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S A TS A T

S A TThe SAT Reasoning Test is a standard test for college admission in the United States.

The college board states that SAT measure critical thinking skills that are needed for academic success in colleges. It analyze how well the test takers analyze and solve problems.

The SAT is typically taken by high school juniors and seniors.

SAT generally consists of three major sections:SAT generally consists of three major sections:

SATSAT

Mathematics(Three scored sections)

Mathematics(Three scored sections)

Critical Reading(Three scored sections)

Critical Reading(Three scored sections)

WritingWriting

25 minutes20 Multiple choice

questions

25 minutes20 Multiple choice

questions

25 minutes8 – Multiple choice10 – Grid questions

25 minutes8 – Multiple choice10 – Grid questions

20 minutes16- shorter multiple choice questions

20 minutes16- shorter multiple choice questions

25 minutes25 minutes

20 minutes20 minutes

25 minutes25 minutesIncludes Multiple choice questions and a brief essay

Includes Multiple choice questions and a brief essay

Mathematics Section

Number and OperationsNumber and Operations

Algebra and FunctionsAlgebra and Functions

GeometryGeometry

Statistics and ProbabilityStatistics and Probability

Data AnalysisData Analysis

Example:

Let’s see few common questions of SAT exam.Let’s see few common questions of SAT exam.

Solution:

If and , what is the value of ?If and , what is the value of ?3

2

b

a

3

2

b

a

9

8

b

c

9

8

b

c

c

ac

a

Eliminate b by using the fact that .

Since , inverting fractions makes .

To get the value of , multiply together the numerical

values of and .

c

a

c

b

b

a

9

8

b

c

8

9

c

b

c

a

b

a

c

b

24

18

8

9

3

2

c

b

b

a

c

a

4

34

3

Example: Look at this:Look at this:

If m + n is an odd number where m and n are positive integers, which expression always represents an even numbers?If m + n is an odd number where m and n are positive integers, which expression always represents an even numbers?

Solution: Pick simple numbers for m and n such that m + n is an odd number.

Let m = 2 and n = 1, then m + n = 3 and 3 is an odd number.

Try the answer choices in turn:

(a) m – n = 2 – 1 = 1

(b) m2 + n2 = 22 + 12 = 4 + 1 = 5

(c) (m + n)2 = (2 + 1)2 = 32 = 9

(d) m2 – n2 = 22 – 12 = 4 – 1 = 3

(e) (mn)2 = (2 1)2 = 22 = 4

Since only even number among the transformed answer choices is 4.

So, the correct choice is (e).

(a) m – n (b) m2 + n2 (c) (m + n)2 (d) m2 – n2 (e) (mn)2(a) m – n (b) m2 + n2 (c) (m + n)2 (d) m2 – n2 (e) (mn)2

Definition

• Percent means “out of 100.”

Percents to Fractions

• Drop the percent sign• Put number over 100• Simplify

Example: 80 % =

(Don’t forget to simplify!)

5

4

10

8

100

80

Percents to FractionsExpress the following percents as fractions:

1. 60%

2. 75%

3. 150%

4. 8.5%

Fractions to Percents

Convert to a percent

Step 3:- Write ‘%’ sign with answer 80%

5

400100

5

4

Step 2:- Simplify

Step 1:- Multiply the fraction by 100

805

400

5

4

Fractions to PercentsExpress the following fractions as percents:

1.

2.

3.

5

2

5

3

100

17

Finding Percent of a Number

STEP 1: Rewrite the percent as decimal

STEP 2: Multiply the given number by the

decimal form of the percent

Calculate the following: 25% of 200

Rewrite 25% as 0.25. Then multiply

25% of 200 = 0.25 ×200 = 50

Calculate the following:

20 % of 820


40 % of 725


60 % of 692

Percentage Increase

Percentage Increase

Percentage Increase

= [Increase in value/ old value] x 100 %

where,

Increase in value = New value – Old Value

ApplicationsApplications

If Old and New Value are given,

First, find Increase in ValueIncrease in value = New value – Old Value

Then, find Percentage Increase.Percentage increase = (Increase in value/old value) x 100

Let’s see an Example…

ExampleExample

If the price of a book has been increased from $10 to $20, then what is the percentage increase?

Here, New Value = $20

Old Value = $10

Increase in value = New Value – Old Value

= $20 - $10 = $10

Percentage increase = (Increase in value/old value) x 100

= 10/10 x 100 = 100%

Hence, Percentage increase is 100%

ApplicationsApplications

If Increase in value and New Value are given,

First, find Old Value

Then, find Percentage Increase.

Let’s see an Example…

If the new price of an item is $25 and increase in value from the old price is $5. What is the percentage increase?

ExampleExample

Here, New Value = $25

Increase in Value = $5

Increase in Value = New Value – Old Value

Old Value = New Value – Increase in Value

= $25 – $5 = $20

Percentage Increase = (Increase in value/old value) x 100

= 5/20 x 100 = 25%

Hence, Percentage increase is 25%.

PracticePractice

A boy earns $20 daily. If he works more, he can earn $30 daily. Calculate percentage increase in his daily earning.

# 1

Use this space to show your work:

PracticePractice

Sam’s weight was 120 lb last year.This year he weighs 138 lb. Find the percentage increase in his weight.

# 3


PracticePractice

Suppose you bought shirts and the total bill was $238. Sales tax amounting to $38 was included in the bill. What was the sales tax rate and the original price?

# 1


PracticePractice

Maria weighs 120 lb after gaining 20 lb. Find the percentage increase in her weight.

# 2


In a movie theater, 480 of the 500 seats were occupied. What percent of the seats were NOT occupied?

(A) 0.4% (B) 2% (C) 4% (D) 20% (E) 40%

After 2 months on a diet, John’s weight dropped from 168 pounds to 147 pounds. By what percent did John’s weight drop?

(A) (B) (C) 21% (D) 25% (E)%2

112 %

7

214 %

7

428

Which expression is equal to 0.01%?

(A) (B) (C) (D) (E)100

1

10

01.0

100

1

101

1001

410

1

Which is 20% of 25% of ?5

4

(a) 0.0025 (b) 0.004 (c) 0.005 (d) 0.04 (e) 0.05

If a is 40% of b, then b exceeds a by what percent of a?

(a) 60% (b) 100% (c) 140% (d) 150% (e) 250%

After the length and width of a rectangle are each reduced by 40% the length and width of the new rectangle are each increased by 1/3 of their new values . In producing the final rectangle, by what percent is the area of the original rectangle reduced?

(a) 20% (b) 24% (c) 30% (d) 36% (e) 40%

sat- final

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