SAT数学考试问答题练习题(十一)

2022-05-30 07:56:21

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  1. The area of a rectangle with sides x and 3x, is how many times greater than the area of a right angled isosceles triangle with side x?

  2. If $81 is to be divided among n people, where n > 1, so that each gets $x, where x is a whole number > 1, how many different values could there be for n?

  

 

  3. If the area of the triangle shown above is 108 square centimeters, what is its perimeter in centimeters?

  4. A charity organisation sells greetings cards in packs costing $10 or $2.50 each. A total of 75 packs were sold at a fair for a total of $375. How many of the $2.50 packs were sold?

  5. The length of a rectangle is 2/7 of the perimeter. What is the value of the diagonal of the rectangle if the perimeter is 14 units?

  6. A = {A, B, C, D, E, F, G}

  B = {0, 1, 2}

  C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

  The filing system in an office requires each file to have an alphanumeric code name of the form abc. A, B and C are the sets from which a,b, and c must be chosen. How many possible code names are there?

  7. A measuring cylinder is filled one third full with ethanol. A mixture of ethanol, water and propanol is used to fill the measuring flask to capacity. What fraction of the final mixture is ethanol?

  8. The equation y = 6 is graphed on the same coordinate axes as the circle with center (4,4) and radius 3.

  One of the points of intersection of the line and the circle has x-coordinate 1.76. What is the x coordinate of the other point of intersection?

  9. If a and b are positive integers, and (ab3/2)2 = 108, what is the value of ab?

  

 

  10. The line through AB is tangent to two circles with centers D and C and whose areas are in the ratio 4: 1

  If AB = 5 and BC =4, what is the length of line segment DC (not shown)? Grid your answer correct to three significant figures.

  SAT数学填空题练习题11参考答案

  1.Correct Answer: 6

  Explanation:

  The area of the rectangle is 3x²

  Area of right isosceles triangle = ½ x²

  Divide the area of the rectangle by the area of the triangle

  3x²/ ½ x² = 6

  2.Correct Answer: 3

  Explanation:

  n must be a factor if the result of dividing 81 by n is a whole number.

  Factorize 81 to give factors of 9, 3, 27

  Therefore n can take 3 different values

  3.Correct Answer: 54

  Explanation:

  Draw out the figure and add a perpendicular height from the base.

  Since area = ½ base x height, and area = 108

  108 = 12 x height = 9

  Now you need to recognize that each triangle formed by half the base, the height and the side marked �a�, is a 3-4-5 right triangle. Therefore �a� = 15

  Perimeter of the large triangle = 24 + 15 + 15 = 54

  4.Correct Answer: 50

  Explanation:

  Frame an equation. Let the number of $2.50 packs be n. the number of 410 packs sold = 75 - n.

  Total cost = n (2.5) + (75-n)10

  375 = 2.5n + 750 - 10n

  7.5n = 375; n = 50

  5.Correct Answer: 5

  Explanation:

  Half the perimeter = length + breadth = 7

  The length = 2/7 x 14 = 4; the breadth = 7 - 4 = 3

  The length and the breadth form the legs of a 3-4-5 right triangle with the diagonal of the rectangle forming the hypotenuse. So the diagonal = 5

  6.Correct Answer: 189

  Explanation:

  We have a choice of 1/7 for a, 1/3 for b and 1/9 for c. Therefore we have 7 x 3 x 9 = 189 possible code names. (You multiply the choices because any one from a set can be combined with any from the other sets)

  7.Correct Answer: 5/9

  Explanation:

  If one third is full, then 2/3 is empty initially. One third of the mixture that is to be added is ethanol. Therefore we are adding 1/3 x 2/3 ethanol = 2/9

  But the flask already has 1/3 ethanol. New fraction will be 1/3 + 2/9 = 5/9

  8.Correct Answer: 6.24

  Explanation:

  

 

  Draw a sketch. The points of intersection will lie symmetrically: one will be x units to the right of the center of the circle and one will be x units to the left. The x-coordinate of the center of the circle is 4, and so 1.76 lies (4 � 1.76) = 2.24 units to the left and the other point will lie 2.24 units to the right = 4 + 2.24 = 6.24#p#分页标题#e#

  9.Correct Answer: 6

  Explanation:

  First simplify by taking out the brackets: a²b6/2 =108 ; a²b³ = 108

  Now we are stuck unless we realize that if a and b are both integers there is probably only one solution to this equation, which we should be able to find if we find the prime factors of 108.

  108 = 2 x 2 x 3 x 3 x 3 x 3, and so a must be 2 and b must be 3. Hence, ab = 6

  10.Correct Answer: 5.39

  Explanation:

  Angles DAB and ABC are right angles. Because the areas of the circles are in the ratio of 4:1 the radii must be in the ratio of √4:√1 which is 2: 1. We are told the radius (BC) of the larger circle is 4, hence, the radius of the smaller circle must be 2.

  If we draw a line from D perpendicular to BC we divide ABCD into a rectangle and a right triangle. The right triangle has sides 5 (because it is equal to AB), 2 (half of BC), and DC. Using Pythagoras theorem we have 5² + 2² = DC² DC = √29 = 5.3852 To three significant figures this is 5.39 (We can�t grid in more anyway)

  以上就是SAT数学考试问答题练习题(十一)的详细内容,考生可针对文中介绍的方法进行有针对性的备考。

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