SAT考试数学练习题 2

SAT是Scholastic Aptitude Test的缩写，是申请几乎所有美国大学必须参加的考试。通常，希望继续接受高等教育的高中生需要参加SAT考试，并且SAT考试得分是获取奖学金的重要标准之一。大部分美国大学要求SAT考试作为录取的条件并根据SAT得分授予奖学金。 

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 = ½ base x height
=1/2 x 9 = 4.5