The Gary Gruber SAT test: Which one is best for you?

Which test would be better for you to take the New SAT or the Current SAT?

This is a 30 question test that should take 32 minutes -- developed by Gary Gruber, an expert on standardized testing and the SAT (www.drgarygruber.com and

www.unigo.com/Gruber).

Your performance on these tests will help determine which exam will be better for you,

the new SAT, ACT or current SAT. You also will get an approximate new SAT score and

an approximate current SAT score you can expect to receive in addition to strategies you

will need for each question and methods for increasing your score.

Here is the Test:

Reading Test -- 8 minutes

Classical music is termed classical because it can be heard over and over again without the listener tiring of the music. A symphony of Brahms can be heard and heard again

with the same or even heightened enjoyment a few months later. It is unfortunate that the

sales of classical music are dismal compared to other types of music. Perhaps this is

because many people in our generation were not exposed to classical music at an early

age and therefore did not get to know the music.

In contrast to classical music, contemporary non-classical music has a high impact on the

listener but unfortunately is not evergreen. Its enjoyment lasts only as long as there is

current interest in the topic or emotion that the music portrays, and that only lasts for

three months or so until other music replaces it, especially when another bestselling song

comes out. The reason why the impact of this type of music is not as great when it first

comes out is thought to be because technically the intricacy of the music is not high and

not sophisticated, although many critics believe it is because the music elicits a particular

emotional feeling that gradually becomes worn out in time.

1. According to the passage, it can be assumed that the majority of younger people do not

like classical music because they:

A. buy only the bestselling songs

B. do not have the sophistication of a true music lover

C. grow tired of classical music D. did not hear that type of music in their youth

2. The reason the enjoyment of a particular piece of contemporary music may not last as

long as a piece of classical music is the

A. emotion of a person, which is thought to change in time B. high sophistication of the classical music and its technical intricacy C. fact that there is always another piece of contemporary music that replaces the

one before it

D. economy and marketing of the songs

3. Which choice provides the best evidence for the answer to the previous question?

A. Lines (Paragraph 1): Perhapsmusic. B. Lines (Paragraph 2): In contrastevergreen C. Lines (Paragraph 2): The reasonhigh D. Lines (Paragraph 2): becausetime

4. The graph below illustrates the number of listeners of a particular type of

music per day in a metropolitan area.

According to the graph,

A. the listeners of classical music and non-classical music was steadily declining B. the gap between the listeners of classical music and non-classical music steadily

increased through the years 1950-2015

C. the number of listeners of classical music was at some time as large as the listeners of non-classical music

D. it can be assumed that the number of classical music listeners will exceed the number of listeners of non-classical music at some point in time

5. The term "evergreen" at the beginning of the second paragraph most nearly means

A. colorful B. lasting C. current D. encompassing

(Current SAT) SENTENCE COMPLETIONS (2 minutes):

Fill in the blank(s) with the appropriate choice:

6. The instructor displayed extreme stubbornness; although he....the logic of the students argument, he....to acknowledge her conclusion as correct.

(A) accepted...refused

(B) concluded...consented

(C) denounced....declined

(D) asserted....acceded

(E) rejected....preferred

------------------------------------------------------------------------------------------------------------

7. In spite of the ....of her presentation, many people were.... with the speakers concepts and ideas.

(A) interest....enthralled

(B) power...taken

(C) intensity...shocked

(D)greatness...gratified

(E) strength...bored

Writing and Language Test- 5 minutes

The symbol in parenthesis, like (1), indicates that question, like question 1 references that

portion of the passage.

About the Sea:

(1) Sometimes the meaning of glowing water is ominous. (2) On the Pacific Coast of

North America, it may mean that the sea is filled with a minute plant that contains a

poison of strange and terrible virulence (3) about four days after this minute plant comes

to dominate the coastal plankton, some of the fishes and shellfish in the vicinity become

toxic. (4) This is because in (5) their normal feeding, they have strained the poisonous

plankton out of the water.

