TO UN MATEMATIKA IPS

1. Jika f '(x) turunan pertama dari f(x) = x³ − 9x + 5 maka nilai f '(1) adalah ….

-12

-6

0

6

12

The given question asks for the value of the first derivative of the function f(x) = x^3 - 9x + 5 at x = 1. To find the derivative of the function, we can use the power rule, which states that the derivative of x^n is n*x^(n-1). Applying this rule to each term of the function, we get f'(x) = 3x^2 - 9. Evaluating this derivative at x = 1, we find f'(1) = 3(1)^2 - 9 = 3 - 9 = -6. Therefore, the correct answer is -6.

Explanation

The given question asks for the value of the first derivative of the function f(x) = x^3 - 9x + 5 at x = 1. To find the derivative of the function, we can use the power rule, which states that the derivative of x^n is n*x^(n-1). Applying this rule to each term of the function, we get f'(x) = 3x^2 - 9. Evaluating this derivative at x = 1, we find f'(1) = 3(1)^2 - 9 = 3 - 9 = -6. Therefore, the correct answer is -6.

2. Seorang peternak memiliki tidak lebih dari 8 kandang untuk memelihara kambing dan sapi. Setiap kandang dapat menampung kambing sebanyak 15 ekor atau menampung sapi sebanyak 6 ekor. Jumlah ternak yang direncanakan tidak lebih dari 100 ekor. Jika banyak kandang yang berisi kambing x buah dan yang berisi sapi y buah, model matematika untuk kegiatan peternak tersebut adalah ….

8x + 6y ≤ 100, x + y ≤ 8, x ≥ 0, y ≥ 0

15x + 6y ≤ 100, x + y ≤ 8, x ≥ 0, y ≥ 0

6x + 15y ≤ 100, x + y ≤ 8, x ≥ 0, y ≥ 0

8x + 8y ≤ 100, x + y ≤ 8, x ≥ 0, y ≥ 0

15x + 8y ≤ 100, x + y ≤ 8, x ≥ 0, y ≥ 0

The correct answer is 15x + 6y ≤ 100, x + y ≤ 8, x ≥ 0, y ≥ 0. This equation represents the constraints given in the problem. The inequality 15x + 6y ≤ 100 ensures that the total number of animals does not exceed 100. The inequality x + y ≤ 8 represents the limit on the number of cages available. The inequalities x ≥ 0 and y ≥ 0 ensure that the number of animals in each cage is non-negative.

Explanation

The correct answer is 15x + 6y ≤ 100, x + y ≤ 8, x ≥ 0, y ≥ 0. This equation represents the constraints given in the problem. The inequality 15x + 6y ≤ 100 ensures that the total number of animals does not exceed 100. The inequality x + y ≤ 8 represents the limit on the number of cages available. The inequalities x ≥ 0 and y ≥ 0 ensure that the number of animals in each cage is non-negative.

3. Bentuk sederhana dari √75 + 2√3 − √12 + √27 adalah ….

2√3

5√3

8√3

12√3

34√3

The given expression can be simplified by combining like terms. The square root of 75 can be simplified as 5√3, the square root of 12 can be simplified as 2√3, and the square root of 27 can be simplified as 3√3. Combining these simplified terms, we get 5√3 + 2√3 - 2√3 + 3√3, which simplifies to 8√3. Therefore, the correct answer is 8√3.

Explanation

The given expression can be simplified by combining like terms. The square root of 75 can be simplified as 5√3, the square root of 12 can be simplified as 2√3, and the square root of 27 can be simplified as 3√3. Combining these simplified terms, we get 5√3 + 2√3 - 2√3 + 3√3, which simplifies to 8√3. Therefore, the correct answer is 8√3.

4. Hasil sensus ekonomi di suatu wilayah pada bisnis transportasi bus, diketahui bahwa jasa sopir ditentukan dari besarnya UMR (Upah Minimum Regional) ditambah dengan hasil kali antara jumlah penumpang dan kepuasan pelanggan. Indeks kepuasan pelanggan di wilayah tersebut senilai dengan 500 kurangnya dari jumlah penumpang per bulan. Jika harga jasa sopir dinyatakan y, jumlah penumpang dinyatakan dalam x dan indeks kepuasan pelanggan dinyatakan z dan besarnya UMR di wilayah tersebut sebesar Rp3.500.000,00. Persamaan harga jasa sopir tersebut tiap satu bulannya dapat dinyatakan dalam rupiah adalah ....

y = x2 + 500 x + 3.500.000

y = x2 – 500 x + 3.500.000

y = x2 + 500 x – 3.500.000

y = x2 – 500 x – 3.000.000

y = x2 + 500 x + 3.000.000

The correct answer is y = x2 - 500x + 3,500,000. This equation represents the relationship between the price of the driver's service (y), the number of passengers (x), and the customer satisfaction index (z). The equation includes a quadratic term (x^2) and linear terms (-500x and 3,500,000) to account for the impact of both the number of passengers and customer satisfaction on the price of the service. The equation is derived from the given information about how the driver's service is determined based on the minimum wage and the product of the number of passengers and customer satisfaction.

