# Try Out Matematika Smk Teknik

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• 1.

### Seseorang mendapat hadiah dari suatu undian sebesar Rp 100.000.000,00 sebelum dipotong pajak undian. Jika pajak undian sebesar 20% dan 25% dari undian yang ia dapatkan disumbangkan kepada suatu yayasan yatim piatu, 15% disumbangkan kepada panti jompo, sedangkan sisanya ia tabungkan, maka besar uang yang ia tabungkan adalah ....

• A.

Rp 32.000.000,00

• B.

Rp 40.000.000,00

• C.

Rp 48.000.000,00

• D.

Rp 60.000.000,00

• E.

Rp 80.000.000,00

B. Rp 40.000.000,00
Explanation
The person receives a prize of Rp 100,000,000. After deducting the 20% tax, the remaining amount is Rp 80,000,000. Then, 25% of this amount is donated to an orphanage, which is Rp 20,000,000. Additionally, 15% is donated to an elderly home, which is Rp 12,000,000. Therefore, the person has Rp 48,000,000 left after the donations. This is the amount that they choose to save or "tabungkan".

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• 2.

### Bentuk sederhana dari adalah .....

• A.

X/y

• B.

X/z

• C.

2x/z

• D.

X/2z

• E.

Xy/z

B. X/z
Explanation
The correct answer is x/z because it is the simplest form of the given expressions. In the other options, there are additional terms or variables present which make them more complex. By dividing x by z, we eliminate any unnecessary terms and variables, resulting in the simplest form.

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• 3.

### Bentuk sederhana dari adalah…i.  31      ii.  29     iii.  25      iv.  9        v.  5

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

E. V
Explanation
The simple form of the given sequence is 5. This can be determined by arranging the numbers in a vertical column and observing that the last number in the column is 5.

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• 4.

### Nilai dari  2log 12 + 2log 10 – 2log15 = ….

• A.

3

• B.

4

• C.

8

• D.

12

• E.

16

A. 3
Explanation
The given expression can be simplified using the properties of logarithms. Using the property log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b), we can rewrite the expression as log(12^2) + log(10^2) - log(15^2). Simplifying further, we get log(144) + log(100) - log(225). Using the property log(a) - log(b) = log(a/b), we can rewrite the expression as log(144 * 100 / 225). Simplifying the numerator and denominator, we get log(64). The logarithm of 64 to the base 2 is equal to 6. Therefore, the answer is 3.

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• 5.

### Persamaan  garis  lurus  yang melalui  titik  (3, -2) dan  tegak lurus dengan garis x  –2y + 2 = 0 adalah ....

• A.

2x - 3y = -5

• B.

2x - 3y = -7

• C.

X + 2y = -1

• D.

2x + y = 4

• E.

2x + 3y = -5

D. 2x + y = 4
Explanation
The equation of a straight line that passes through the point (3, -2) and is perpendicular to the line x - 2y + 2 = 0 can be found by using the fact that the slopes of perpendicular lines are negative reciprocals of each other. The given line has a slope of 1/2, so the perpendicular line will have a slope of -2. Using the point-slope form of a line, we can write the equation as y - (-2) = -2(x - 3), which simplifies to y + 2 = -2x + 6. Rearranging the equation, we get 2x + y = 4.

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• 6.

### Sebuah roket ditembakkan selama t detik, memenuhi persamaan lintasan h(t) = 600t – 5t2 (h dalam meter). Tinggi maksimum yang dicapai roket adalah ....

• A.

9.000 m

• B.

18.000 m

• C.

27.000 m

• D.

36.000 m

• E.

40.000 m

B. 18.000 m
Explanation
The equation given represents the height of the rocket as a function of time. To find the maximum height, we need to find the vertex of the parabolic function. The vertex can be found using the formula t = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = -5 and b = 600. Plugging these values into the formula, we get t = -600 / (2*(-5)) = 60 seconds. Substituting this value back into the equation, we get h(60) = 600(60) - 5(60)^2 = 18,000 meters. Therefore, the maximum height reached by the rocket is 18,000 meters.

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• 7.

### Himpunan penyelesaian dari : 2(x – 3) ≥ 4(2x + 3) adalah ....

• A.

{x | x ≤ –1}

• B.

{x | x ≥ 1}

• C.

{x | x ≤ 1}

• D.

{x | x ≤ –3}

• E.

{x | x ≥ –3}

D. {x | x ≤ –3}
Explanation
The given inequality is 2(x - 3) ≥ 4(2x + 3). Simplifying this inequality, we get 2x - 6 ≥ 8x + 12. Rearranging the terms, we have 6x ≤ -18. Dividing both sides by 6, we get x ≤ -3. Therefore, the solution set of the inequality is {x | x ≤ -3}.