1. Which sentence could appear as the sentence preceding the first sentence of this

passage?

A. The sea has many interesting attributes.

B. The Pacific Coastline is frightening.

C. Ships sometimes take Southern routes to avoid bad weather conditions.

D. There are strange plants in the sea.

2.

A. NO CHANGE B. Off C. Apart from D. Not from

3.

A. NO CHANGE B. . About four days C. ; about four days D. , about four days

4. At this point the author is considering adding the following true statement right before

the last sentence: "The fishes and shellfish die soon after." Should the author make this

addition here?

A. No, because this destroys the connection between the last sentence and the initial

preceding one.

B. No, because there is too much of a leap from "toxicity" to "death." C. Yes, because it follows that if fish are toxic they will soon die.

D. Yes, because this qualifies the last sentence and puts it in its right place.

5.

A. NO CHANGE B. theyre C. its D. its

Current SAT -WRITING - 4 questions-2 minutes

Identifying Sentence Errors

Which part (A,B,C,or D) in the sentence is incorrect? Choose E if there is no error.

6. If any signer of the Constitution (A) was to return to life (B) for a day, his opinion (C)

of our amendments (D) would be interesting. (E) No error

7. (A) After we were waiting in line (B) for three hours, (C) much to our disgust, the

tickets had been sold out (D) when we reached the window. (E) No error.

[or if can be drawn, use]:

6. If any signer of the Constitution was to return to life for a day, his opinion A B

of our amendments would be interesting. No error.

C D E

7. After we were waiting in line for three hours, much to our disgust, the tickets had

A B C

been sold out when we reached the window. No error.

D E

Improving Sentences:

Which choice correctly replaces the sentence?

8. He never has and never will keep his word.

(A)He never has and never will keep his word.

(B) He has never yet and never will keep his word. (C) He has not ever and will not keep his word. (D) He never has or will keep his word. (E) He never has kept and he never will keep his word.

9. In spite of Marco wanting to study, his sister made him wash the dishes.

(A) In spite of Marco wanting to study, his sister made him wash the dishes. (B) In spite of the fact that Marco wanted to study, his sister made him wash the

dishes.

(C) In spite of Marcos need to study, his sister made him wash the dishes. (D) In spite of Marcos wanting to study, his sister made him wash the dishes. (E) In spite of Marco studying, his sister made him wash the dishes.

Math Test- 15 minutes

Questions 1-3 Calculator allowed

1. In a college biology class, 60 students are chosen to study

microorganisms. The study groups have been divided into 18 sections where each section

will have 3 or 6 students. How many of the sections will have exactly 3 students?

A. 2

B. 4

C.12

D.16

2. If -5/4

A. 16/3 B. 8/3 C. -8/3 D. -16/3

5.

Triangle is not drawn to scale.

In triangle AEF, AE = AF and EF = 24. EBD and DCF = 90O. The ratio of BD to CD

is 4:6. What is the length of ED?

A. 48/5 B. 44/5 C. 42/5 D. 8

6. If 8x 2y = 6y +14 and 4x + 16y = 9, what is the value of xy?

A. 7/40 B. 9/50 C. 37/200 D. 19/100

7. Mr. Martinezs tenth-grade class took a survey to see what activities each student engages in one hour before bed. When the survey was complete, 5 students selected

Play video games and Watch TV. 14 students selected Watch TV, and 8 students selected Play video games. How many students are in Mr. Martinezs class? (Assume that every student in the class watches TV only, plays video games only, or does both.)

A. 11 B. 17 C. 22 D. 25

8. A band wants to produce CDs from their music. They have an original CD but need

to duplicate the CD to sell to the public. The band buys a CD burning machine for

$169.99. Each blank CD they use will cost $1.50. What is the total production cost for

making x CDs from their original CD?

