Success step english 7 ppsx

Here’s this process in algebraic form: = Average What makes CBEST average problems more dif-ficult is that not all the numbers will be given for you to add.. 80.2% Answer Use the four Su

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

 M a t h 8 : Av e r a g e s , P r o b a b i l i t y,

a n d C o m b i n a t i o n s

In this lesson, you’ll have a chance to do sample

aver-age questions as well as problems on probability and

on the number of possible combinations They may be

a little more advanced than those you did in school,

but they will not be difficult for you if you master the

information in this section

Averages

You probably remember how you solved average

prob-lems way back in elementary school You added up the

numbers, divided by the number of numbers, and the

average popped out Here’s this process in algebraic

form:

= Average

What makes CBEST average problems more

dif-ficult is that not all the numbers will be given for you

to add You’ll have to find some of the numbers

Sample Average Question

1 Sean loved to go out with his friends, but he

knew he’d be grounded if he didn’t get 80% for the semester in his English class His test scores were as follows: 67%, 79%, 75%, 82%, and 78%

He had two more tests left to go One was tomor-row, but his best friend Jason had invited him to his birthday party tonight If he studied very hard and got 100% on his last test, what could he get by with tomorrow and still have a chance at the 80%?

a 65%

b 72%

c 76.2%

d 79%

e 80.2%

Answer

Use the four Success Steps to solve the problem

1 Draw the horizontal line: 

2 Write in the information: 7= 80%

3 Multiply the number of numbers by the average to

obtain the sum of the numbers: 7 × 80 = 560

4 560 has to be the final sum of the numbers So far,

if you add up all the scores, Sean has a total of 381 With the 100 he plans to get on the last test, his total will be 481 Since he needs a sum of 560 for the average of the seven tests to come out 80, he

needs 79 more points The answer is d.

Sample Average Question

2 On an overseas trip, Jackie and her husband are

allowed five suitcases that average 110 pounds each They want to pack in all the peanut butter and mango nectar they can carry to their family

in Italy They weighed their first four suitcases

Four Success Steps

for Average Problems

1 In order to use the formula above, draw the

horizontal line that is under the sum and over

the number of numbers in the average

formula

2 Write in all the information you know Put the

number of numbers under the line and the

average beside the line Unless you know the

whole sum, leave the top of the line blank

3 Multiply the number of numbers by the

aver-age This will give you the sum of the

numbers

4 Using this sum, solve the problem.

Sum of the Numbers

Number of Numbers

120 How much weight are they allowed to stuff

into their fifth bag?

Answer

1 Draw the horizontal line:

2 Write in the information: 5= 110

3 Multiply the number of numbers by the average to

obtain the sum of the numbers:

5 × 110 = 550

4 Since the total weight they can carry is 550 lb and

they already have 420 lb (135 + 75 + 90 + 120), the

fifth suitcase can weigh as much as 550 − 420, or

130 lbs

Frequency Charts

Some average problems on the CBEST use frequency

charts

Sample Frequency Chart Question

3 The following list shows class scores for an easy

Science 101 quiz What is the average of the scores?

a 28.5

b 85

c 91

d 95

e 100

Answer

Use the four Success Steps to solve the problem

1 In this frequency chart, the test score is given on

the right, and the number of students who received each grade is on the left: 10 students got

100, 15 got a 90, etc

2 Multiply the number of students by the score,

because to find the average, each student’s grade has to be added individually:

10 × 100 = 1,000

15 × 90 = 1,350

3 × 80 = 240

2 × 70 = 140

3 Then add the multiplied scores:

1,000 + 1,350 + 240 + 140 = 2,730

4 Then divide the total number of students,

30 (10 + 15 + 3 + 2), into 2,730 to get the average:

2,37030 = 91

10 15 3 2

10 15 3 2

10 15 3 2

100 90 80 70

# of

Four Success Steps for

Frequency Chart Questions

1 Read the question and look at the chart Make

sure you understand what the different

columns represent

2 If a question asks you to find the average,

multiply the numbers in the first column by the

numbers in the second column

3 Add the figures you got by multiplying.

4 Divide the total sum by the sum of the left

col-umn This will give you the average

Other Average Problems

There are other kinds of averages besides the mean,

which is usually what is meant when the word average

is used:

■ Median is the middle number in a range.

■ Mode is the number that occurs most frequently.

