SAT II Math IIC Practice Questions

  1. Vectors u and v are given by u = (2 , 0) and v = (-3 , 1). What is the length of vector w given by w = –u – 2v?

    A) 10
    B) 6
    C) √26
    D) 2√5
    E) 2

  1. What is the smallest distance between the point(-2,-2) and a point on the circumference of the circle given by

(x – 1)2 + (y – 2)2 = 4?

A) 3
B) 4
C) 5
D) 6
E) 7

  1. What is the equation of the horizontal asymptote of function

f(x) = 2/(x + 2) – (x + 3)/(x + 4)?

A) – 4
B) – 2
C) – 1
D) 0
E) 1

  1. The lines with equations x + 3y = 2 and -2x + ky = 5 are perpendicular for k =

    A) -3
    B) -2
    C) -1
    D) 0
    E) 2/3

  1. If f(x) = (x – 1)2 and g(x) = √x, then (g o f)(x) =

    A) |x – 1|
    B) x – 1
    C) 1 – x
    D) √x(x – 1)2
    E) (√x – 1)2

  1. The domain of f(x) = √(4 – x2) / √(x2 – 1) is given by the interval

    A) (-2 , 2)
    B) (-1 , 2)
    C) (-2 , -1) U (1 , 2)
    D) (-2 , 2) U (-1 , 1)
    E) [-2 , -1) U (1 , 2]

  1. The area of the circle x2 + y2 – 8y – 48 = 0 is

    A) 96Pi
    B) 64Pi
    C) 48Pi
    D) 20Pi
    E) Pi


SAT Sentence Completion – Practice Questions

1. Biological clocks are of such ____ adaptive value to living organisms, that we would expect most organisms to ____ them.

A. clear – avoid
B. meager – evolve
C. significant – eschew
D. obvious – possess
E. ambivalent – develop

2. The peasants were the least ____ of all people, bound by tradition and ____ by superstitions.

A. free – fettered
B. enfranchised – rejected
C. enthralled – tied
D. pinioned – limited
E. conventional – encumbered

3. Many people at that time believed that spices help preserve food; however, Hall found that many marketed spices were ____ bacteria, moulds and yeasts.

A. devoid of
B. teeming with
C. improved by
D. destroyed by
E. active against

4. If there is nothing to absorb the energy of sound waves, they travel on ____ , but their intensity ____ as they travel further from their source.

A. erratically – mitigates
B. eternally – alleviates
C. forever – increases
D. steadily – stabilizes
E. indefinitely – diminishes

5. The two artists differed markedly in their temperaments; Palmer was reserved and courteous, Frazer ____ and boastful.

A. phlegmatic
B. choleric
C. constrained
D. tractable
E. stoic

6. The intellectual flexibility inherent in a multicultural nation has been ____ in classrooms where emphasis on British-American literature has not reflected the cultural ____ of our country.

A. eradicated – unanimity
B. encouraged – aspirations
C. stifled – diversity
D. thwarted – uniformity
E. inculcated – divide

7. The conclusion of his argument, while ____ , is far from ____ .

A. stimulating – interesting
B. worthwhile – valueless
C. esoteric – obscure
D. germane – relevant
E. abstruse – incomprehensible

SAT Practice Questions for Critical Reading

The ground is full of seeds that cannot rise into seedlings;
the seedlings rob one another of air, light and water, the
strongest robber winning the day, and extinguishing his
competitors. Year after year, the wild animals with which
5 man never interferes are, on the average, neither more nor
less numerous than they were; and yet we know that the
annual produce of every pair is from one to perhaps a
million young; so that it is mathematically certain that,
on the average, as many are killed by natural causes as
10 are born every year, and those only escape which happen
to be a little better fitted to resist destruction than
those which die. The individuals of a species are like
the crew of a foundered ship, and none but good swimmers
have a chance of reaching the land.

Adapted from an essay by T H Huxley

1. The “robber” in the first sentence is most like which of the following mentioned in the paragraph

A. wild animals
B. produce of every pair
C. individuals of a species
D. crew of a foundered ship
E. good swimmers

2. The main point the author conveys is that

A. natural populations of animals in the wild increase in numbers exponentially
B. all members of a species are in violent competition with one another
C. in the struggle to survive, the fittest survive
D. members of one generation of a population are all more or less alike
E. man’s interference destroys the natural balance

Girls doing schoolwork.

