2019年SAT考试数学经典试题练习3

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1. The number 0.127 is how much greater than 1/8 ?

A. ½

B. 2/10

C. 1/50

D. 1/500

E. 2/500

2. Which of the following could not be the lengths of the sides of a right angled triangle?

A. 3, 4, 5

B. 5, 12, 13

C. 8, 15, 17

D. 12, 15, 18

E. 9, 12, 15

3. Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?

A. 104

B. 78

C. 54

D. 27

E. 13

4.

A. a² + b² + 1

B. a + b

C. a - b

D. ab

E. it cannot be simplified further

5. x = y - (50/y), where x and y are both > 0

If the value of y is doubled in the equation above, the value of x will

A. decrease

B. stay the same

C. increase four fold

D. double

E. increase to more than double

6. Which of the following could be a solution of the equation │x│ = │4x - 3│

A. -1

B. -0.6

C. 0

D. 0.6

E. 1.5

7. The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is

A. 720

B. 180

C. 75

D. 65

E. 60

8. Jeff takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long?

A. 6

B. 8

C. 10

D. 12

E. 14

9. A and B are equidistant from the line l. How many circles can be drawn with their centres on line l and that pass through both A and B?

A. 1

B. 2

C. 3

D. 4

E. >10

10. A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy

B. 100y - x

C. 100x - y

D. 100y / x

E. 100x / y

1.Correct Answer: D

Explanation:

0.127 expressed as a fraction = 127/1000

1/8 can also be expressed as (1 x 125) / (8 x 125) = 125/1000

The difference is 2/1000, which is 1/500

2.Correct Answer: D

Explanation:

Using Pythagoras theorem we can see that 122 + 152 is not equal to 182

(All the others obey the theorem a2 + b2 = c2)

3.Correct Answer: D

Explanation:

Area remaining is the area of the rectangle - 2 x area of a circle.

(16 x 8) - 2π r2

But r = 4; so area remaining is 128 - 101(approx) = 27 (approx)

4.Correct Answer: C

Explanation:

a2 - b2 can be expressed as (a + b)(a - b)

So the fraction can be written as (a + b)(a - b)/ (a + b)

Which is equal to (a - b)

5.Correct Answer: E

Explanation:

The best approach is to pick a number that satisfies the rules that x and y are greater than 0. So for example you could choose 25 for y.

The value of x before doubling is then 25 - 50/25 = 23

The value after doubling y will be 50 - 50/50 = 49, which is more than double.

6.Correct Answer: D

Explanation:

This could be tricky unless you realize that the absolute value signs lead to the conclusion that x = 4x – 3 and also –x = 4x – 3

If we solve these equations we get x = 1 and x = 3/5 = 0.6 and so since 1 is not an option, the answer is D.

(You could also have substituted the answer choices in the equation.)

7.Correct Answer: C

Explanation:

The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.

8.Correct Answer: B

Explanation:

Average speed = total distance / total time

Total distance covered = 6 miles; total time = 45 minutes = 0.75 hours

Average speed = 6/ 0.75 = 8 miles/hour

9.Correct Answer: E

Explanation:

Do not assume that a circle must have its origin where AB intersects the line l.

You could take any point on line l and use if as the center of a circle such that the distance from that point to either A or B is the radius.

10.Correct Answer: E

Explanation:

Total distance covered by the first wheel = d, which is the equivalent of 100 x circumference. Circumference = 2xπ

Circumference of the second wheel = 2yπ

Revolutions covered by the second wheel = 100(2xπ / 2yπ , which simplifies to 100x/y

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