Mathematics 1 Ara 7. Deneme Sınavı
Toplam 8 Soru1.Soru
If the half-life of a radioactive material is 3000 years, how much of the 100 grams will remain after 5000 years?
15.6 |
22.7 |
26.8 |
28.6 |
31.5 |
The quantity at time t is given by the formula Q(t)=Q(0)*ekt where Q(0) is the initial amount.
Since the half life is 3000 years, we can write:
0.5Q(0)=Q(0)*e3000k which means that:
0.5=e3000k
ln0.5=lne3000k
ln0.5=3000k
ln0.5/3000=k
Thus, after finding k we can calculate:
Q(t=5000)=100*e5000*ln0.5/3000
=100*e5*ln0.5/3
=100*e-1.155=31.49
2.Soru
f : R › R, f(x) = 3 x2 – 5. f –1(x) = ?
(3 x2 – 5)-1 |
(-3 x2 + 5)-1 |
((x + 5) / 3)1/2 |
((-x + 5) / 3)-1/2 |
(-3 x2 + 5)-1/2 |
x = ((y + 5) / 3)1/2 . Correct answer is C.
3.Soru
Which of the following statements is false?
If A is subset of B and B is subset of A, then A=B. |
Empty set is subset of any set. |
A set is subset of itself. |
If A is subset of B and C is subset of B, then intersection of A and C can not be empty set. |
If A is subset of B and B is subset of C, then A is subset of C. |
Assume that B={1, 3, 5, 7}, A={1, 3} and C={5, 7}. Both A and C are subsets of set B, but their intersection is empty set. All the other statements are true.
4.Soru
Given the sets A={3,4,1,9,12}, B={7,3,4,10} and C={3,9,10}. Find(A∪B)\C.
Given the sets A={3,4,1,9,12}, B={7,3,4,10} and C={3,9,10}. Find(A∪B)\C.
{3, 5, 1, 8, 9} |
{3,1,9,12} |
{4,1,12,7} |
{7,3,4,10} |
{3,4,1,9,12} |
A ∪ B = {3,4,1,9,12,7,10} The set of elements A ∪ B which are not in C is {4,1,12,7}. Therefore (A ∪ B) \ C = {4,1,12,7}.
5.Soru
Wich one of the following numbers is greater?
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|
|
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|
Correct answer is D.
6.Soru
Given the sets A = {a, b, c, d}, B = {a, c, f, g}
and C= {c, d, g, h, i}. Find (A ? B) ? C.
{a, c, d} |
{c, d, g} |
{c, d, h} |
{g, h, i} |
{a, d, g} |
A ? B = {a, b, c, d, f, g}. Intersection of this set with C is (A ? B) ? C = {c, d, g}.
7.Soru
Which of the following ones is a polynomial function, with degree 3 ?
3 x |
x3 + x |
1 + x + x2 |
x – 3 |
3 + 31/3 |
x3 + x . pg. 50. Correct answer is B.
8.Soru
f : R › R, f(x) = 2 + 3 x3 ; g : R › R , g(x) = -x + 1. (f . g)(-1) = ?
0 |
10 |
-5 |
-2 |
4 |
y = -2 x + 2 - 3 x4 + 3 x3 = -2 . Correct answer is D.