下面为大家整理了
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。