SAT数学模拟练习题（1）

　　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