Practice Tips for the SAT MATH Section – STANDARD MULTIPLE CHOICE:

1. Make sure you have read the question correctly. Be sure to select the best answer for the variable, value, or expression that is requested.
2. Learn well all of the critical definitions, formulas, and concepts that appear in common questions that are covered in the SAT syllabus.
3. Remember to use the test booklet for scratch work, as well as for marking up any diagrams/graphs.
4. Complete the early questions soon. They are the easier ones.
5. Always prefer doing short cuts and tricks as compared to long and detailed calculations. Time consuming questions can be avoided for the time being and dealt with later.
6. When a question contains a weird symbol, just substitute the accompanying definition when figuring out the best answer choice.

in the library - pretty, female student with laptop and books wo

Practice Tips for the SAT MATH Section — STUDENT PRODUCED RESPONSE (GRID):

1. You can always safely guess if you can’t figure it out. There is no penalty for wrong answers in this section.
2. This section’s answers will not contain negative numbers. So if your answer comes to a negative, you should know its wrong. You must repeat it then.
3. You may begin to enter a short answer in any column. For instance, .6 can be entered in columns 1-2, or 2-3, or 3-4.
4. If an answer is a repeating decimal (like .33333333), just enter as many decimals as will fit in the grid (.333).
6. You may enter an equivalent decimal for a fraction as your answer, but why waste the time evaluating the fraction?
7. Do not try to enter mixed numbers. For example, if your answer is 3 1/2, enter it as 3.5 or 7/2.

SAT Practice Questions in Math – Grid In Type

1. A rectangular box is made by putting together pieces of the dimensions shown above. What is the volume of the resulting box?
2. x² – y² = 9, and x – y = 1. What is the value of x + y ?
3. Sam’s test scores are History 76, Geography 74, Math 92, English 81 and Chemistry 80. If the average (arithmetic mean) score is M, and the median score is m, what is the value of M-m ?
4. A tree of height 50 feet casts a shadow 80 feet long at a certain time of day. A second tree near to the first casts a shadow 100 feet long at the same time. How many feet taller is the second tree than the first?
5. If p² – q² = 12, and p + q = 4
What is the value of p ?
6. x + y = 15, y + z = 25, and x + z = 20
What is the average (arithmetic mean) of x,y and z ?
7. A field covers 149.8 square yards. A farmer harvests the crop from the field in three days. The first day he covers 2/7 of the area. The next day he covers twice as much. How many square yards does he cover on the last day?

SAT Grammar Questions

There are 49 grammar questions on the SAT writing section. Grammar accounts for over two thirds of the marks on this section. Questions are of 3 types:

Identification of sentence errors
Sentence correction (improving sentences)
Editing in context (improving paragraphs)
Identification of sentence errors

1. In suchA areas as sports, ranking of individual performance isB relatively well accepted sinceC the parameters on which the rating areD based are generally objective. No errorE.

2. Determination ofA the long-term effects ofB aerosols on the upper atmosphere isC currently one of the more challengingD problems in climate research. No errorE.
Sentence correction
1. Bombast is when high sounding words for effect, not suitability, are used.

A. is when high sounding words for effect, not suitability, are used.
B. is the use of high-sounding words for effect rather than for suitability.
C. is where high-sounding words are used for effect not suitability.
D. is the using of high-sounding words for effect only.
E. is when you use high-sounding words for effect rather than for suitability.

2. I would like to thank whoever it was that wrote that piece of music: it has given me so much pleasure.

A. I would like to thank whoever it was that wrote that piece of music:
B. I would like to thank whomever it was that has written that piece of music:
C. I would like to thank whomever it might be that wrote that piece of music:
D. Whoever it was that wrote that piece of music, I would like to thank because
E. I would like to thank whoever it was that wrote that piece of music



