Mathematics 1 Ara 1. Deneme Sınavı
Toplam 17 Soru1.Soru
Which of the following statements is true?
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Every real number is a rational number also. |
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Every integer is a rational number. |
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Every integer is a natural number. |
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Every rational number is an integer. |
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Every rational number is a natural number. |
?2 is a real number but it is not rational (It is impossible to write ? 2 as a/b where a and b are integers), so A is false.
-3 is an integer but it is not a natural number, so C is false also.
5/7 is a rational number but it is not an integer so D is false.
5/7 is rational but it is not a natural number so E is false also.
Only statement in B is true.
2.Soru
There are 22 students in a class. 16 of them has blue pens. 18 of them has red pens. How many of them has both blue and red pens?
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8 |
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10 |
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12 |
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14 |
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16 |
s(B)=16
s(R)=18
s(B ∪ R)=28
s(B ∩ R) = s(B) + s(R) – s(B ∪ R)=16+18-22=12
3.Soru
The population of a bacteria doubles in 4 hours. How many bacteria would we have in 10 hours given that we have 1000 bacteria now?
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5657 |
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3568 |
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2563 |
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1896 |
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567 |
Given the initial bacteria population Q(0), the population at time t is given by Q(t)=Q(0)ekt.
Since we know that population doubles in 4 hours, we can write:
2Q(0)=Q(0)e4k
2=e4k
ln2=4k, so k=ln2/4=0.1733
Then Q(t=10)=1000e10k
=1000.e1.733
=5657 (approximately)
4.Soru
Which of the following linear function has slope -2?
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y=-2-x |
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y=-2-2x |
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y=-2 |
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y=2-4x |
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y=-3x |
The slope of y=-2-2x is -2 because the slope of a linear functin of the form y=mx+n is m. The answer is B.
5.Soru
What is the solution set of the inequality 5x-25>0?
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(0, 5) |
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(-5, 5) |
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(-5, ꝏ) |
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(-ꝏ, 5) |
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(5, ꝏ) |
The answer is E.
6.Soru
(28 + 26) / (43 + 44) = ?
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2 |
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1 |
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0.25 |
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8 |
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16 |
x = (22 (26 + 1)) / (4 (1 + 43)) = 1. pg. 11. Correct answer is B.
7.Soru
Find the solution set of the equation 0=6+e2x - 5ex
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(2,3) |
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(ln2, 3) |
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(2, ln3) |
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(ln2, ln3) |
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(ln1, ln4) |
0=6+e2x - 5ex
0=(ex - 3)(ex - 2)
So the system has 2 roots:
ex - 3=0 then ex=3 so x=ln3
ex - 2=0 then ex=2 so x=ln2
Therefore solution set is (ln2, ln3)
8.Soru
Given the function f: R›R, f(x)=7x²+12, what is the value of f(2)?
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17 |
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36 |
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40 |
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51 |
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66 |
f(x)=7x²+12, f(2)=7.2²+12 ,then f(2)=7.4+12=40
9.Soru
If log2? 5=a , what is the expression of log4? 100 in terms of a?
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a2+1 |
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2a+1 |
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a+1 |
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4a-1 |
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4a+1 |
10.Soru
- Ø
- {a}
- {b}
- {c}
- {a, b}
- {a, c}
- {b, c}
- {a, b, c}
Let A = {a, b, c}. Which of the above are the subsets of A?
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II, III and IV |
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III, IV, V and VI |
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V, VI, VII and VIII |
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I, II, III, IV, V, VI and VII |
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I, II, III, IV, V, VI, VII and VIII |
If A is a finite set and n is the number of its elements, that is s(A) = n, then the number of all subsets of A is 2n.
For example, if A = {1, 2, 3} then the subsets of A
are Ø, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.
The set A has 23 = 8 subsets. Recall that, by convention, every set is its own subset, that is A ? A. The empty set Ø is a subset of any set.
As also understood from the information given the subsets of A are
Ø, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, so the correct answer is E.
11.Soru
Which of the following is a linear function with the slope of 2?
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y=2x - 7 |
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y=2- 7x |
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y=x2 + 7 |
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y=x3 + 7 |
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y=2 |
The slope of a linear function of the form y=mx+n is m. Hence, y=2x - 7 is a linear function, and its slope is 2.
12.Soru
Which power of 6 is between 1200 and 1500?
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4 |
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5 |
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6 |
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7 |
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8 |
6*6*6*6=1296
The correct answer is A.
13.Soru
f : R › R, f(x) = 5 x3 + x – 2. f(-1) = ?
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-8 |
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6 |
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4 |
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-5 |
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-2 |
y = -5 – 1 – 2 = -8 . Correct answer is A.
14.Soru
e-2x + e-x = 0. x = ?
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e |
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-e |
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no solution |
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1 / e |
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-1 / e |
for all x : e-2x > 0, e-x > 0 ; no solution. Correct answer is C.
15.Soru
Which of the following is not a point on the line y=5x-2?
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(0, -2) |
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(2/5, 0) |
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(1, 3) |
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(2, 8) |
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(1/5, -2) |
y=5x-2, (1/5, -1) is not on the line y=5x-2 because if x=1/5 then y=5*1/5-2=-1. Therefore, the answer is E.
16.Soru
What is the logarithm of 10000 with respect to the base 10?
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2 |
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3 |
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4 |
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5 |
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6 |
17.Soru
Which power of 4 is between 250 and 650?
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3 |
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4 |
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5 |
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6 |
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7 |
4*4*4*4=625
The correct answer is C.