Soal Matematika Kelas Xii IPA

1.

12

14

16

18

20

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2.

2 X 1

2 X 2

2 X 3

3 X 2

3 X 3

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3. Jika f`(x) = 1 -2x dan f(3) = 4, maka f(x) adalah ...

2x2 - x - 11

- 2x2 + x + 19

X2 - 2x - 1

X2 + 2x + 11

- x2 + x + 10

The given question is asking for the function f(x) based on the given information. We are given that f'(x) = 1 - 2x, which means that the derivative of f(x) is 1 - 2x. To find f(x), we need to integrate 1 - 2x with respect to x. Integrating 1 gives x, and integrating -2x gives -x^2. The constant of integration is found by using the given information that f(3) = 4. Plugging in x = 3 into the function, we get 4 = -3^2 + 3 + C, which gives C = 10. Therefore, the function f(x) is -x^2 + x + 10.

Explanation

The given question is asking for the function f(x) based on the given information. We are given that f'(x) = 1 - 2x, which means that the derivative of f(x) is 1 - 2x. To find f(x), we need to integrate 1 - 2x with respect to x. Integrating 1 gives x, and integrating -2x gives -x^2. The constant of integration is found by using the given information that f(3) = 4. Plugging in x = 3 into the function, we get 4 = -3^2 + 3 + C, which gives C = 10. Therefore, the function f(x) is -x^2 + x + 10.

4. Ditentukan titik-titik A(– 2, 1) dan B(3, - 4). Jika C terletak pada garis AB sehingga AC : CB = 8 : - 3, maka koordinat titik C adalah...

(6,7)

( - 6,7)

(6, - 7)

( - 7,6)

( - 7, -6)

The coordinates of point A are (-2, 1) and the coordinates of point B are (3, -4). The ratio AC:CB is given as 8:-3. To find the coordinates of point C, we can use the concept of section formula. Let the coordinates of point C be (x, y). According to the section formula, the x-coordinate of point C is given by (8 * 3 + (-3) * (-2)) / (8 - 3) = 6. Similarly, the y-coordinate of point C is given by (8 * (-4) + (-3) * 1) / (8 - 3) = -7. Therefore, the coordinates of point C are (6, -7).

Explanation

The coordinates of point A are (-2, 1) and the coordinates of point B are (3, -4). The ratio AC:CB is given as 8:-3. To find the coordinates of point C, we can use the concept of section formula. Let the coordinates of point C be (x, y). According to the section formula, the x-coordinate of point C is given by (8 * 3 + (-3) * (-2)) / (8 - 3) = 6. Similarly, the y-coordinate of point C is given by (8 * (-4) + (-3) * 1) / (8 - 3) = -7. Therefore, the coordinates of point C are (6, -7).

5.

3x3 - 4x2 + 5x + c

3x3 - 2x2 + 5x + c

X3 - 2x2 + 5x + c

X3 - 4x2 + 5x + c

- x3 + 2x2 + 5x + c

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Explanation

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6.

- 2 dan 1

- 2 dan - 1

- 2 dan 3

-2 dan - 1

- 3 dan 2

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7.

30o

45o

60o

90o

120o

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8.

4

2

1

- 1

- 4

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9. Sebuah perusahaan pelayaran hendak mengangkut 420 mobil sedan dan 120 bus, dengan 2 kapal feri, yaitu feri jenis A dan feri jenis B. Feri A dapat mengangkut hingga 30 bus dan 30 sedan, sedangkan feri B dapat emngangkut 10 bus dan 70 sedan dalam sekali angkut. Jika biaya menggunakan sebuah feri A dan sebuah feri B masing-masing adalah Rp. 500.000,00 dan Rp. 300.000,00, biaya minimum yang dikeluarkan untuk mengangkut semua kenderaan tersebut menggunakan kedua jenis feri adalah ...

Rp. 2.500.000,00

Rp 2.750.000,00

Rp. 3.000.000,00

Rp. 3.250.000,00

Rp. 3.500.000,00

To minimize the cost, we need to find the most efficient way to transport all the vehicles. The ferry A can carry a maximum of 30 buses and 30 sedans, while the ferry B can carry a maximum of 10 buses and 70 sedans. Since we have 120 buses and 420 sedans, we can use ferry A twice to transport all the buses and ferry B once to transport all the sedans. The cost of using ferry A twice is Rp. 500,000 x 2 = Rp. 1,000,000, and the cost of using ferry B once is Rp. 300,000. Therefore, the total minimum cost is Rp. 1,000,000 + Rp. 300,000 = Rp. 3,000,000.

Explanation

To minimize the cost, we need to find the most efficient way to transport all the vehicles. The ferry A can carry a maximum of 30 buses and 30 sedans, while the ferry B can carry a maximum of 10 buses and 70 sedans. Since we have 120 buses and 420 sedans, we can use ferry A twice to transport all the buses and ferry B once to transport all the sedans. The cost of using ferry A twice is Rp. 500,000 x 2 = Rp. 1,000,000, and the cost of using ferry B once is Rp. 300,000. Therefore, the total minimum cost is Rp. 1,000,000 + Rp. 300,000 = Rp. 3,000,000.