■ Range is the difference between the highest and

lowest number

Sample Median Question

4 What is the median of 6, 8, 3, 9, 4, 3, and 12?

a 2

b 6

c 9

d 10

e 12

Answer

To get a median, put the numbers in order—3, 3, 4, 6,

8, 9, 12—and choose the middle number: 6 If there

are an even number of numbers, average the middle

two (you probably won’t have to do that on the

CBEST)

Mode

The mode is the number used most frequently in a

series of numbers In the above example, the mode is

3 because 3 appears twice and all other numbers are

used only once Look again at the frequency table from

the frequency chart sample question Can you find the

mode? More students (15) earned a score of 90 than

any other score Therefore the mode is 15

Range

To obtain the range, subtract the smallest number from

the largest number The range in the median sample

question is 12 − 3 or 9 The range in the frequency

Probability

Suppose you put one entry into a drawing that had 700 entrants What would be your chances of winning? 1 in

700 of course Suppose you put in two entries Your chances would then be 2 in 700, or reduced, 1 in 350 Probabilities are fairly simple if you remember the few tricks that are explained in this section

Sample Probability Question

5 If a nickel were flipped thirteen times, what is the

probability that heads would come up the thir-teenth time?

a 1:3

b 1:2

c 1:9

d 1:27

e 1:8

Answer

Use the four Success Steps to solve the problem

1 Form a fraction.

2 Each time a coin is flipped, there are 2

possibili-ties—heads or tails—so 2 goes on the bottom of the fraction The thirteenth time, there are still going to be only two possibilities

3 The number of chances given is 1 There is only

Four Success Steps for Probability Questions

1 Make a fraction.

2 Place the total number of different possibilities

on the bottom

3 Place the number of the chances given on the

top

4 If the answers are in a:b form, place the

numerator of the fraction first, and the denom-inator second

“Thirteen times” is extra information and does

not have a bearing on this case

4 The answer is b, 1:2 The numerator goes to the

left of the colon and the denominator to the

right

Sample Probability Question

6 A spinner is divided into 6 parts The parts are

numbered 1–6 When a player spins the spinner,

what are the chances the player will spin a

num-ber less than 3?

Answer

Once again, use the four Success Steps

1 Form a fraction.

2 Total number of possibilities = 6 Therefore, 6 goes

on the bottom

3 Two goes on top, since there are 2 numbers less

than 3: 1 and 2

4 The answer is 26or reduced 13= 1:3

Combinations

Combination problems require the solver to make as

many groups as possible given certain criteria There

are many different types of combination problems, so

these questions need to be read carefully before

attempting to solve them One of the easiest ways to

make combination problems into CBEST points is to

make a chart and list in a pattern all the possibilities

The following sample question is a typical CBEST

combination problem

Sample Combination Question

7 Shirley had three pairs of slacks and four

blouses How many different combinations of one pair of slacks and one blouse could she make?

a 3

b 4

c 7

d 12

e 15

Answer

To see this problem more clearly, you may want to make a chart:

Each pair of slacks can be matched to 4 different blouses, making 4 different outfits for each pair of the

3 pairs of slacks, 3 × 4, making a total of 12 possible combinations

Sample Combination Question

9 Five tennis players each played each other once.

How many games were played?

a 25

b 20

c 15

d 10

e 5

This combination problem is a little trickier in that

there are not separate groups of items as there were for

the slacks and blouses This question involves the same

players playing each other But solving it is not

diffi-cult First, take the total number of players and

sub-tract one: 5 − 1 = 4 Add the numbers from 4 down: 1

+ 2 + 3 + 4 = 10 To learn how this works, take a look

at the following chart:

Letter the five players from A to E:

■ A plays B, C, D, and E (4 games)

■ B has already played A, so needs to play C, D, E (3

games)

■ C has already played A and B, so needs to play D,

E (2 games)

■ D has already played A, B, and C, so needs to play

E (1 game)

■ E has played everyone

Adding up the number of games played (1 + 2 + 3 + 4)

gives a total of 10, choice d.

This same question might be asked on the

CBEST using the number of games 5 chess players

played or the number of handshakes that occur when

5 people shake hands with each other once

Other Combination Problems

Although the above combination problems are the

most common, other kinds of problems are possible

The best way to solve other combination problems is

to make a chart When you notice a pattern, stop and

multiply For example, if you’re asked to make all the

possible combinations of three letters using the letters

A through D, start with A:

There seem to be 16 possibilities that begin with

A, so probably there are 16 that begin with B and 16 that begin with C and D, so multiplying 16 × 4 will give you the total possible combinations: 64

 M a t h 9 : T h e Wo r d P r o b l e m

G a m e

The directions for the word problem game are simple: While carefully observing a word problem, find all the math words and numbers in the problem Eliminate the nonessential words and facts in order to find your answer

Operations in Word Problems

To prepare for the game, make five columns on a sheet

of paper Write one of these words on the top of each

column: Add, Subtract, Multiply, Divide, Equals.

Now try to think of five words that tell you to add, five that tell you to subtract, and so on If you can think of five for each column, you win the first round If you can’t think of five, you can cheat by looking at the list below

How did you do?

0 = keep studying 1–3 for each = good 4–6 for each = excellent 7+ for each = Why are you reading this book?

■ Add: sum, plus, more than, larger than, greater

than, and, increased by, added to, in all,