Mathematics 1

Yanıt Açıklaması: x = c – b + a – b + c – a = 2c – 2 b . pg. 17. Correct answer is A.

Yanıt Açıklaması: Let's combine a and b to single element that we call *. Then our set will become A= { 0,1,2,3,* }. Since this set has 5 elements it has 32 subsets (2 5 =32). Out of these 32 sets, there are 16 sets that doesn't contain *. (If we delete *, there remains a set containing 4 elements which has 2 4 =16 subsets). A subset will either contain * or it will not contain *. Thus 32-16=16 sets contain *, namely a and b.

Yanıt Açıklaması: 2 7 =128 The correct answer is D.

Yanıt Açıklaması: x = max {2 / 5, 1 / 4, 3 / 8, 3 / 10, 7 / 16} = max {32, 20, 30, 24, 35} / 80 = 7 / 16. pg. 12. Correct answer is E.

Yanıt Açıklaması: we can calculate that: 4²=16, 4³=64, 4 4 =256, 4 5 =1024, 4 6 =4096 Then the power of 4, which lies between 4000 and 4100, is 6.

Yanıt Açıklaması: From the graph we see that f(5/2)=-6 and f(-3)=8, so 2 f (5/2)– f (-3) =(2.-6)-8=-20

Yanıt Açıklaması: Note that one can rewrite; 5 2x+3 =1/25=5 2x+3 =5 -2 Since the exponential function 5 x is one-to one, we have 2x+3=-2 then x=-5/2

Yanıt Açıklaması: 5 0 =1 The correct answer is B.

Yanıt Açıklaması: Since 20 percent is lost, 80 percent is remaining at the end of 10 years. Thus we can write: 0.8Q=Q.e 10k ln0.8/10=k=-0.0223 So we can find the half life by: 0.5Q=Q.e- 0.0223t ln0.5=-0.0223t, then t=31.06 years

Yanıt Açıklaması: 3x-6=0, x=2. Therefore the answer is C.

Yanıt Açıklaması: (x – 2) (x + 1) = 0 ; x = 2, x = -1 . pg. 55 . Correct answer is C.

Yanıt Açıklaması: The answer is A.

Yanıt Açıklaması: -2 ln(x – 1) = -4 ; ln(x – 1) = 2 = ln e 2 ; x – 1 = e 2 ; x = e 2 + 1. Correct answer is A.

Yanıt Açıklaması: Venn diagram showing A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) Correct answer is A.

Yanıt Açıklaması: For the first earthquake, the intensity is; M = log 10 I› 7.1=log 10 I› I=10 7.1 For the second earthquake, the intensity is; M = log 10 I› 5.2=log 10 I› I=10 5.2 on the Richter scale yields an intensity change by a factor of 10 7.1 /10 5.2 = 10 1.9 =79.43 Strictly speaking; the fist earthquake had a magnitude about 80 times greater than second earthquake.

Yanıt Açıklaması: Denote by M and S the set of all students who are members of the Mathematics and Sports clubs, respectively. Then, s(M ? S) = 250-17 = 233. Using the formula (M ? S) = s(M) + s(S) – s(M ? S), we have s(M ? T) = 233 = 153 + 110 - x, where x is the required number. Then we find that x = 153 + 110 - 233. Thus, x equals to 30.

Yanıt Açıklaması: Total value at the end=10.000(1.2) 4 =2.0736*10000=20736

Yanıt Açıklaması: x + x -1 + 1 ; -1 is not natural number ; all powers of the variable x must be natural numbers. pg. 50. Correct answer is D.

Yanıt Açıklaması: a 0 = 1 for all nonzero numbers a. If a = 0, a 0 is called indeterminate. ? (infinity) is not a number. It represents an infinitely large quantity. The whole real line is an interval denoted by (–?, ?). Powers are used when we multiply a real number by itself repeatedly. As also understood from the information given, the correct answer is C. The statements in the options I a 0 = 1 for all nonzero numbers a.”, III “? (infinity) is not a number. It represents an infinitely large quantity.”, IV “The whole real line is an interval denoted by (–?, ?).” and V “Powers are used when we multiply a real number by itself repeatedly.” are correct. The statement in the option II “If a = 0, a 0 is called power of a.” is not correct because of the fact that if a = 0, a 0 is called indeterminate.