Preliminary SAT/
National Merit Scholarship Qualifying Test
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Time—25minutes
20 Questions
(1—20)
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Directions:For this section ,solve each problem and decide which is the best of choice given. Fill in the corresponding oval on the answer sheet. You may use any available space for scratch work.
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The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of the triangle is 180.
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1.What is the sum of"(x=√x-1)" and (x-1)² when x=5?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 32
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2.In the diagram above,circle T represent the set all multiple of 10,circle N represent the set of all negative numbers,and circle O represent the set of all odd integers. Which of the following numbers is in the set that the shaded region represents?
(A) -20
(B) -18
(C) -11
(D) 10
(E) 13
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3.If 3abc=24 and ab=4,then c=?
(A) 2
(B) 4
(C) 20/3
(D) 12
(E) 32
4.If the figure above,point p is on line l. What is the value of x?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
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5.Both x=3 and x=2 are solutions for which of the following questions?
Ⅰ.(x+3)(x+2)=0
Ⅱ.(x-3)(x-2)=0
Ⅲ.2x=6
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I ,II,and III
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6.The graph above shows the results of a survey in which high school students were asked how many meals they typically eat per day. If 900 students responded to the survey,how many of them reported that they typically eat two meals per day?
(A) 252
(B) 162
(C) 135
(D) 123
(E) 117
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7.If 10<3t+7<13,which of the following could be a value of t?
(A) -2
(B) 0
(C) 1/2
(D) 1
(E) 3/2
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8.The length of one side of the square above is10.What is the value of x?
(A) 5√2
(B) 10
(C) 20√2
(D) 10√3
(E) 20
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9.Box A contains 142 marbles,box B contains 152 marbles,and box C contains 136 marbles.Marbles are to be transferred only from box B to box C. What is the least number of marbles that must be transferred so that box C will contain more marbles then each of the other two boxes?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
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10.In the xy-plane above,if the area of the shaded semicircular region is 8π,what is the value of t?
(A) 1
(B) 2
(C) 4
(D) 8
(E) 16
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11.T The members of a school club are ordering T-shirts. There is one-time charge of $150 for artwork on the T-shirts and a $10 charge for each T-shirt ordered. If x represent the number of T-shirts ordered. Which of the following represents the total cost,in dollars,per T-shirt?
(A)10+150x
(B)x+15
(C)10x+150x
(D)(10+150x)/x
(E)(10x+150)/x
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12. In the top row of the table above,the first term of the sequence is 24,and each term after the first is 2 more than the preceding term. In the bottom row,the first is 5 more than the preceding term. If these sequences continue indefinitely,in how many columns of the table will the terms from both sequences be equal?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
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13.If one face of rectangular solid R is known to be a rectangle that is not a square,what is the greatest number of faces of the solid that could be square?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
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14.Which of the following is the graph of a function f for which there is exactly one value of x that satisfies the equation ƒ(x)=0?
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15.The two spinners in the figure above are to be spun,and each arrow will stop inside a numbered region. It is equally likely that a spinner will stop in any one of its numbered regions. What is the probability that the sum of the numbers in the regions where the arrows stop will be at least 8?
(A) 1/24
(B) 1/12
(C) 1/8
(D) 1/4
(E) 1/3
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16.The table above shows values for the function f. What is the value of 2f(5)-f(4) ?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
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17.The three points shown on the number line above coordinates x,y and z. If x,y,and z are each integers such that xyz is a negative odd integer,which of the following must be true ?
I. x,y,and z are each odd integers.
II. x<0
III. yz>0
(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I,II ,and III
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18. Note:Figure not drawn to scale
In the circle above ,the two diameters shown intersect. If the sum of the areas of the unshaded regions is equal to the average(arithmetic mean) of the areas of the shaded regions,what is the value of x ?
(A) 120
(B) 90
(C) 60
(D) 45
(E) 30
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19.How many positive integers less than 1,000 do not have 7 as any digit ?