10.

I

II

III

IV

V

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11.

17

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12. Boneka jenis A yang harga belinya Rp. 35.000,00 dijual dengan harga Rp. 59.000,00 per buah, sedangkan boneka jenis B yang harga belinya Rp. 70.000,00 dijual dengan harga Rp. 95.000,00 per buah. Seorang pedagang boneka mempunyai modal Rp. 3.500.000,00 dan kiosnya dapat menampung paling banyak 80 buah boneka akan mendapat keuntungan maksimum jika ia membeli ...

20 buah boneka jenis A dan 60 buah boneka jenis B

60 buah boneka jenis A dan 20 buah boneka jenis B

30 buah boneka jenis A dan 50 buah boneka jenis B

80 buah boneka jenis A saja

80 buah boneka jenis B saja

The peddler will maximize his profit by buying 60 pieces of type A dolls and 20 pieces of type B dolls. This is because the profit margin for type A dolls is higher (selling price - purchase price = Rp. 59,000 - Rp. 35,000 = Rp. 24,000) compared to type B dolls (Rp. 95,000 - Rp. 70,000 = Rp. 25,000). Therefore, by buying more type A dolls, the peddler can make a higher profit. Additionally, buying 60 type A dolls and 20 type B dolls will not exceed the maximum capacity of 80 dolls in his kiosk.

Explanation

The peddler will maximize his profit by buying 60 pieces of type A dolls and 20 pieces of type B dolls. This is because the profit margin for type A dolls is higher (selling price - purchase price = Rp. 59,000 - Rp. 35,000 = Rp. 24,000) compared to type B dolls (Rp. 95,000 - Rp. 70,000 = Rp. 25,000). Therefore, by buying more type A dolls, the peddler can make a higher profit. Additionally, buying 60 type A dolls and 20 type B dolls will not exceed the maximum capacity of 80 dolls in his kiosk.

13.

- 6

- 2

2

3

6

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14.

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15.

2

3

4

5

6

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16.

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17.

Luas daerah yang dibatasi oleh kurva y=x² + 6x, y= x² – 2x, sumbu y dan garis x = 3 adalah . . . satuan luas.

16

18

36

64

72

The area bounded by the curves y=x^2 + 6x, y= x^2 – 2x, the y-axis, and the line x=3 can be calculated by finding the points of intersection between the curves and the line x=3. By solving the equations, we find that the curves intersect at x=1 and x=3. Therefore, the area is the integral of (x^2 + 6x) - (x^2 - 2x) from x=1 to x=3. Simplifying this expression gives us the integral of 8x from x=1 to x=3, which equals 36. Therefore, the correct answer is 36.

Explanation

The area bounded by the curves y=x^2 + 6x, y= x^2 – 2x, the y-axis, and the line x=3 can be calculated by finding the points of intersection between the curves and the line x=3. By solving the equations, we find that the curves intersect at x=1 and x=3. Therefore, the area is the integral of (x^2 + 6x) - (x^2 - 2x) from x=1 to x=3. Simplifying this expression gives us the integral of 8x from x=1 to x=3, which equals 36. Therefore, the correct answer is 36.

18.

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19. Volume benda putar apabila daerah yang diputar terhadap sumbu x memiliki y = x² dan y= -x + 2 adalah . . . satuan volume.

The volume of the rotating object can be determined by finding the area between the curves y = x^2 and y = -x + 2 when rotated around the x-axis. This can be done by integrating the difference between the two curves from their intersection points. The intersection points can be found by setting the two equations equal to each other and solving for x. Once the intersection points are found, the integral can be set up and evaluated to find the volume in the given units.

Explanation

The volume of the rotating object can be determined by finding the area between the curves y = x^2 and y = -x + 2 when rotated around the x-axis. This can be done by integrating the difference between the two curves from their intersection points. The intersection points can be found by setting the two equations equal to each other and solving for x. Once the intersection points are found, the integral can be set up and evaluated to find the volume in the given units.

20. Diketahui empat pernyataan berikut :

Nilai paling besar bagi 4x – 3y adalah 60
Nilai terkecil bagi 3y +2x adalah 60
Jumlah 2y dan 3x tidak boleh melebihi 90
Nilai bagi 3y – x lebih dari 15

Model matematika dalam bentuk sistem pertidaksamaan dari keempat pernyataan tersebut ...

The given statements can be represented by the following system of inequalities:

1) 4x - 3y ≤ 60 (since the maximum value is 60)
2) 3y + 2x ≥ 60 (since the minimum value is 60)
3) 2y + 3x ≤ 90 (since the sum cannot exceed 90)
4) 3y - x > 15 (since the value is greater than 15)

These inequalities represent the mathematical model for the given statements.

Explanation

The given statements can be represented by the following system of inequalities:

1) 4x - 3y ≤ 60 (since the maximum value is 60)
2) 3y + 2x ≥ 60 (since the minimum value is 60)
3) 2y + 3x ≤ 90 (since the sum cannot exceed 90)
4) 3y - x > 15 (since the value is greater than 15)

These inequalities represent the mathematical model for the given statements.