SAT数学模拟练习题（7）

　　SAT数学模拟练习题（7）

　　6. What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?

　　A. 3

　　B. √31

　　C. √41

　　D. 7

　　E. 9

　　Correct Answer: C

　　解析:

　　Sketch a diagram and calculate the distance (hypotenuse of a right triangle) using Pythagoras theorem.

　　Vertical height of triangle = 5 ; horizontal side = 4 ; hypotenuse = √(25 + 16) = √41

　　7. n is an integer chosen at random from the set

　　{5, 7, 9, 11 }

　　p is chosen at random from the set

　　{2, 6, 10, 14, 18}

　　What is the probability that n + p = 23 ?

　　A. 0.1

　　B. 0.2

　　C. 0.25

　　D. 0.3

　　E. 0.4

　　Correct Answer: A

　　解析:

　　Each of the integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs. Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14). This means that the probability of getting a sum of 23 is 2/20 = 1/10

　　8. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?

　　A. 0.75D

　　B. 0.76D

　　C. 0.765D

　　D. 0.775D

　　E. 0.805D

　　Correct Answer: C

　　解析:

　　If the price is reduced by 15 %, then the new price will be 0.85D. If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D

　　9. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?

　　A. 2

　　B. 2√2

　　C. 3

　　D. √10

　　E. √20

　　Correct Answer: E

　　解析:

　　The longest line segment that can be drawn without passing through any dots other than those at the beginning and end of the segment, such a line could go from the middle dot in the top row to either the bottom left or right dot. In any case the segment will be the hypotenuse of a right triangle with sides 2 and 4. Using Pythagoras theorem the hypotenuse will be √(2 2 + 4 2 ) = √20

　　10. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?

　　A. 9

　　B. 10

　　C. 11

　　D. 12

　　E. 13

　　Correct Answer: D

　　解析:

　　If the radius is 7, the circumference = 14π. The length of the arc is 100/360 of the circumference. Taking π as 22/7 we get. (100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)