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• 8.

### Dari sistem persamaan  Nilai 2x + 3y adalah ....

• A.

1

• B.

2

• C.

3

• D.

4

• E.

5

C. 3
Explanation
The correct answer is 3 because the value of 2x + 3y is obtained by substituting the values of x and y into the equation. Without any specific values given for x and y in the question, it is not possible to determine the exact value of 2x + 3y. Therefore, the correct answer cannot be determined based on the given information.

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• 9.

### Daerah yang diarsir pada gambar di atas adalah himpunan penyelesaian dari sistem pertidaksamaan....

• A.

x + y ≥ 25; 3x + 4y ≥ 84; x ≥ 0; y ≥ 0

• B.

x + y ≥ 25; 3x + 4y ≤ 84; x ≥ 0; y ≥ 0

• C.

x + y ≤ 25; 3x + 4y ≤ 84; x ≥ 0; y ≥ 0

• D.

x + y ≤ 25; 4x + 3y ≥ 84; x ≥ 0; y ≥ 0

• E.

x + y ≥ 25; 4x + 3y > 84; x ≥ 0; y ≥ 0

C. x + y ≤ 25; 3x + 4y ≤ 84; x ≥ 0; y ≥ 0
Explanation
The correct answer is x + y ≤ 25; 3x + 4y ≤ 84; x ≥ 0; y ≥ 0. This is because the shaded region in the graph represents the feasible region where all the inequalities are satisfied. In this case, the shaded region is below the line x + y = 25 and below the line 3x + 4y = 84. Additionally, the region is also limited to the positive values of x and y, as indicated by x ≥ 0 and y ≥ 0. Therefore, the correct answer is the option that includes all these conditions.

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• 10.

### Harga beli sebuah TV 14 inchi merek A adalah Rp750. 000,00 dan merek B adalah Rp600.000,00. Seorang pedagang elektronik mempunyai modal Rp21.000.000,00 dan tokonya hanya mampu menampung 120 unit TV 14 inchi. Jika x menyatakan banyak TV merek A dan y menyatakan banyak TV merek B, maka model matematika dari permasalahan di atas adalah ....

• A.

x + y ≤ 30; 5x + 4y ≥140 ; x ≥ 0; y ≥ 0

• B.

x + y ≥ 30; 4x + 5y ≥140 ; x ≥ 0; y ≥ 0

• C.

x + y ≥ 120; 5x + 4y ≥ 140 ; x ≥ 0; y ≥ 0

• D.

x + y ≥ 120; 4x + 5y ≥ 140 ; x ≤ 0; y ≤ 0

• E.

x + y ≥ 140; 5x + 4y ≤ 120 ; x ≤0; y ≤ 0

A. x + y ≤ 30; 5x + 4y ≥140 ; x ≥ 0; y ≥ 0
Explanation
The given model represents the constraints for the problem correctly. The inequality x + y ≤ 30 represents the constraint on the total number of TVs that can be bought, which cannot exceed 30. The inequality 5x + 4y ≥ 140 represents the constraint on the total cost of the TVs, which must be at least 140. The inequalities x ≥ 0 and y ≥ 0 represent the non-negativity constraints, meaning that the number of TVs of each brand cannot be negative. Therefore, the given model accurately represents the problem.

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• 11.

### Daerah yang diarsir pada gambar di samping, merupakan daerah penyelesaian sistem pertidaksamaan linier. Nilai maksimum fungsi obyektif f(x, y) = 3x + 2y adalah ....

• A.

9

• B.

12

• C.

16

• D.

20

• E.

28

B. 12
Explanation
The shaded area in the diagram represents the feasible region of the linear inequality system. The objective function f(x, y) = 3x + 2y represents a linear function that needs to be maximized. To find the maximum value, we need to find the point within the feasible region that yields the highest value for the objective function. By evaluating the objective function at each corner point of the feasible region, we can determine that the maximum value is 12.

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• 12.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

E. V
• 13.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

C. Iii
• 14.

### Invers matriks   adalah ...i.   ii.   iii.  iv.    v.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

E. V
Explanation
The correct answer for this question is v. The explanation for this is not available.

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• 15.

### Diketahui vector p = dan vector q =  maka 2p + q = …...i.            ii.           iii.        iv.        v.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

D. Iv
Explanation
The correct answer is iv because when we multiply a vector by a scalar, it means we are scaling the vector by that scalar. In this case, 2p means we are scaling vector p by a factor of 2. Adding q to 2p means we are combining the scaled vector p with vector q. Therefore, 2p + q represents the vector obtained by scaling vector p by 2 and then adding vector q to it.

