Success step english 5 pps

Sample Three-Step Ratio Question Use the three steps above to help you work out the fol-lowing problem.. Put the quantities in order and in the form given by the answer choices.. The Fou

Measuring the area and perimeter of a square is

basi-cally the same as a rectangle, only the length and width

are the same measurement

Area: side × side

Perimeter: side × 4

Triangle

Remember that a triangle is half a rectangle

Area:12b × h Multiply the height and the base.

Since the triangle is half, divide by two Note:

The height of a triangle is not always one of the

sides For example, in triangle ABC which

fol-lows, side AB is not the height, BD is the height.

AC is the base To find the area, ignore all the

numbers but the base and the height The base

can be found by adding 4 and 8: 4 + 8 = 12 The

height is 5.12× 5 × 12 = 620or 30

Perimeter: Add the sides all around: 12 + 6 + 9 = 27

Circle

The diameter of a circle goes from one point on the

circle, through the middle, and all the way across to

another point on the circle The radius (r) is half of the

diameter When working with π, consider the

follow-ing: The symbol π is usually found in the answers so

you don’t have to worry about converting it to a num-ber But ifπ is not found in the answers, and the ques-tion calls for an approximate answer, substitute 3 for π The question may tell you to use 272or 3.14

Area:πr2 Square the radius and look at the answers

Ifπ is not found in the answers, multiply by 3 In

the example above, A = π42or 16π

Circumference: 2πr Circumference is to a circle what

perimeter is to a rectangle Multiply the radius by

2 and look for the answers Ifπ is not in the answer choices, multiply by 3 In the example above, the circumference is 2π4, or 8π

Other Areas

Cut the figure into pieces, find the area of each, and add If you’re asked to find the area of a figure with a piece cut out of it, find the area of the whole figure, find the area of the piece, and subtract

Other Perimeters

For any perimeter, just add the outside lengths all the way around

Practice

8 Find the area of a circle with a diameter of 6.

a 36π

b 24π

c 16π

d 9π

e 6π

9 What is the area of the triangle above?

a 48

b 9

c 12

d 18

e 24

10 A box measured 5′′ wide,12′ long, and 4′′ high

How many one-inch cube candies could fit in

the box?

a 10 candies

b 60 candies

c 90 candies

d 120 candies

e 150 candies

Answers

8 d If the diameter is 6, the radius is 3 A = π(3)2

= 9π

9 c 8 is the base, b, and 3 is the height, h. 12 × 8

× 3 = 12

10 d The words “one-inch cube” are there to throw

you off; volume is always measured in one unit

cubic space Since 12foot = 6 inches: 6 × 4 × 5 =

120

 M a t h 6 : R a t i o s , P r o p o r t i o n s ,

a n d P e r c e n t s

Ratios and proportions, along with their cousins,

per-cents, are reportedly on every CBEST A good

under-standing of these topics can help you pick up valuable

points on the math section of the test

The Three-Step Ratio

The three-step ratio asks for the ratio of one quantity

to another

Sample Three-Step Ratio Question

Use the three steps above to help you work out the fol-lowing problem

1 Which of the following expresses the ratio of 2

yards to 6 inches?

a 1:3

b 3:1

c 1:12

d 9:1

e 12:1

Answer

1 One yard is 36 inches, so 2 yards is 72 inches.

Thus, the ratio becomes 72:6 (The quantities can also be put in yards.)

2 This ratio can be expressed as 762or 72:6 In this problem, 72:6 is the form that is used in the answers

3 Since the answer is not there, reduce 72 inches: 6 inches = 12:1 The answer is e Notice that choice

c, 1:12, is backwards, and therefore incorrect.

Three Success Steps for Three-Step Ratios

1 Put the quantities in the same units of

meas-urement (inches, yards, seconds, etc.)

2 Put the quantities in order and in the form

given by the answer choices

3 If the answer you come up with isn’t a choice,

reduce

Try the three steps on the following problems

2 Find the ratio of 3 cups to 16 ounces.

a 2:3

b 3:16

c 16:3

d 3:1

e 3:2

3 Find the ratio of 6 feet to 20 yards.

a 10:1

b 6:20

c 3:10

d 20:6

e 1:10

4 Find the ratio of 2 pounds to 4 ounces.

a 2:4

b 2:1

c 1:8

d 8:1

e 8:5

5 In a certain class, the ratio of children who

pre-ferred magenta to chartreuse was 3:4 What was

the ratio of those who preferred magenta to the

total students in the class? Hint: Add 3 and 4 to

get the total

a 7:3

b 3:4

c 4:3

d 3:7

e 4:7

6 In a certain factory, employees were either

fore-men or assembly workers The ratio of forefore-men

to assembly workers was 1 to 7 What is the ratio

of the assembly workers to the total number of employees?

a 1:7

b 7:1

c 7:8

d 8:7

e 2:14

Answers

2 e.

3 e.

4 d.

5 d.

6 c.

