SAT考試數(shù)學練習題及答案解析（二）

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SAT考試數(shù)學練習題SAT Math Practice 2

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

A. 75

B. 25

C. 0

D. -25

E. -75

☆7. （ √2 - √3 ）2 =

A. 5 - 2√6

B. 5 - √6

C. 1 - 2√6

D. 1 - √2

E. 1

☆8. 230 + 230 + 230 + 230 =

A. 8120

B. 830

C. 232

D. 230

E. 226

☆9. 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

☆10. 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

答案見下頁

SAT考試數(shù)學練習題SAT Math Practice 2參考答案

☆6.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

☆7.Correct Answer: A

Explanation:

Expand as for （a + b）2.

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

☆8.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

☆9.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

☆10.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