.03 (percent) ×12(year) = $75

 M a t h 7 : A l g e b r a

Algebra is like a perfectly balanced scale The object is

to keep both sides balanced while isolating the part you need on one side of the scale For example, suppose you know a novel weighs 8 ounces and you want to find out how much your thick phone book weighs You have five novels on one side of the scale, and your phone book and two novels on the other side They perfectly balance By taking two novels off each side, your phone book is alone and perfectly balances with the three novels on the other side Then you know that your phone book weighs 3 × 8, or 24 ounces

100 400

100 4

x

100

100 100 400

×

100 1

=

120 100

6,000

6,000

×

Plugging in Numbers

There are several types of algebra problems you may

see on the CBEST The first consists of a formula,

per-haps one you have never seen, such as Y = t + Z − 3z.

You think, “I have never seen this ” and you are

tempted to skip it But wait you read the question:

What is Y if t = 5, Z = 12, and z = 1? All you do is plug

in the numbers and do simple arithmetic

Y = t + Z − 3z

Y = 5 + 12 − 3(1) = 14

Sample Question

1 Given the equation below, if t = 5 and h = 7,

what is Q?

Q = t2− 3h

Answer

You were right if you said 4

Q = t2− 3h

Q = 52− 3(7)

Q = 25 − 21 = 4

Solving an Equation

In the second type of question, you may actually be

called upon to do algebra

Sample Algebra Question

2 Given the equation below, if Q = 15 and h = 1,

what is the value of t?

Q = t − 3h

Answer

First, plug in the numbers you know and do as much arithmetic as you can:

Q = t − 3h

15 = t− 3(1)

15= t− 3

1 What numbers are on the same side as the

vari-able? 3

2 How are the numbers and the variable connected?

With a minus sign

3 The Opposite is what? Addition.

With that, add 3 to both sides to get your answer:

15 = t− 3

18 = t

Practice

Try these problems You can probably do them in your head, but it’s a good idea to practice the algebra because the problems get harder later

3 3x = 21

4 6 + x = 31

5 x− 7 = 24

6. 3x= 9

7. 13x = 5

Three Success Steps

for Algebra Problems

In order to make a problem less confusing, try

the WHO method:

1 What numbers are on the same side as the

variable? There are two sides of the equal

sign, the right side and the left side

2 How are the numbers and the variable

connected?

3 The Opposite is what? The opposite of

sub-traction is addition

3 x = 7

4 x = 25

5 x = 31

6 x = 27

7 x = 15

Other Operations You Can Use

The following are some other ways you can manipulate

algebra on the CBEST

Square Both Sides

When you’re faced with a problem like x = 5, you

have to get x out from under the square root sign in

order to solve it The way to do this is to square both

sides of the equation Squaring is the opposite of a

square root, and cancels it

x = 5

x2= 52

x = 25

Take the Square Root of Both Sides

If the variable is squared, take the square root of both

sides

x2= 25

x2

= 25

x = 5

Flip Both Sides

If the answer calls for x and the x ends up as a

denom-inator, the answer is unacceptable as is, because the

question called for x, not 1x If you have gotten this far

in a problem, you can find the answer easily by flipping

both sides

1x= 67

1x= 76

x = 76or 116

Divide by a Fraction

To divide by a fraction, you take the reciprocal of the fraction and multiply

35x = 15

Since the reciprocal of35is 53, multiply both sides

by 53:

(53)35x = 15(53)

x = 115(53)

Reduce the fractions and multiply:

Practice

Solve for x:

8 x2= 144

9. x = 7

10.1x= 34

11.23x = 14

Answers

8 12

9 49

10. 43or 113

11 21

=

= 15 53 25

x 51 ( )

1

Multi-Step Problems

Now that you have mastered every algebraic trick you

will need, let’s juggle them around a little by doing

multi-step problems Remember the order of

opera-tions: Please Excuse My Dear Aunt

Sally—Parenthe-ses, Exponents, Multiply and Divide, Add and

Subtract? That order was necessary when putting

numbers together In algebra, numbers are pulled

apart to isolate one variable In general, then, it is

eas-ier to reverse the order of operations—add and

sub-tract, then multiply and divide, then take square roots

and exponents Here is an example:

35 = 4x− 3

In this problem, you would add the 3 to both

sides first There is nothing wrong with dividing the 4

first, but remember, you must divide the whole side

like this:

345= 4x4− 3or 345= 44x−34

As you can see, by adding first, you avoid

work-ing with fractions, makwork-ing much less work for yourself:

35 = 4x− 3

38 = 4x

Then divide both sides by 4 resulting in the

answer:

x = 129= 912

Practice

Try these:

12 5y− 7 = 28

13 x2+ 6 = 31

14.45x− 5 = 15

15 If a − 2b = c, what is a in terms of b and c?

Hint: When a question calls for a variable in

terms of other variables, manipulate the equa-tion until that variable is on a side by itself

16 Ifp3+ g = f, what is p in terms of g and f?

Answers

12 y = 7

13 x = 5

14 x = 25

15 a = c + 2b

16 p = 3(f − g)

Problems Involving Variables

Sometimes you’ll find a problem on CBEST that has almost no numbers in it

Sample Variable Question

17 John has 3 more than 10 times as many students

in his choir class than Janet has in her special education class If the number of students in

John’s class is v, and the number in Janet’s class is

s, which of the equations below does NOT

express the information above?

a v = 3 + 10s

b v − 3 = 10s

c. v1−03 = s

d 10s − v = −3

e v + 3 = 10s

=

38

2

4x

4

19

After reading question 17, you’re likely to come up

with the equation in answer a Since a is correct, it is

not the right choice Now manipulate the equation to

see whether you can find an equivalent equation If

you subtract 3 from each side, answer b will result.

From there, dividing both sides by 10, you come up

with c All those are equivalent equations Choice d can

be derived by using b and subtracting v from both

sides Choice e is not an equivalent and is therefore the

correct answer

Distance, Rate, and

Time Problems

One type of problem made simpler by algebra are

those involving distance, rate, and time Your math

review would not be complete unless you had at least

one problem about trains leaving the station

Sample Distance Problem

18 A train left the station near your home and went

at a speed of 50 miles per hour for 3 hours How

far did it travel?

a 50 miles

b 100 miles

c 150 miles

d 200 miles

Answer

Use the three Success Steps to work through the problem

1 D = R × T

2 D = 50 × 3

3 50 × 3 = 150

Practice

Try these:

19 How fast does a dirt bike go if it goes 60 miles

every 3 hours?

20 How long does it take to go 180 miles at 60 miles

per hour?

Answers

19 R = 20

20 T = 3

H O T T I P

Another way to look at the distance formula is

When you’re working out a problem, cross out the let-ter that represents the value you need to find What remains will tell you the operation you need to perform

to get the answer: the horizontal line means divide and the vertical line means multiply For example, if you

need to find R, cross it out You’re left with D and T.

The line between them tells you to divide, so that’s

how you’ll find R This is a handy way to remember the

formula, especially on tests, but use the method that makes the most sense to you.

Three Success Steps for Distance,

Rate, and Time Problems

1 First, write the formula Don’t skip this step!

The formula for Distance, Rate, and Time is D

= R × T Remember this by putting all the

let-ters in alphabetical order and putting in the

equal sign as soon as possible Or think of the

word DIRT where the I stands for is, which is

always an equal sign

2 Fill in the information.

3 Work the problem.

D

R T