(A) 700
(B) 728
(C) 736
(D) 770
(E) 819
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20.Points A,B,and X do not all lie on the same line. Point X is 5 units from A and 3 units from B. How many other points in the same plane as A,B,and X are also 5 units from S and 3 units from B?
(A) None
(B) One
(C) Two
(D) Three
(E) More than four
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Time—25minutes
20 Questions
(21—38)
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Directions:This section contains two types of questions.You have 25 mintues to complete both types.For the questions 21-28 ,solve each problem and decide which is the best of choice given. Fill in the corresponding oval on the answer sheet. You may use any available space for scratch work.
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21.If a²=4,a^6=?
(A) 12
(B) 16
(C) 24
(D) 32
(E) 64
22.What is the average(arithmetic mean) of the first nine positive integers?
(A) 4
(B) 4.25
(C) 4.5
(D) 4.75
(E) 5
23.If the xy-coordinate system above,AB is one side of a square. Of the following,which could be the coordinate of a vertex of this square?
(A) (3,-1)
(B) (3,10)
(C) (6,7)
(D) (7,2)
(E) (7,10)
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24.What is the smallest integer whose square root is greater than 2?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
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25. In ABC above,AB=BC. What is the value of y?
(A) 40
(B) 55
(C) 65
(D) 70
(E) 90
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26.If there are m minutes in h hours,what is m in terms of h?
(A) 60/h
(B) h/60
(C) 60+h
(D) 60h
(E) 3,600h
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27.The lengths of the three sides of a triangle are a,b,and c. Where a≦b≦c. If a,b,and c are integers and the perimeter of the triangle is 8,what is the greatest possible value of b ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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For all integers x and y that are greater
than 1,xy>x+y.
28. Of the following values for x and y,which shows that the statement above is not true?
(A) x=0,y=2
(B) x=1,y=2
(C) x=2,y=2
(D) x=3,y=1
(E) x=4,y=3
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Each of the remaining 10 questions requires you to solve the problem and enter your answer by marking the ovals in the special grid,as shown in the example below. You may use any available space for scratch work.
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Note: You may start your answer in any column,space permitting. Column not needed should be left blank.
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Decimal Answer: If you obtain a decimal answer with more digits than the grid can accommodate,it may be either rounded of truncated,but it must fill the entire grid. For example,if you obtain an answer such as 0.6666……,you should record your result as .666 or. 667.A less accurate value such as. 66 or. 67 will be scored as incorrect.
Acceptable ways to grid (2/3)are:
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29.In a fund-raiser for a chairty,100 people registered for a 5-mile run. The charity earned $25 for each person who registered and an additional $50 for each person who completed the run. If 93 of the people completed the run,what was the total amount,in dollars,earned for the chairty?(Disregard the $ sign when grinding your answer.)
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30. If 0.607=(6.07)10-n,what is the value of n?
31.If 1/4 of x is 100 and 1/3 of y is 900,what is the value of x+y ?
32.In the figure above,ABCD and PQRS are squares with areas 36 and 16,respectively. MDQP is a rectangle with area 32.What is the area of rectangle DCLQ?
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33.The table above shows the five types of doughnuts that were sold at Wey's Cafe on a certain day. If 225 glazed doughnuts were sold,how many coconut doughnuts were sold on that day?
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34.If the figure above,AC∥GD and CE∥BF.What is the value of x ?
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35.The lockers in a school are numbered from1to1000.Joan's locker number is an even number that is divisible by both 5 and 31.What is one possible locker number that Jean could have ?
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36.If 0≤x≤5 and -5≤y≤0,what is the minimum value of 12/(Ix-yI)?
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37.The total cost of 8 hats and 5 scarves is the same as the total cost of 5 hats and 7 scarves. The cost of each scarf is d times the cost of each hat.What is the value of d ?
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38.If the xy-plane,the line with equation ax+by=1,where a and b are constants,intersects the y-axis where y=2. Whatis the value of b ?
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备注:(1)2009年10月14日(周三)的预考题。Wednesday,October14,2009。(2)供中国高中生及其家长参考。