Cheap SAT Tricks

There are some tricks for those who are desparate for the last minute prep tips. Only two Cases of Desperation on Improving Sentences questions merit resorting to Cheap Tricks:
1.You can’t eliminate even one answer choice.
2.You’ve eliminated all but two answer choices and find yourself wasting time agonizing over which answer choice is correct.
Here’s a warning: Don’t apply these techniques blindly, they could cause more harm than good. Cheap Tricks will help you get a higher percentage of questions right. They won’t help you get every question right.
Here are they:
Go with the shortest answer.
We’ll make this quick. When you find yourself staring blankly at two or three answer choices, go with the shorter answer choice. The SAT likes to keep the right answers concise.
Cut answer choices that change the meaning of the sentence.
Be suspicious of answer choices that tweak the meaning of the sentence.
Cut answer choices that begin with words ending in -ing.
More often than not, gerunds (words ending in –ing) do not appear in correct answer choices.
Get your A in gear.
It’s worth reiterating that about one-fifth of the answers on this section will be A—“no error.”

SAT GRAMMAR – Editing in context

Questions 1-6 refer to the following passage, which is a draft of an essay:
(1)I recently revisited the city which I was born in, which is a place well known for a castle built on a rock overlooking the surrounding plains, and even better known for a legendary figure who robbed the rich to give to the poor. (2)As I toured the castle and its museum, visited the town center, and roamed around old haunts, I reflected on how the buildings that people of different eras build reflect their central preoccupations.

(3)The castle was originally built in the eleventh century, and remained important for several centuries. (4)Throughout the medieval period castles and fortified houses were built. (5)The powerful landowners surveyed and dominated the surrounding lands, the source of their wealth and prestige.

(6)Once the industrial era began, castles were sidelined. (7)The merchants and factory owners built town halls, churches, factories and imposing office buildings. (7)The town center reflects this era. (8)An imposing town hall, complete with massive pillars and monumental lions, overlooks the town square. (9)The square is surrounded by equally massive blocks of shops, banks and offices, built to reflect the power of trade in the heyday of the British Empire.

(10)Most people who enter the city today never visit the castle or the old market square, they head for the two shopping malls situated at either end of the city center. (11)Here the visitor can shop to their hearts content in an environment of glass and polished chrome. (12)Modern man is no longer a warrior defending his land, or a builder of churches, or a governor of people: he is primarily a consumer. (13)The buildings our generation leaves to posterity will reflect our predominant interest – shopping.

1. The author’s approach to the topic can best be described as

A. rhetorical
B. a reminiscence
C. a specific example to illustrate a general point
D. personal narrative
E. several examples used to contradict a viewpoint

2. The sentence (or sentences) which most clearly expresses the author’s primary purpose is

A. (1)
B. (2)
C. (12)
D. (13)
E. (1) and (13)

3. Which is the best version of the underlined portion of sentence (1), (reproduced below)?
I recently revisited the city which I was born in, which is a place well known for a castle built on a rock overlooking the surrounding plains, and even better known for a legendary figure who robbed the rich to give to the poor.
A. I recently revisited the city which I was born in, which is a place
B. I recently revisited the city in which I was born in, which is
C. I recently revisited the city in which I was born, a city
D. Recently I revisited the place which I was born in, which is a city
E. Recently I revisited the city which I was born in, which is

The SAT Reasoning Test Syllabus

The reasoning syllabus of SAT exam covers three sections, namely Writing, Maths, and Reading Comprehension. There are 171 questions in the test. The following table lists the section-wise breakup of each topic.

Subject Type of Question with number Total Number of Questions
Reading: 70 minutes Extended Reasoning: 36-40 67
Literal Comprehension: 4-6
Vocabulary in Context: 4-6
Sentence Completions: 19
Maths: 70 minutes Number and Operations: 11-14 54
Algebra and Functions: 19-22
Geometry and Measurement: 14-16
Data Analysis, Statistics and Probability: 5-8
Writing: 60 minutes Essay: 1 50
Improving Sentences: 25
Identifying Sentence Errors: 18
Improving Paragraphs: 6

As is evident, more than two-thirds of the syllabus of SAT exam comprises of English and vocabulary. Thus, it is important that you do not neglect these areas. All sections are equally important and you need to make sure that you pace yourself well during the test in order to complete the paper. Remember that the SAT reasoning test carries negative marking; that is, you lose 1/4th marks for an incorrect response. You do not get points for unanswered questions.