A. $168.49 B. $169.99 + $1.50x C. $169.99x + $1.50 D. $171.49

9. In the following figure, adjacent sides meet at right angles. What is the perimeter of

the figure?

A. 35 m B. 70 m C. 140 m D. 160 m

10. A ladder is set up against the wall as shown below. The bottom of the ladder is 6 feet

from the wall. Which is true of the angle the ladder makes with the ground if the ladder is

10 feet in length?

A. sin xO = 4/5 B. cos xO = 4/5 C. cot xO = 4/3 D. tan xO = 3/4

11. Sarah is twice as old as John. Six years ago Sarah was four times as old as John was

then. In years, how old is John now?

(A) 3 (B) 9 (C) 18 (D) 20 (E) Cannot be determined

Fill-In Answers Math In questions 12 and 13, you must find an answer without referring to choices:

12. If x + y = 7 and xy = 4, then find the value of x2 + y2 [Editorial note: if you cannot

draw exponents, you can write x2 + y2 as x squared plus y squared] ------------------------------------------------------------------------------------------------------------

13. If y + 2q = 15, q + 2p = 5 and p + 2y = 7, then find the value of p + q + y.

------------------------------------------------------------------------------------------------------------

14 . A four-sided figure ABCD contains interior right angle C. AB equals 12, BC equals

3, CD equals 4 and AD equals 13. What is the area of the figure ABCD?

3

C B

4 12

D 13 A

Note: Figure not drawn to scale.

[Editorial note: If it is too difficult to draw figure, actual figure need not be drawn]

(A) 36 (B) 108 (C)156 (D) 1,872 (E) It cannot be determined

New Shortest SAT test

How did you score on this test?

CN means question is related to Current SAT or New SAT-total of 11 questions of CN

type

N means question is related only to New SAT- total 9 questions of N type

C means question is related only to Current SAT-total of 10 questions of C type

If you get more questions of the C type right than the N type right, you should take the

Current SAT-if you get more questions of the N type right than the C type , you should

take the New SAT. Either way if you learn the strategies for each you should do well on

both tests.

Correct Score Increase if you learn strategies shown in answers for either test

Answers

Reading

1. D -CN 50

2. A -CN 50

3. D -N 50

4. B -N 40

5. B -CN 40

6.A -C 70

7.E -C 80

Note: (1) Questions 3,4 are applicable only to the New SAT/ACT. (2) Questions 6,7 are applicable only to the Current SAT.

(3) Questions 1,2,5 are applicable to both the Current and New SAT/ACT. If you got most of the questions in (1) right and most of the questions in (2) wrong, you should take the New SAT/ACT. If you got most of the questions in (2) right and most of the questions in (1) wrong, you should take the Current SAT.

Writing and Language

1. A -CN 30

2. B -N 30

3. B -N 30

4. A -CN 40

5. A -N 30

6. A -C 50

7. C -C 60

8. E -C 60

9. D -C 40 Note: (1) Questions 2,3,5 are applicable only to the New SAT/ACT. (2) Questions 6,7,8,9 are applicable only to the Current SAT. (3) Questions 1,4 are applicable to both the Current and New SAT/ACT. If you got most of the questions in (1) right and most of the questions in (2) wrong, you should take the New SAT/ACT. If you got most of the questions in (2) right and most of the questions in (1) wrong, you should take the Current SAT.

Math

1. D -N 60,30

2. Anything less than 15/4 or greater than +3 -CN 30

2. D for Alternate Question 2 -CN 30

3. D -N 70

4. A -CN 60,20

5. A -CN 60,50

6. C -CN 70,30

7. B -CN 20

8. B -N 60

9. B -CN 50

10.A -N 70

11.B -C 80

12. 41 -C 50

13. 9 -C 40

14. A C 50 Note: (1) Questions 1,3,8,10 are applicable only to the New SAT/ACT. (2) Questions 11,12,13,14 are applicable only to the Current SAT. (3) Questions 2,4,5,6,7,9 are applicable to both the Current and New SAT/ACT.