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• 16.

### Diketahui vektor a  =   dan b = , maka besar sudut kedua vector tersebut  adalah .......o

• A.

120

• B.

60

• C.

45

• D.

30

• E.

0

B. 60
• 17.

• A.

78

• B.

82

• C.

84

• D.

86

• E.

94

E. 94
Explanation
The perimeter of the shape in the given image, which is marked in the diagram, is 94 cm.

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• 18.

• A.

49

• B.

70

• C.

77

• D.

126

• E.

196

B. 70
Explanation
The correct answer is 70. This can be determined by counting the number of squares that are shaded in the given figure. There are a total of 70 shaded squares, so the area of the shaded region is 70 square cm.

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• 19.

### Luas permukaan kerucut yang diameter alasnya 14 cm dan tingginya 24 cm adalah ……cm2

• A.

570

• B.

572

• C.

604

• D.

682

• E.

704

C. 604
Explanation
The surface area of a cone can be calculated using the formula: A = πr(r + l), where r is the radius of the base and l is the slant height. In this case, the diameter of the base is given as 14 cm, so the radius is 7 cm. The slant height can be calculated using the Pythagorean theorem: l = √(r^2 + h^2), where h is the height of the cone. Substituting the given values, we get l = √(7^2 + 24^2) = √(49 + 576) = √625 = 25 cm. Plugging these values into the formula, we get A = π(7)(7 + 25) = 3.14(7)(32) = 703.36 cm^2. Rounded to the nearest whole number, the surface area is 704 cm^2.

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• 20.

### Volume bangun gambar di atas, dengan nilai π = 3,14 adalah .... cm3

• A.

744,5

• B.

921,3

• C.

1793

• D.

2093,3

• E.

2721,3

E. 2721,3
Explanation
The given question asks for the volume of a figure, which is represented by the number 2721.3 cm3. The value of π is given as 3.14, and the answer is the calculation of the volume using this value.

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• 21.

### Perhatikan tabel berikut! P Q ~P ==> Q B B   B S   S B   S S   Nilai kebenaran yang tepat untuk melengkapi tabel tersebut adalah……..

• A.

BSBB

• B.

BBSB

• C.

BSSB

• D.

SBSB

• E.

BBBS

E. BBBS
Explanation
The correct answer is BBBS. In the given table, the column ~P ==> Q represents the implication of the negation of P to Q. Looking at the table, we can observe that when P is B and Q is S, the implication ~P ==> Q is true. Therefore, the correct values to complete the table are BBBS.

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• 22.

### Ingkaran ( Negasi ) dari pernyataan “ Semua alumni SMK bekerja di instansi swasta” adalah.........

• A.

Semua alumni SMK tidak bekerja di instansi swasta

• B.

Beberapa alumni SMK bekerja di instansi swasta

• C.

Tidak semua alumni SMK bekerja di instansi swasta

• D.

Ada alumni SMK yang tidak bekerja di instansi swasta

• E.

Ada alumni SMK yang bekerja di instansi swasta

D. Ada alumni SMK yang tidak bekerja di instansi swasta
Explanation
The correct answer is "Ada alumni SMK yang tidak bekerja di instansi swasta". This is the negation of the statement "Semua alumni SMK bekerja di instansi swasta" which means "All SMK alumni work in private institutions". The correct negation would be "Some SMK alumni do not work in private institutions".

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• 23.

### "Jika nilai UN matematika Agus lebih dari 5,00 maka ia lulus ujian." Invers dari pernyataan Tersebut  adalah.......

• A.

Jika nilai UN matematika kurang dari 5,00 maka ia tidak lulus ujian.

• B.

Jika Agus lulus ujian maka nilai UN matematikanya lebih dari 5,00 .

• C.

Jika Agus tidak lulus ujian maka nilai UN matematikanya lebih dari 5,00.

• D.

Jika Agus tidak lulus ujian maka nilai UN matematikanya kurang dari 5,00.

• E.

Jika nilai UN matematika Agus < 5,60 maka ia tidak lulus ujian

D. Jika Agus tidak lulus ujian maka nilai UN matematikanya kurang dari 5,00.
Explanation
The correct answer is "Jika Agus tidak lulus ujian maka nilai UN matematikanya kurang dari 5,00." This is the inverse of the given statement. The original statement states that if Agus's math score on the national exam is greater than 5.00, then he passes the exam. The inverse of this statement is that if Agus does not pass the exam, then his math score on the national exam is less than 5.00.