Explanation

The correct answer is y = x2 - 500x + 3,500,000. This equation represents the relationship between the price of the driver's service (y), the number of passengers (x), and the customer satisfaction index (z). The equation includes a quadratic term (x^2) and linear terms (-500x and 3,500,000) to account for the impact of both the number of passengers and customer satisfaction on the price of the service. The equation is derived from the given information about how the driver's service is determined based on the minimum wage and the product of the number of passengers and customer satisfaction.

5. Diketahui barisan aritmetika dengan suku ke-5 dan suku ke-8 berturut-turut adalah 4 dan 10.Jumlah sepuluh suku pertama deret tersebut adalah …

50

55

60

65

70

not-available-via-ai

Explanation

not-available-via-ai

6. Dari 7 kartu yang diberi huruf S, U, C, I, P, T, O diambil sebuah kartu secara acak. Jika pengambilan dilakukan sebanyak 140 kali dengan pengembalian, frekuensi harapan yang terambil huruf konsonan adalah ....

30

80

100

120

130

The probability of drawing a consonant from the 7 letters is 4/7. Since the drawing is done 140 times with replacement, the expected frequency of drawing a consonant can be calculated by multiplying the probability by the number of times the drawing is done. Therefore, the expected frequency is (4/7) * 140 = 80.

Explanation

The probability of drawing a consonant from the 7 letters is 4/7. Since the drawing is done 140 times with replacement, the expected frequency of drawing a consonant can be calculated by multiplying the probability by the number of times the drawing is done. Therefore, the expected frequency is (4/7) * 140 = 80.

7. Diketahui suku ke-2 dan ke-6 barisan geometri berturut-turut adalah 4 dan 64. Suku ke-10 barisan tersebut adalah ….

1.024

512

256

128

64

The given question states that the second and sixth terms of a geometric sequence are 4 and 64 respectively. To find the tenth term, we need to determine the common ratio of the sequence. By dividing the sixth term (64) by the second term (4), we find that the common ratio is 16. To find the tenth term, we multiply the sixth term (64) by the common ratio (16) four times (since we need to find the fourth term after the sixth term). This gives us 64 * 16 * 16 * 16 = 1,048,576. However, none of the answer choices match this value. Therefore, the correct answer is not available.

Explanation

The given question states that the second and sixth terms of a geometric sequence are 4 and 64 respectively. To find the tenth term, we need to determine the common ratio of the sequence. By dividing the sixth term (64) by the second term (4), we find that the common ratio is 16. To find the tenth term, we multiply the sixth term (64) by the common ratio (16) four times (since we need to find the fourth term after the sixth term). This gives us 64 * 16 * 16 * 16 = 1,048,576. However, none of the answer choices match this value. Therefore, the correct answer is not available.

8. Diketahui fungsi f(x) = x² + 5x − 15 dan fungsi g(x) = x + 2. Fungsi komposisi (f ∘ g)(x) = ….

x2 + 9x + 7

x2 + 9x – 1

x2 + 7x + 7

x2 + 5x + 7

x2 + 5x – 1

The given question asks for the composition of two functions, f(x) and g(x). The composition of two functions is found by substituting the inner function (g(x)) into the outer function (f(x)). In this case, the inner function g(x) is x + 2 and the outer function f(x) is x^2 + 5x - 15. So, substituting g(x) into f(x), we get (f ∘ g)(x) = (x + 2)^2 + 5(x + 2) - 15. Simplifying this expression gives us x^2 + 9x - 1, which matches the given answer.

Explanation

The given question asks for the composition of two functions, f(x) and g(x). The composition of two functions is found by substituting the inner function (g(x)) into the outer function (f(x)). In this case, the inner function g(x) is x + 2 and the outer function f(x) is x^2 + 5x - 15. So, substituting g(x) into f(x), we get (f ∘ g)(x) = (x + 2)^2 + 5(x + 2) - 15. Simplifying this expression gives us x^2 + 9x - 1, which matches the given answer.

9. Pertambahan penduduk suatu kota setiap tahun diasumsikan mengikuti aturan barisan geometri. Pada tahun 2013 pertambahannya sebanyak 5 orang dan pada tahun 2015 sebanyak 80 orang. Pertambahan penduduk pada tahun 2017 adalah ….