If you got most of the questions in (1) right and most of the questions in (2) wrong, you should take the New SAT/ACT. If you got most of the questions in (2) right and most of the questions in (1) wrong, you should take the Current SAT.

Heres the table to calculate your score and thus your approximate actual NEW SAT score.

Reading and Writing (Reading Questions 1-5; Writing- Questions 1-5) Questions New SAT Score

Right

10. 800 9 . 780 8 . 700 7. 630 6. 540 5. 500 4. 430 3. 320 2. 250 1. 210

Math (Questions 1-10)

Questions New SAT Score

Right

10.800 9 .780 8 . 700 7. 650 6. 550 5. 500 4. 450 3. 350 2. 250 1. 220

Explanatory Answers with Important Strategies

Reading Test Answers

1. Choice D is correct. See lines where it states that many people in our generation were not exposed to classical music. Dont be lured into the distractor Choice A, even though there was mention of sales.

Strategy1: Determine the Type of Question: Main Idea, Detecting

Details,Inference or Tone/Mood. Strategy 2: Underline Key Parts of Passage.

2. Choice A is correct. See lines where it mentions that the emotional feeling gradually wears out in time.

Strategy1: Determine the Type of Question: Main Idea, Detecting


3. Choice D is correct. The phrase, although many critics believe it is because the music elicits a particular emotional feeling that gradually becomes worn out in

time. Strategy1: Determine the Type of Question: Main Idea, Detecting


4. Choice B is correct. You can see that the difference (gap) between the number of classical music lovers and non-classical music lovers gets greater as time goes on.

Choice A is incorrect: The listeners of non-classical music was not steadily

declining. Choice C is incorrect: The number of listeners of classical music was

always less than the listeners of non-classical music. Choice D is incorrect: It

seems that the number of classical music lovers is diminishing in time while the

number of non-classical music lovers is increasing or remaining steady.

Strategy: Determine the Type of Question: Main Idea, Detecting

Details,Inference or Tone/Mood. Strategy.

5. Choice B is correct. Since the next sentence after the word evergreen qualifies that enjoyment lasts only for a short time, lasting would be an appropriate definition of evergreen in this context. Be careful of the distractor choice colorful. Strategy: Get meanings of words using context method.

6. Choice A is correct. Use SENTENCE COMPLETION STRATEGY : Watch for

KEY words--words that signal contrast, support or opposition.--Although signals

contrast--the blanks should be opposites.

7. Choice E is correct. Use SENTENCE COMPLETION STRATEGY : Watch for

KEY words--words that signal contrast, support or opposition."In spite of" shows an

"opposite" situation. Look for opposites in the choices.

Writing and Language Test Answers

1. Choice A is correct. In a passage, we start generally, then discuss specifics. Choice B is incorrect. We are discussing the sea, not the Pacific Coastline. Choice

C is incorrect. There is no direct connection between this sentence and the first

sentence in the passage. Choice D is incorrect. Plants are discussed later in the

passage, so the first sentence about plants would not be appropriate here. Strategy: Know how to connect sentences in a passage.

2. Choice B is correct. We are talking about something away from, or off, the Pacific Coast. Choice A is incorrect. We are not talking about

something on the Coastwe are talking about something in the water off the coast. Choice C is incorrect. We are not contrasting the coast and the

sea, so we do not use the word apart. Choice D is incorrect. Not from does not make sense here, since we eventually talk about the sea.

Strategy: Know how to use appropriate words to describe something.

3. Choice B is correct. We need a new sentence here, because something new

is discussed. Choice A is incorrect. The dash is not appropriate since the

part is not directly linked to the preceding parta new idea is discussed. Choice C is incorrect. The semicolon is not appropriate since a new idea is

discussed here. Choice D is incorrect. The comma would create a run-on

sentence. Strategy: Know how to use punctuation to link parts of the passage.

