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SAT数学模拟练习题(1)

2012-02-17 18:12

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  SAT数学模拟练习题(1)

  1. If f(x) = │(x2 – 50)│, what is the value of f(-5) ?

  A. 75

  B. 25

  C. 0

  D. -25

  E. -75

  2. ( √2 - √3 )2 =

  A. 5 - 2√6

  B. 5 - √6

  C. 1 - 2√6

  D. 1 - √2

  E. 1

  3. 230 + 230 + 230 + 230 =

  A. 8120

  B. 830

  C. 232

  D. 230

  E. 226

  

 

  4. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

  A. 10

  B. 8

  C. 6

  D. 4

  E. 2

  

 

  5. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

  A. 18

  B. 13.5

  C. 9

  D. 4.5

  E. 3

  答案:

  1.Correct Answer: B

  Explanation:

  If x = -5, then (x2 – 50) = 25 – 50 = -25

  But the sign │x│ means the absolute value of x (the distance between the number and zero on the number line). Absolute values are always positive.

  │-25 │ = 25

  2.Correct Answer: A

  Explanation:

  Expand as for (a + b)2.

  (√2 - √3)(√2 - √3) = 2 - 2(√2 + √3) + 3 = 5 - 2 √6

  3.Correct Answer: C

  Explanation:

  All four terms are identical therefore we have 4 (230).

  But 4 = 22, and so we can write 22. 230

  Which is equivalent to 232

  4. Correct Answer: B

  Explanation:

  Amy can travel clockwise or anticlockwise on the diagram.

  Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.

  Similarly, anticlockwise she has four different routes.

  Total routes = 8

  5.Correct Answer: D

  Explanation:

  If we take AE as the base of triangle AEC, then the height is CD.

  The height of the triangle is therefore, 9 (given).

  To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1.

  The area of AEC = base x height

  =1/2 x 9 = 4.5 

 

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