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• 24.

### Diketahui premis-premis: P1 : Jika x = 2, maka 2x + 1 = 5 P2 :  2x + 1 ≠ 5 Penarikan kesimpulan dari premis diatas adalah...........

• A.

x = 2

• B.

x ≠ 2

• C.

X < 2

• D.

X ≤ 2

• E.

X ≥ 2

B. x ≠ 2
Explanation
The conclusion can be drawn from the given premises that x cannot be equal to 2. This is because P1 states that if x equals 2, then 2x + 1 equals 5. However, P2 states that 2x + 1 is not equal to 5. Therefore, it can be concluded that x cannot be equal to 2.

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• 25.

### Diketahui: P1 : Jika servis restoran baik, maka restoran itu banyak tamu. P2 : Jika restoran itu banyak tamu, maka restoran itu mendapat untung. Kesimpulan dari Argumentasi di atas adalah…

• A.

Jika servis restoran baik maka restoran itu mendapat untung

• B.

Jika servis restoran tidak baik, maka restoran itu tidak mendapat untung.

• C.

Jika restoran ingin mendapat untung, maka servisnya baik.

• D.

Jika restoran itu tamunya banyak, maka servisnya baik.

• E.

Jika restoran servisnya tidak baik, maka tamunya tidak banyak

A. Jika servis restoran baik maka restoran itu mendapat untung
Explanation
The conclusion can be inferred from the premises because the first premise states that if the restaurant service is good, then the restaurant will have many customers. The second premise states that if the restaurant has many customers, then the restaurant will make a profit. Therefore, it can be concluded that if the restaurant service is good, then the restaurant will make a profit.

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• 26.

### Diketahui tan A = 3/4  dan A sudut lancip, maka nilai Sin 2A = ….i.          ii.              iii.              iv.               v.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

E. V
Explanation
The correct answer is v. The value of Sin 2A can be determined using the double angle formula for sine. Since A is an acute angle, we can use the formula Sin 2A = 2Sin A * Cos A. Given that Sin A = 3/4, we can substitute this value into the formula to get Sin 2A = 2 * (3/4) * (Cos A). Since A is an acute angle, Cos A is positive. Therefore, the value of Sin 2A is positive.

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• 27.

### Nilai Sin  75O = …..i.                ii.                 iii. iv.               v.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

B. Ii
Explanation
The correct answer is "ii" because the question asks for the value of Sin 75O, which refers to the sine of an angle of 75 degrees. The sine of 75 degrees is a specific value that can be calculated using trigonometric functions.

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• 28.

### Jika diketahui koordinat kutub ( 5, 45o ), maka koordinat kartesiusnya adalah….. i. ( 25, 5)                 iii. ( 5, 5 )                     v . ( 5, 5 ) ii.  ( 5, 5)                 iv.  ( 5 , 5 )

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

C. Iii
Explanation
The correct answer is iii. (5, 5). This is because in polar coordinates, the first value represents the distance from the origin (5 units) and the second value represents the angle from the positive x-axis (45 degrees). To convert to Cartesian coordinates, we use the formulas x = r * cos(theta) and y = r * sin(theta). Plugging in the values, we get x = 5 * cos(45) = 5 * 0.7071 = 3.5355 and y = 5 * sin(45) = 5 * 0.7071 = 3.5355. Therefore, the Cartesian coordinates are (3.5355, 3.5355), which is equivalent to (5, 5) when rounded.

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• 29.

### Ada 6 orang pria dan 3 wanita. Mereka akan membentuk sebuah panitia yang terdiri dari 5 orang. Berapa cara panitia dapat terbentuk bila harus terdiri dari 3 pria dan 2 wanita?

• A.

25

• B.

30

• C.

40

• D.

45

• E.

60

D. 45
Explanation
There are 6 men and 3 women, and the committee needs to consist of 3 men and 2 women. The number of ways to choose 3 men from 6 is given by the combination formula C(6,3) = 6! / (3! * (6-3)!) = 20. Similarly, the number of ways to choose 2 women from 3 is C(3,2) = 3! / (2! * (3-2)!) = 3. Therefore, the total number of ways to form the committee is 20 * 3 = 60. However, since the order of selection does not matter, we need to divide by the number of ways to arrange the committee members, which is 2! = 2. Therefore, the final answer is 60 / 2 = 30.

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• 30.

### Dari 5 macam warna cat yang berbeda akan dibuat warna baru dengan mencampur 2 warna yang ada. Banyak macam warna cat baru yang dapat dibuat adalah ......

