SAT数学重要的练习题10

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　　1. Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ?

　　A. 1155

　　B. 1145

　　C. 1040

　　D. 950

　　E. 259

　　2. AB and DE are parallel. Angle BAC = 30 , angle CDE = 50. What is the measure of angle ACD ?

　　A. 100

　　B. 90

　　C. 80

　　D. 70

　　E. cannot be determined from the information

　　3. If x / y is an integer, which of the following statements must be true?

　　A. both x and y are integers

　　B. x is an integer

　　C. either x or y is negative

　　D. y / x is an integer

　　E. x = ny where n is an integer

　　4. What is the average of four tenths and five thousandths?

　　A. 25002

　　B. 2502

　　C. 0.225

　　D. 0.2025

　　E. 0.02025

　　5. What is the simplified result of following the steps above in order?

　　(1) add 5y to 2x

　　(2) multiply the sum by 3

　　(3) subtract x + y from the product

　　A. 5x + 14y

　　B. 5x + 16y

　　C. 5x + 5y

　　D. 6x + 4y

　　E. 3x + 12y

　　6. If the equation of a line p in the coordinate plane is y = 3x + 2, what is the equation of line q which is a reflection of line p in the x-axis?

　　A. y = -3x + 2

　　B. y = -3x - 2

　　C. y = 3x - 2

　　D. y = -1/3x - 5

　　E. y = -1/3x + 5

　　7. If y ¤ x = y2x for all positive integers, then (3 ¤ 4) ¤ 2 =

　　A. 38

　　B. 312

　　C. 316

　　D. 324

　　E. 332

　　8. The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

　　A. 2.5

　　B. 3

　　C. 5

　　D. 25

　　E. 50

　　9. The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surface area of the large brick?

　　A. 32

　　B. 40

　　C. 60

　　D. 72

　　E. 80

　　10. (3x + 2) (2x - 5) = ax2 + kx + n .

　　What is the value of a - n + k ?

　　A. 5

　　B. 8

　　C. 9

　　D. 10

　　E. 11

　　1.Correct Answer: B

　　Explanation:

　　The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g

　　250 + 900 = 1150

　　This is the maximum weight that can be sent at that price. But, weights exceeding

　　250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).

　　Hence a package weighing 1145 (ans. B) will be charged $1.55

　　2.Correct Answer: C

　　Explanation:

　　Imagine a third parallel line drawn through C. The angle ACD will be made of two angles, one alternate to BAC, and therefore = 30. The other is alternate to CDE and therefore = 50. Total for angle ACD = 80

　　3.Correct Answer: E

　　Explanation:

　　You can eliminate answer choices by picking numbers.

　　In case (A), x and y could, for example, both be equal fractions and x/y would be an integer.

　　For the same reason (B) does not have to be correct.

　　There is no reason for either of them to be negative.

　　Answer (D) does not need to be correct. Consider x/y = 6/3. Then y/x = 3/6, which is a fraction not an integer.

　　But rearranging x/y = n, we get x = ny which is therefore always true.

　　4.Correct Answer: D

　　Explanation:

　　Four tenths = 0.4

　　Five thousandths = 0.005

　　The average is (0.4 + 0.005)/2 = 0.2025

　　5.Correct Answer: A

　　Explanation:

　　Step one 2x + 5y

　　Step two 3(2x + 5y) = 6x + 15y

　　Step three (6x + 15y) - (x +y) = 6x + 15y - x - y (watch that last minus sign!)

　　This gives 5x + 14y

　　6.Correct Answer: B

　　Explanation:

　　The reflection of the line in the x-axis will change the signs for the slope and the intercept but the absolute value of the intercept and slope will be unchanged.

　　7.Correct Answer: E

　　Explanation:

　　The strange sign tells us what operation to carry out on x and y

　　Carry out the same procedure on 3 and 4 first. So 38 is the result.

　　Now carry out the procedure on 38 and 2. So (38)4 is the result, which is equivalent to 332

　　8.Correct Answer: B

　　Explanation:

　　Start constructing the sequence until you see the pattern

　　1...5...(average of 1 and 5 = 3)...(average of 1, 5, and 3 = 3)...(average of 1,5,3 and 3 = 3)

　　now you can see that all subsequent terms will be 3

　　9.Correct Answer: B

　　Explanation:

　　Surface area of one small brick = 6; total number of bricks = 12; total surface when disassembled = 6 x 12 = 72

　　Surface of whole big block= area of four larger faces + area of the two smaller faces = (4 x 6) + (2 x 4) = 24 + 8 = 32

　　The increase is 40 units

　　10.Correct Answer: A

　　Explanation:

　　This is a quadratic equation. To find n we multiply the last terms in each bracket together (2 times -5) = -10

　　To find ‘a’ we multiply the first terms in each bracket together (3x times 2x) = 6x2, So a = 6.

　　Thus a - n = 16

　　To find k we multiply the first term in the first bracket by the second term in the second bracket and add the result to the product of the second term in the first bracket and the first term in the second. (-15x + 4x) = -11x. So k = -11

　　16 - 11 = 5

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