The Four-Step Ratio

The four-step ratio solution is used when there are two groups of numbers: the ratio set, or the small numbers; and the actual, real-life set, or the larger numbers One

of the sets will have both numbers given, and you will

be asked to find one of the numbers from the other set

H O T T I P

■ You can almost do question 2 by the process of

elimination You know that 3:16 or 16:3 can’t be

right because the units haven’t been converted yet.

You also know that test makers like to turn the

cor-rect ratio around in order to try to catch you, so a or

e must be the answer If you know that 3 cups is

more than 16 ounces, you have it made.

■ In question 3, b and c are the same quantity There

can’t be two right answers, so they can be

elimi-nated Why change yards into feet? Six feet is two

yards Reducing 2:20 makes 1:10 Aren’t these fun?

Sample Four-Step Ratio Question

7 The ratio of home games won to total games

played was 13 to 20 If home teams won 78

games, how many games were played?

Answer

This problem can be solved in four steps

1 Notice there are two categories: home team wins

and total games played Place one category over

the other in writing

THootmalegawminess or HT

Note: This step is frequently omitted by test

takers in order to save time, but the omission of

this step causes most of the mistakes made on

ratio problems If you reversed the H and T,

put-ting T on top, that is not wrong, as long as you

make sure to put the total games on top on both

sides of the equation

2 In the problem above, the small ratio set is

com-plete (13 to 20), and you’re being asked to find the

larger, real-life set Work with the complete set

first Decide which numbers from the complete

set go with each written category Be careful; if

you set up the ratio wrong, you will most

proba-bly get an answer that is one of the answer choices, but it will be the wrong answer

Notice which category is mentioned first: “The number of HOME games won to TOTAL games played ” Then check to see what number is first:

“ was 13 to 20.” Thirteen is first, so 13 goes with home games; 20 goes with the total games

HT= 1230

3 Determine whether the remaining number in the

problem best fits home wins or total games “If home teams won 78 games” indicates that the 78 goes in the home-team row The number of total games played isn’t given, so that spot is filled with

an x.

HT= 1230= 7x8

4 Now cross multiply Multiply the two numbers on

opposite corners: 20 × 78 Then divide by the number that is left (13)

201×378= 1,15360= 120

Practice

Try the four steps on the following problems

H O T T I P

After you cross multiply and wind up with one fraction, you can divide a top number and the denominator by the same factor and thus avoid long computations In the above example, 13 ÷ 13 = 1 and 78 ÷ 13 = 6.

The problem would then be much simpler: 20 × 6 = 120.

Four Success Steps

for Four-Step Ratios

1 Label the categories of quantities in the

prob-lem to illustrate exactly what you’re working

with

2 Set up the complete set in ratio form.

3 Set up the incomplete set in ratio form.

4 Cross multiply to get the missing figure.

20 1 78

13 × 6 = 120

8 On a blueprint,12inch equals 2 feet If a hall is

supposed to be 56 feet wide, how wide would the

hall be on the blueprint?

a 116

b 423

c 913

d 14

e 1823

9 In a certain recipe, 2 cups of flour are needed to

serve five people If 20 guests were coming, how

much flour would be needed?

a 50

b 30

c 12

d 10

e 8

10 A certain district needs 2 buses for every 75

students who live out of town If there are 225

students who live out of town, how many buses

are needed?

a 4

b 6

c 8

d 10

e 11

Answers

8 d.

9 e.

10 b.

Percents

There are only five basic types of percent problems on

the CBEST These will be explained below As is true

with most other types of problems on the CBEST,

per-cent problems most often appear in word-problem

format Percents can be done by using ratios or by

alge-bra Since ratios have just been covered, this section

Percents can be fairly simple if you memorize these few relationships:oisf,wphaortle,pe1r0ce0nt

Eight Success Steps for Solving Percent Problems

Feel free to skip steps whenever you don’t need them

1 Notice the numbers Usually you are given two

numbers and are asked to find a third Are you given the whole, the part, or both (wphaorlte)? Is the percent given (pe1r0c0ent)? Is the percent large or small? Is it more or less than half? Sometimes you can estimate the answer enough to elimi-nate some alien answers

2 If there are pronouns in the problem, write the

number to which they refer above the pronoun

3 Find the question and underline the question

word Question words can include how much

is, what is, find, etc In longer word problems,

you may have to translate the problem into a simple question you can use to find the answer

4 Notice the verb in the question The quantity

that is by itself on one side of the verb is

con-sidered the is Place this number over the number next to the of ( ) If a question word

is next to an is or of, put a variable in place of the number in that spot If there is no is or no

of, check to see whether one is implied See

whether you can rephrase the question, keep-ing the same meankeep-ing, but puttkeep-ing in the miss-ing two-letter word If all else fails, check to make sure the part is over the whole

5 Place the percent over 100 If there is no

per-cent, put a variable over 100 (pe1r0c0ent)

6 Make the two fractions equal to each other.

7 Solve as you would a ratio.

8 Be sure to answer the question that was

asked

is

 of

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×

500 1

5

100