 SAT数学模拟练习题（1）

2012-02-17 18:12

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：

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

Explanation:

Expand as for (a + b)2.

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

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

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

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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