對(duì)國(guó)內(nèi)SAT考生而言，SAT數(shù)學(xué)題的絕大部分內(nèi)容，不超過(guò)高一數(shù)學(xué)的程度，SAT數(shù)學(xué)題較難部分的矩陣、統(tǒng)計(jì)與概率分析試題，僅涉及這些數(shù)學(xué)概念的最簡(jiǎn)單題型，國(guó)內(nèi)考生通過(guò)有效的SAT備考培訓(xùn)與模擬測(cè)試，可很快掌握這部分試題的答題方法與技巧。下面來(lái)看5道SAT數(shù)學(xué)經(jīng)典試題。
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 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 = ½ base x height =1/2 x 9 = 4.5
