Princeton Review Math 1 Practice 1余补角 inscribed angle

 

Actually, I use a calculator to calculate the result. But here is the better way 

1.73999= (1.739)100 = 128.8100

2799 almost 2800= (28)100=256100

3500= (35)100=243100

4400= (44)100= 256100

250100= (44)100

John Adams

 “The science of government it is my duty to study, more than all other sciences; the arts of legislation and administration and negotiation ought to take the place of, indeed exclude, in a manner, all other arts. I must study politics and war, that our sons may have liberty to study mathematics and philosophy. Our sons ought to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry and porcelain.”

― John Adams, Letters of John Adams, Addressed to His Wife

Kaplan SAT Subject Math Level 1-Practice 4

 

Better solution is xy = 28, xz = 20, yz = 35, then (xyz)^2 = 28 * 20 * 35, square root is 140. It is the answer. 

Q9: Within a given area code, how many seven-digit numbers are available, given the restriction that the first three digits cannot be 911 or 411 and the first digit cannot be a 1 or a 0?

My solution is : total options is 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^7

since first digit cannot be a 1 or a 0, then minus  10 * 10 * 10 * 10 * 10 * 10  (the first digit must be 1) and 10 * 10 * 10 * 10 * 10 * 10 ( (the first digit must be 0). It will be 8 * 10 * 10 * 10 * 10 * 10 * 10. 

When the first three digits must be 911, it has 10 * 10 * 10 * 10. 

When the first three digits must be 411, it has 10 * 10 * 10 * 10. 

Thus, final result is  8 * 10 * 10 * 10 * 10 * 10 * 10 - 10 * 10 * 10 * 10 - 10 * 10 * 10 * 10 = 7,980,000

I doubt my solution since I don't think it could involve so many steps. But it turns out it has to be.

What I did is to try all choices such that a * 1/a = 1.

先算三个交集的人数，再用总数减去这个数既是答案。

（18－10）+ （ 25－10） + （15－10） +10 = 38

50－38 = 12

The median is not average of 9th and 10th numbers

Kaplan SAT Subject Math Level 1-Practice 3

 Kaplan SAT Subject Test Mathematics Level 1-Practice 3

注意raw score 不是做对题的数目，要减去错的题数 ×0.25。

Errors: Q33

Q29. The number of employees who work at Company A increased by 18% during the year 2003. During 2004, the number of employees increased by 26%. What was the approximate percent of increase, to the nearest percent, in employment over the two-year period?

(A) 31%   (B) 44%  (C) 49%   (D) 53%    (E) 65%

I make a mistake by selecting the middle one. 

Kaplan SAT Subject Math Level 1-Practice 2

Kaplan SAT Subject Test Mathematics Level 1-Practice 2

注意raw score 不是做对题的数目，要减去错的题数 ×0.25。

Errors: Q6, 15, 17, 22, 28,

900度，tan 从正无穷大到负无穷大

Q34. 不能想象是什么样的球，所以不会做题。球绕着x-axis 转360度