关键词：SAT数学真题
摘要：数学作为SAT考试中的一个重要部分，它的备考除了掌握大量知识点以外，还要勤加练习，小编为大家整理大量习题，希望对备考的同学有所帮助!
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
6. Which of the following could be a value of x, in the diagram above?
A. 10
B. 20
C. 40
D. 50
E. any of the above
7. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
A. 10
B. 15
C. 20
D. 25
E. 30
8. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
A. 5 : 1
B. 10 : 5
C. 15 : 2
D. 20 : 2
E. 25 : 2
9. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
10. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.
参考答案及解析：
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
6. Correct Answer: B
Explanation:
The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB. Also ABC is not a straight line and must be less than 180. Therefore 90 < 5x < 180 The only value of x which satisfies this relation is 20.
7.Correct Answer: A
Explanation:
20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.
8.Correct Answer: E
Explanation:
Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number. US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.
Now US : Indian = 25 : 10, and Indian : British = 10 : 2 Hence the two ratios can be combined and US : British = 25 : 2
9. Correct Answer: C
Explanation:
Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5. Circumference = π.diameter = 5π
10.Correct Answer: D
Explanation:
If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as n + (n + 1) + (n + 2) + (n + 3 ) and (n + 3) + (n + 4) + (n + 5) + (n + 6) Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12