4. Choice A is correct. We need to maintain a connection herewhen it says the fish become toxic, we need another sentence immediately following this

one explaining why they become toxic. Choice B is incorrect. There is not

too much of a leap from toxicity to death. Choice C is incorrect. This may be so, but inserting the sentence would destroy a connection, as

described before. Choice D is incorrect. This is not true since a connection

would be destroyed between the last sentence and the one preceding

initially. Strategy: Know when and how to make connections by using another sentence.

5. Choice A is correct. Since we mean more than one, we use their. Choice B

is incorrect. Theyre means they are, which does not make sense. Choice C is incorrect. Since we are referring to more than one, we do not use its.

Choice D is incorrect. Its means It is, which does not make sense. Strategy: Know what to use when we are talking about quantity.

WRITING

6. A. If any signer of the Constitution were to return to life The verb in the if clause of a present contrary-to-fact conditional statement must have a past subjunctive form(were).

7. C. Avoid squinting constructions-that is, modifiers that are so placed that the reader

cannot tell whether they are modifying the words immediately preceding the construction

or the words immediately following the construction. The correct sentence would read,

After we were waiting in line for three hours, the tickets had, much to our disgust, been sold out when we reached the window.

That is, as the sentence initially reads, we dont know whether much to our disgust modifies After we were waiting in line for three hours or modifies the tickets had been sold out when we reached the window.

8. E. Avoid improper ellipses. Choices A,B,C,and D are incorrect for this reason. The

word kept must be included since the second part of the sentence uses another form of the verb (keep).

9. D. Choice A is incorrect because the possessive form of the noun (Marco) must be used to modify the gerund (wanting). Choice B is too wordy. Choice C changes the meaning of the original sentence. Choice E is incorrect for the same reason that Choice A

is incorrect. Also Choice E changes the meaning of the original sentence.

Math Test- Answers

1. Choice D is correct.

Strategy: Translate words into math.

Let the number of sections with 3 students be denoted as x and the number of sections

with 6 students denoted as y.

Then (1) 3x + 6y = 60 (the total number of students)

And (2) x + y = 18 (the number of sections)

Now use a strategy of simplifying the equations.

Simplify equation (1) by dividing both sides by 3:

(1) becomes: x + 2y = 20.

But we have (2): x + y = 18.

Now use a strategy of subtracting equations (2) from (1):

We get y = 2.

Now substitute y = 2 into equation (2) and we get x = 16.

2. Anything less than 15/4 or greater than +3.

Look at (1) -5/4 < -2p +3

Use the strategy of representing 6p 9 in a form you already have: (-2p + 3) (-3) = 6p -9

So multiply inequality (1) by (-3).

You need to use the basic skill: You reverse the inequality when you multiply by a

negative number.

So (-5/4)(-3) > (-2p + 3) (-3)

or

15/4 > 6p -9

Now look at the given -2p + 3 < - 1

Multiply this by (-3):

You again have to reverse the inequality sign and get:

(-2p +3)(-3) > (-3)(-1)

or

6p 9 > 3

So the value of 6p 9 is such that 15/4 > 6p -9 > 3

or if we use second version:


Anything less than 15/4 or greater than +3.

Look at (1) -5/4 < -2p +3

Use the strategy of representing 6p 9 in a form you already have: (-2p + 3) (-3) = 6p -9

So multiply inequality (1) by (-3).

You need to use the basic skill: You reverse the inequality when you multiply by a

negative number.

So (-5/4)(-3) > (-2p + 3) (-3)

or

15/4 > 6p -9

Now look at the given -2p + 3 < - 1

Multiply this by (-3):

You again have to reverse the inequality sign and get:

(-2p +3)(-3) > (-3)(-1)

or

6p 9 > 3

So the value of 6p 9 is such that 15/4 > 6p - 9 > 3

or 3 > 6p 9 >3

Thus one value of 6p 9 can be 3 .


Strategy: Use given information effectively.

