SAT Practice Questions

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Mathematics

Directions:
Each of the following problems contains five possible answer choices. Solve the problem and choose the answer that is the best solution to the problem.

Example:

1.   What is x?
(A) 3b+2y+8y
(B) 3b+2y+8y
(C) 24by+16y2-2b
(D) 6by+4y2-½b
(E)

2.   The area of a circle with a radius of 3 units is what percentage of a circle with a radius of 6 units?
(A) 15%
(B) 25% 
(C) 45% 
(D) 50%
(E) 75%

 

3.   If , What is the value of the following expression?
(A) -13
(B) -13/3
(C) -13/2
(D) 13/3
(E) 13/2
Critical Reading

Directions:
Read the passage below carefully and answer the questions that follow. For each question, use the information provided in the passage to select the best possible answer.

The following passage is an excerpt from an essay on colonial science and mathematics. The author argues that although Britain was an important centre of scientific and mathematical learning in the nineteenth-century, colonial mathematicians – including those in Australia, Canada and India – developed their own approaches to mathematics, which distinguished them from mathematicians in Britain.

Example:

Baber and Bishop are two authors who have argued that British mathematics in the colonial era was synthesized into local cultures in ways that have not been fully analyzed from an historical perspective. Mathematical cultures arose in periphery locations that were distinct from the centres of mathematical learning in Britain and at Cambridge University specifically. Indigenous knowledge existed as the output of local users who navigated through varied conceptual terrains. The case study of the Cambridge-trained mathematician, John Michell (1863- 1940), founder of the Mathematical Association of Victoria and reformer of mathematics at the University of Melbourne, is a good example. Although Michell was trained in Cambridge, his efforts to build an Australian-focused curriculum forced a revamping of British mathematics in Australia, resulting in a unique blend of alternative pedagogical styles. Another case study is that of the superintendent of education in Nova Scotia, William Dawson, who was hired as principal of McGill to modify the university’s curriculum. Modernization of the Canadian railway resulted in a focus on engineering sciences in both Upper and Lower Canada. The rise of engineering mathematics at McGill University allowed users of British textbooks to develop a uniquely Canadian (that is, “Anglophone”) mathematical culture. A third case is that of the Cambridge-trained Indian reformer, Sir Syed Ahmed Khan, a jurist and employee of the British East India Company. Concerned that a lack of engagement with scientific developments in Europe hindered Indian Muslims, Syed founded the Scientific Society of Aligarh in 1864. He aimed to build a “Cambridge of India” by establishing the Muhammadan Anglo-Oriental College in 1875 with a curriculum based on mathematical physics and experimental science. Syed relied on Cambridge mathematical textbooks, but the mathematics taught at his college indicated a local culture in Muslim mathematics had developed as indigenous users reapplied standardized British mathematical tools to meet their local needs.

4.   The author would most likely disagree with which of the following claims?
(A) Mathematics in the colonies was a direct replication of British mathematics.
(B) Mathematicians in the colonies sought to apply British mathematics to their local needs.
(C) Mathematics in the colonies differed from mathematics as practiced in Britain.
(D) Historical accounts of colonial science have failed to fully understand the relationship between mathematical producers in Britain and mathematicians in the colonies.
(E) Examples of colonial mathematics demonstrate that mathematicians in Australia, Canada and India developed unique approaches to mathematics.

5.   The phrase “indigenous users” in the last phrase of the passage refers to
(A) British mathematicians
(B) Australian mathematicians
(C) Canadian mathematicians
(D) Indian mathematicians
(E) Mathematicians in general

6.   The author’s main point is that
(A) British mathematicians were world leaders in mathematical research in the nineteenth-century.
(B) The spread of colonial science is a poorly understood phenomenon.
(C) Cambridge played a significant role in shaping British mathematics.
(D) Mathematics in Australia, Canada and India was taught in a way that differed from the way in which it was taught throughout the rest of the world.
(E) Although Britain was an influential centre of learning, colonial mathematicians developed mathematical curricula that responded to their local needs.

Writing

Directions:
In each of the following questions, you are presented with a sentence that may or may not contain a grammatical or syntactical error. Spot the error which, if corrected, would render the sentence grammatically correct or choose answer choice (E) if there is no error in the sentence.

7.   None of us are (A) going to the opera tonight as (B) we (C) couldn’t find tickets that were within (D) our price range. No error. (E)
(A)
(B)
(C)
(D)
(E)

8.   Paulina studied (A) advanced physics, integral (B) calculus and (C) biology class (D) for her Grade 12 exams. No error. (E)
(A)
(B)
(C)
(D)
(E)

9.   Neither his aunt, who (A) was an engineer, or (B) his mother, who was an astrophysicist, encouraged him to abandon his dreams of being (C) a ballet dancer to pursue (D) a scientific career. No error. (E)
(A)
(B)
(C)
(D)
(E)

 
Essay

Directions:
Read the following topic carefully. Take a few minutes to think about the topic and to organize your thoughts.  You have 25 minutes to write an essay that responds to the quotation below.

Topic:
"When one door of happiness closes, another opens; but often we look so long at the closed door that we do not see the one which has been opened for us." -- Helen Keller.

Assignment:
Do you agree or disagree with the statement above? Write an essay to support your position. Use examples from literature, history, science, politics or personal experience to justify your view.

 

 

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