SAT数学Problem Solving练习题一.

(a) a = 18 and b = 1

(b) a = 9 and b = 2

(c) a = 18 and b = 9

(d) a = 6 and b = 3

(e) a = 6 and b = 6

• Answer: a / b = 2 a = 2·b. a·b = (2· b)· b a·b = 2· b ². 2· b ² = 18 b ² = 9, b = 3 because b > 0, a = 2· b a = 6.

(a) perimeter ratio = 1/6, area ratio = 36

(b) perimeter ratio = 36, area ratio = 6

(c) perimeter ratio = 6, area ratio = 36

(d) perimeter ratio = 1/8, area ratio = 8

(e) perimeter ratio = 1/6, area ratio = 6

• Answer: r₁ / r₂ = 6; Perimeter₁ / Perimeter₂ = (2· ¶· r₁)/(2· ¶· r₂) = r₁/ r₂ = 6 Area₁ / Area₂ = (¶· r₁²)/ (¶· r₂²) = r₁² / r₂² = 36

(a) x = 1

(b) x = -5

(c) x = -1

(d) x = 7

(e) x = 6

• Answer: x ²> 16 means (x - 4)· (x + 4) > 0. x can be lower than -4 or higher than 4. 1/x < 1/7; (7-x) / 7x < 0. x can be lower than 0 or higher than 7.

  In conclusion, x can be lower than -4 or higher than 7. The only correct answer is x = -5.

(a) 3/5

(b) 1/2

(c) 2/5

(d) 1/5

(e) 4/5

• Answer: There are 400 tickets sold in New Jersey out of a total of 1000, so the probability will be 400/1000 = 2/5.

(a) 40

(b) -40

(c) -20

(d) 20

(e) -30

• Answer: x = (5/9)· (x - 32). 9·x = 5·(x - 32). In conclusion, x = -40C = -40F

(a) y = (5/4)· x + 4

(b) y = (4/5)· x - 4

(c) y = (4/5)· x + 4

(d) y = -(5/4)· x + 5

(e) y = (5/4)· x + 5

• Answer: The equation of a line is y = m · x + n First point, x = 0, y = 5, results in 5 = n Second point: x = 4, y = 0, means 0 = m · 4 + n, or m = -n/4 or m= -5/4. In conclusion, y = -(5/4) · x + 5 is the correct answer.

(a) ¶ + 1

(b) ¶ - 1

(c) ¶ - 2

(d) ¶

(e) ¶ + 2

• Answer: The diagonal of the square is √2 · √2 = (√ 2)² = 2. This is also the diameter of the circle. The area outside the square and inside the circle is: Area_circle - Area_square = ¶ · 2²/4 - 2 = ¶ - 2

(a) 13

(b) 14

(c) 16

(d) 18

(e) 22

• Answer: (x + 2y) ² = x ² + 4 · y ² + 4 · x · y = 2 + 12 = 14

(a) (5/2) · √3

(b) 5 · √3

(c) (5/2) · 3^-3

(d) 5/2

(e) 5

• Answer: The median divides the equilateral triangle in two right triangles. Conform to the Pythagorean theorem, wherein the sum of the squares of the two legs is equal to the square of the hypotenuse, m² + (5/2)²= 5² m² = 5² - (5/2)² = 5² - 5²/4 = (3/4) · 5² m = (5/2) · √3.

(a) median = 0, average = -4/9

(b) median = 0, average = 4/9

(c) median = 2, average = -4/9

(d) median = 2, average = 4/9

(e) median = 2, average = 2/9

• Answer: You must arrange the numbers in order: -12, -8, -4, 0, 2, 2, 2, 4, and 10. The median will be number in the middle of the row, that is 2. The average will be (-12-8-4+0+2+2+2+4+10)/9 = -4/9.