2019年SAT数学经典试题详细解析

>>SAT考试试题：2019年SAT数学经典试题详细解析

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

A. 75 B. 25 C. 0 D. -25 E. -75

2、( √2 - √3 ) =

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 (x – 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 C

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 C

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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