The phrase proportionatelyin each category means that number of tennis players in Category A =

total number of tennis players

number of prizes awarded in Category A

total number of prizes

So, where x is the number of prizes awarded in Category A:

30 = x

180 54

1 = x

6 54

x = 54 = 9

6

4. Choice A is correct.

Strategy: Translate words to math.

(x - 4) is a factor of x2 ax +a means that there is another factor (x + b) of x2 ax + a such that (x 4)(x + b) = x2 ax + a.

Now use the strategy of writing (x 4)(x + b) in another form to get more information.

Multiply out:

(x 4)(x + b) = x2 4x + bx 4b which is equal to x2 ax + a.

From this we get:

-4x + bx 4b = -ax + a

Now think of the possibilities. If x = 0, then

(1) -4b = a

But if -4b = a, then

-4x + bx = -ax for all x and if x = 1, then

(2) -4 + b = -a

or

(3) b = -a + 4

Substituting b in (3) into b in (1), we get:

(4) -4(-a + 4) = a or 4a 16 = a and get 3a = 16, a = 16/3


Strategy: Translate words into math.

The ratio of BD to CD is 4:6 means BD = 4x and CD = 6x. Since the triangle is isosceles,

that is, AE = AF, thenE = F.

Also since EBD = DCF = 90, triangles BED and CDF are similar so corresponding

sides are in proportion.

Now use strategy of labeling sides.

Call ED = y. Then DF = 24 - y since EF = 24.

So since sides are in proportion, BD/CD = 4x/6x =

ED/DF= y/(24 y) 4/6 = y/(24-y)

Cross multiply: (24 y)4 = 6y 96 4y = 6y

96 = 10y

96/10 = y

48/5 = y

6. Choice C is correct.

Strategy: First get all variables on one side of the equation.

(1) 8x 2y = 6y +14 becomes (1) 8x 8y = 14

Now divide Equation (1) by 8 to make it simpler:

(1) x y = 14/8 = 7/4

Also divide the second equation by 4 to make it simpler:

(2) 4x + 16y = 9 becomes

(2) x + 4y = 9/4

Now use the strategy of subtracting equations.

Subtract Equation (1) from Equation (2):

x + 4y = 9/4

- (x y = 7/4) x x + 4y + y = 9/4 7/4

We get: 5y = 9/4 7/4 = 2/4 = 1/2 y = 1/10

Now substitute y = 1/10 into Equation (1):

x = 1/10 = 7/4

x = 7/4 +1/10 = 74/40 = 37/20

Thus, xy = 37/20 X 1/10 = 37/200

7. Choice B is correct.

Draw two intersecting circles.

Above, subtracting: all students who watch TV (14) students who watch TV and also play video games (5), we get 9.

Above, subtracting: all students who play video games (8) students who watch TV and also play video games (5), we get 3.

So the total number of students is 9 + 5 + 3 = 17.


Strategy: Translate words into mathematical expressions.

The total cost of production equals the cost of the machine ($169.99) plus the cost of the

CDs: (cost of 1 CD) X (number of CDs produced). Since we know that 1 CD costs $1.50

and were producing x CDs, the total cost is:

$169.99 + $1.50x


Use Strategy: Label sides.

Label the sides of the figure, adding variables where no number is given. You can see

that for the vertical sides of the figure:

a + 6m + b = 20m

While for the horizontal sides:

c + d + e = 15m

The perimeter equals:

b + e + 6m + d + a + c + 20m +15m

= (a + 6m + b) + (c + d + e) + 20m + 15m

= (20m) + (15m) + 20m + 15m = 70m


Use strategy: Use given information effectively.

First, find the height of the ladder on the wall. Remember a 3-4-5 right triangle. There is

also a 6-8-10 right triangle. So the height is 8 feet.

sin xO = opposite/hypotenuse = 8/10 = 4/5

Note:

Choice B: cos xO = 6/10 = 3/5

Choice C: cot xO = 6/8 = 3/4

Choice D: tan xO = 8/6 = 4/3

11. Choice B is correct. Use STRATEGY : You won't rack your brains if you know how

to translate from words to math. Translate is to equals, Sarah to S, John to J, Six years

ago to minus 6, four times as old as John was then to "4 times the quantity (J minus 6)".

