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SAT数学练习题—Problem Solving (1)

2016-02-25 11:23:13来源：网络

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SAT数学考试是考试中很重要的一部分，新东方在线为大家准备了SAT数学练习题—Problem Solving ，希望可以帮助到大家。

　　Question #1: If a · b = 18 and a / b = 2, a > 0, b > 0 then:

　　(a) a = 18 and b = 1

　　(b) a = 9 and b = 2

　　(d) a = 6 and b = 3

　　(e) a = 6 and b = 6

　　Answer: a / b = 2

　　a = 2·b.

　　a·b = (2· b)· b

　　a·b = 2· b 2.

　　2· b 2 = 18

　　b 2 = 9,

　　b = 3 because b > 0,

　　a = 2· b

　　a = 6.

　　Question #2: The ratio of the radii of two circles is r1/r2 = 6. What is the ratio of the perimeters P1/P2 and the ratio of the areas of the two circles A1/A2?

　　(a) perimeter ratio = 1/6, area ratio = 36

　　(b) perimeter ratio = 36, area ratio = 6

　　(d) perimeter ratio = 1/8, area ratio = 8

　　(e) perimeter ratio = 1/6, area ratio = 6

　　Answer: r1 / r2 = 6;

　　Perimeter1 / Perimeter2 = (2· ¶· r1)/(2· ¶· r2) = r1/ r2 = 6

　　Area1 / Area2 = (¶· r12)/ (¶· r22) = r12 / r22 = 36

　　Question #3: What value x satisfies both 1/x < 1/7 and x 2 > 16?

　　(a) x = 1

　　(b) x = -5

　　(d) x = 7

　　(e) x = 6

　　Answer: x 2> 16 means (x - 4)· (x + 4) > 0.

　　x can be lower than -4 or higher than 4.

　　1/x < 1/7; (7-x) / 7x < 0.

　　x can be lower than 0 or higher than 7.

　　In conclusion, x can be lower than -4 or higher than 7. The only correct answer is x = -5.

　　Question #4: A lottery sells 1000 tickets and there is only one winning number. 200 New Jersey residents buy 2 tickets each, 300 New York

　　residents buy 1 ticket each and the rest are sold in Connecticut. What is the probability that the wining ticket was bought in New Jersey?

　　(a) 3/5

　　(b) 1/2

　　(d) 1/5

　　(e) 4/5

　　Answer: There are 400 tickets sold in New Jersey out of a total of 1000, so the probability will be 400/1000 = 2/5.

　　Question #5: Celsius degrees can be transformed in Fahrenheit degrees by using the formula : °C=(5/9)· (°F-32). What is x, if x degrees Celsius is equal to x degrees Fahrenheit?

　　(a) 40

　　(b) -40

　　(d) 20

　　(e) -30

　　Answer: x = (5/9)· (x - 32).

　　9·x = 5·(x - 32).

　　In conclusion, x = -40C = -40F

　　Question #6: In the (x,y) plane, what is the equation of the line that passes through the points (0,5) and (4,0)?

　　(a) y = (5/4) · x + 4

　　(b) y = (4/5) · x - 4

　　(d) y = -(5/4) · x + 5

　　(e) y = (5/4) · x + 5

　　Answer: The equation of a line is y = m · x + n

　　First point, x = 0, y = 5, results in 5 = n

　　Second point: x = 4, y = 0, means 0 = m · 4 + n, or m = -n/4 or m= -5/4.

　　In conclusion, y = -(5/4) · x + 5 is the correct answer.

　　Question #7: A square with the side equal to square root of 2 is inscribed in a circle. What is the area outside the square that is inside the circle?

　　(a) ¶ + 1

　　(b) ¶ - 1

　　(d) ¶

　　(e) ¶ + 2

　　Answer: The diagonal of the square is √2 · √2 = (√ 2)2 = 2. This is also the diameter of the circle.

　　The area outside the square and inside the circle is:

　　Areacircle - Areasquare = ¶ · 22/4 - 2 = ¶ - 2

　　Question #8: What is the value of (x + 2y) 2 if x 2 + 4 · y 2 = 2 and x · y = 3

　　(a) 13

　　(b) 14

　　(d) 18

　　(e) 22

　　Answer: (x + 2y) 2 = x 2 + 4 · y 2 + 4 · x · y = 2 + 12 = 14

　　Question #9: What is the value of the median of an equilateral triangle with all sides equal to 5?

　　(a) (5/2) · √3

　　(b) 5 · √3

　　(d) 5/2

　　(e) 5

　　Answer: The median divides the equilateral triangle in two right triangles. Conform to the Pythagorean theorem, wherein the sum of the squares of the two legs is equal to the square of the hypotenuse,

　　m2 + (5/2)2= 52

　　m2 = 52 - (5/2)2 = 52 - 52/4 = (3/4) · 52

　　m = (5/2) · √3.

　　Question #10: A parameter is measured during a scientific experiment and the results are -12, 4, -8, 10, 2, 2, 0, -4 and 2. The median and the average of these numbers are:

　　(a) median = 0, average = -4/9

　　(b) median = 0, average = 4/9

　　(d) median = 2, average = 4/9

　　(e) median = 2, average = 2/9

　　Answer: You must arrange the numbers in order: -12, -8, -4, 0, 2, 2, 2, 4, and 10.

　　The median will be number in the middle of the row, that is 2.

　　The average will be (-12-8-4+0+2+2+2+4+10)/9 = -4/9.

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