• A.

20

• B.

10

• C.

8

• D.

6

• E.

4

B. 10
Explanation
Dari 5 macam warna cat yang berbeda, dapat dibuat kombinasi warna baru dengan mencampur 2 warna yang ada. Untuk setiap pasangan warna yang dicampur, akan menghasilkan satu warna baru. Jadi, jumlah warna baru yang dapat dibuat adalah jumlah kombinasi dari 5 warna yang diambil 2-2, yang dapat dihitung dengan rumus C(5,2) = 10.

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• 31.

### Dua buah dadu dilempar bersama-sama satu kali. Peluang muncul mata dadu berjumlah 9 adalah...........i.                     ii.                iii.              iv.                     v.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

E. V
Explanation
The correct answer is v. The question asks for the probability of getting a sum of 9 when two dice are rolled together. To find this probability, we need to count the number of ways we can get a sum of 9 and divide it by the total number of possible outcomes. There are 4 ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3). Since there are 36 possible outcomes when two dice are rolled (6 possible outcomes for each dice), the probability of getting a sum of 9 is 4/36, which can be simplified to 1/9. Therefore, the correct answer is v.

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• 32.

### Nilai ulangan Matematika dan Fisika pada suatu kelas seperti pada grafik di atas. Mean nilai Matematika dan Fisika berturut – turut adalah........

• A.

6,3 dan 6,4

• B.

7,1 dan 7,3

• C.

7,3 dan 7,1

• D.

8,3 dan 7,5

• E.

8,3 dan 8,1

C. 7,3 dan 7,1
Explanation
The mean nilai Matematika and Fisika are 7.3 and 7.1 respectively because those are the average values obtained from the graph.

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• 33.

• A.

73,5

• B.

74,0

• C.

74,5

• D.

75,0

• E.

75,9

A. 73,5
• 34.

### Simpangan baku dari data 4, 5, 6, 7, 8 adalah……….i.         ii.                iii.              iv.             v.

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

C. Iii
Explanation
The correct answer is iii. The question asks for the standard deviation of the data set 4, 5, 6, 7, 8. Standard deviation is a measure of how spread out the data is from the mean. To calculate the standard deviation, we first find the mean of the data set, which is (4+5+6+7+8)/5 = 6. Then, we subtract the mean from each data point, square the result, and find the average of these squared differences. Finally, we take the square root of this average to get the standard deviation. The standard deviation of the given data set is approximately 1.58.

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• 35.

• A.

-1

• B.

0

• C.

1

• D.

2

• E.

~

D. 2
Explanation
The correct answer is 2 because it is the only numerical value given in the options. The other options (-1, 0, 1) are also numerical values, but they are not the correct answer according to the given question. The symbol "~" does not represent a numerical value and therefore cannot be the correct answer.

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• 36.

• A.

-1

• B.

0

• C.

1

• D.

2

• E.

~

C. 1
Explanation
The correct answer is 1 because it is the only value listed among the options.

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• 37.

### Turunan pertama dari   adalah...... i.       f’(x) = 2x2 + 3x + 5ii.        f’(x) = x2 + 6x + 5iii.       f’(x) = 6x2 + 6x + 5iv.       f’(x) = x2 + 3x - 5v.        f’(x) = -2x2 - 6x + 5

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

A. I
Explanation
The correct answer is i. The given function f'(x) = 2x^2 + 3x + 5 represents the first derivative of the original function f(x).

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• 38.

### Turunan pertama dari f(x) =   adalah..... A.        f’(x) = B.        f’(x) =  C.       f’(x) = D.   f’(x) = E.        f’(x) =

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

D. Iv
Explanation
The correct answer is iv. The notation "f’(x) =" is commonly used to represent the first derivative of a function f(x). Therefore, the correct answer is f’(x) =.

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• 39.

### = ...... i.        6x3 + 5x2 + C          iv.       x3 + 5x + Cii.        3x3 + 5x + C           v.        -x3 + x2 + Ciii.       x3 + 5x2 + C

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

V

D. Iv
Explanation
The given answer, iv., is the correct answer because it represents the expression x3 + 5x + C, which matches the given equation. The other options do not match the given equation, as they have different terms or different orders of the terms. Therefore, iv. is the only option that correctly represents the given equation.

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• 40.

### Hasil dari = ......       i.       0     ii.        ¼ iii.       ½ iv.       1¼ v.        1 ¾

• A.

I

• B.

Ii

• C.

Iii

• D.

Iv

• E.

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