12. Answer:41. Use STRATEGY: Remember and Use Classic Forms, like "x squared

plus 2 times x times y plus y squared is equal to the square of the quantity x plus y". Try

to relate the form of "x squared plus y squared" to the equations given-- you can do this

by using the "Classic Forms," above. Square both sides of the equation x + y = 7, then

use the fact that xy = 4.

13. Answer:9. STRATEGY: When you have two or more equations, it is sometimes

easier to just add them to get a result. Add equations, then divide by 3.

14. Choice A is correct. Use STRATEGY : Draw Lines: The best way to do the

problem is to draw or extend lines to get more information. Draw BD, then find length

BD. BD = 5 because triangle BCD is a 3-4-5 right triangle. Now triangle BDA is also a

right triangle because a 5-12-13 triangle is a right triangle. We can then find the area of

triangle BCD to be 3 X 4/2 = 6 and the area of triangle BDA to be 5 X 12 /2 = 30. So the

sum of these areas is the area of the figure ABCD. 36 is the answer.

Long Form of answers 11-14:

11. Correct answer: (B) Here is the best way: You won't rack your brains if you know how to translate from words to math.

STRATEGY: Translate words to math: Translate Sarah to S, John to J, is to =, Six years ago to - 6, four times as old as John was then to 4 (J - 6). Then Sarah is twice as

old as John translates to

(1) S = 2J. And Six years ago, Sarah was 4 times as old as John was then translates to

(2) S 6 = 4(J- 6) , the reason for J- 6 because John was J 6, six years ago. Substituting S = 2J in Equation 1, in Equation 2, we get

2J 6 = 4(J - 6). Then we get:

2J - 6 = 4J 24. And then:

- 6 + 24 = 4J 2J = 2J. So 2J = 18 and J = 9.

12. Correct answer: 41 I hope that you didnt try to solve for both x and y. You are not asked to do thatyou are asked to find the value of x2 + y2 so try to manipulate the equations to get that quantity.

Use STRATEGY: Remember and Use Classic Forms, like

(x + y)2 = x2 + 2xy + y2.

We have (1) (x + y)2 = x2 + 2xy + y2 = 7 X 7 = 49 and since

xy = 4, we get

2xy = 8.

Substituting 2xy = 8 in Equation (1), we get

(x + y)2 = x2 + 2xy + y2 = x2 + 8 + y2 = 49. Subtracting 8 from both sides of the last

equation, we get,

x2 + y2 = 41.

13. Correct answer: 9 I hope you didnt go through the tedium of substitution and solving for q, p, and y. You are not asked for the values of each of the variables. Use STRATEGY : When dealing

with equations, you can add, subtract, multiply, or divide. When you have two or more equations, it is sometimes easier to just add or subtract them

to get a result. Add equations, then divide by 3.

y + 2q = 15

q + 2p = 5

__+_ p + 2y = 7___

3q + 3p + 3y = 27

Factor 3: 3(q + p + y) =27; q + p + y = 9.

14. Correct answer:(A) Use STRATEGY : Draw Lines: The best way to do the problem is to draw or extend

lines to get more information. Draw BD, then find length BD. BD = 5 because triangle

BCD is a 3-4-5 right triangle. Now triangle BDA is also a right triangle because a 5-12-

13 triangle is a right triangle. We can then find the area of triangle BCD to be 3 X 4/2 = 6

and the area of triangle BDA to be 5 X 12 /2 = 30. So the sum of these areas is the area of

the figure ABCD. 36 is the answer.

Note that the complete set of strategies can be found in Dr. Grubers books.

Documents

The Gary Gruber SAT test: Which one is best for you?