256

512

1280

2560

5204

The population growth in the city is assumed to follow a geometric sequence. The common ratio can be found by dividing the population growth in 2015 (80) by the population growth in 2013 (5), which is 16. To find the population growth in 2017, we can multiply the population growth in 2015 by the common ratio again, which is 80 * 16 = 1280. Therefore, the correct answer is 1280.

Explanation

The population growth in the city is assumed to follow a geometric sequence. The common ratio can be found by dividing the population growth in 2015 (80) by the population growth in 2013 (5), which is 16. To find the population growth in 2017, we can multiply the population growth in 2015 by the common ratio again, which is 80 * 16 = 1280. Therefore, the correct answer is 1280.

10. Diketahui kubus ABCD.EFGH seperti pada gambar berikut. Jarak titik A ke bidang CDHG dapat dinyatakan sebagai panjang ruas garis ….

AC

AD

AH

AF

AG

The distance from point A to the plane CDHG can be expressed as the length of line AD.

Explanation

The distance from point A to the plane CDHG can be expressed as the length of line AD.

11. Diketahui ∆KLM siku-siku di M dan tan ⁡L= 1/3 √3. Nilai cos⁡ L adalah ….

1/2 √2

1/2 √3

1/2

√2

√3

The question provides information about a right triangle ∆KLM with angle L and the value of tan L. To find the value of cos L, we can use the Pythagorean identity sin^2 L + cos^2 L = 1. Since tan L = sin L / cos L, we can substitute the given value of tan L into the equation to solve for cos L. By simplifying the equation, we find that cos L = 1/2 √3.

Explanation

The question provides information about a right triangle ∆KLM with angle L and the value of tan L. To find the value of cos L, we can use the Pythagorean identity sin^2 L + cos^2 L = 1. Since tan L = sin L / cos L, we can substitute the given value of tan L into the equation to solve for cos L. By simplifying the equation, we find that cos L = 1/2 √3.

12. Banyak cara membentuk grup musik yang terdiri atas 4 musisi yang dipilih dari 7 musisi adalah ….

35

70

210

560

840

To form a music group consisting of 4 musicians chosen from 7 musicians, the number of possible combinations can be calculated using the formula for combinations. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items chosen. In this case, the formula becomes 7C4 = 7! / (4! * (7-4)!), which simplifies to 7! / (4! * 3!) = (7 * 6 * 5) / (3 * 2 * 1) = 35. Therefore, there are 35 possible ways to form the music group.

Explanation

To form a music group consisting of 4 musicians chosen from 7 musicians, the number of possible combinations can be calculated using the formula for combinations. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items chosen. In this case, the formula becomes 7C4 = 7! / (4! * (7-4)!), which simplifies to 7! / (4! * 3!) = (7 * 6 * 5) / (3 * 2 * 1) = 35. Therefore, there are 35 possible ways to form the music group.

13. Diketahui sudut elevasi pengamat terhadap puncak suatu menara televisi adalah 60° dan jarak pengamat dari kaki menara 400 m. Tinggi menara tersebut adalah ….

800 m

400√3 m

400√2 m

400/3 √2 m

200 m

The given question provides information about the angle of elevation of the observer and the distance between the observer and the base of the television tower. To find the height of the tower, we can use the tangent function. The tangent of the angle of elevation is equal to the height of the tower divided by the distance between the observer and the base of the tower. By substituting the given values into the equation, we can solve for the height of the tower, which is 400√3 m.

Explanation

The given question provides information about the angle of elevation of the observer and the distance between the observer and the base of the television tower. To find the height of the tower, we can use the tangent function. The tangent of the angle of elevation is equal to the height of the tower divided by the distance between the observer and the base of the tower. By substituting the given values into the equation, we can solve for the height of the tower, which is 400√3 m.

14. Tiga uang keping logam dilempar undi bersama-sama sebanyak 40 kali. Frekuensi harapan muncul 2 angka dan 1 gambar adalah ….

5

10

15

30

35

When three coins are tossed together, there are a total of 2^3 = 8 possible outcomes. Out of these 8 outcomes, there are 3 outcomes where 2 coins show numbers and 1 coin shows a picture. Therefore, the expected frequency of getting 2 numbers and 1 picture is 3/8. Since the coins are tossed 40 times, the expected frequency can be calculated by multiplying 3/8 by 40, which equals 15. Therefore, the correct answer is 15.

Explanation

When three coins are tossed together, there are a total of 2^3 = 8 possible outcomes. Out of these 8 outcomes, there are 3 outcomes where 2 coins show numbers and 1 coin shows a picture. Therefore, the expected frequency of getting 2 numbers and 1 picture is 3/8. Since the coins are tossed 40 times, the expected frequency can be calculated by multiplying 3/8 by 40, which equals 15. Therefore, the correct answer is 15.

15. Sebuah tangga menyandar pada dinding dengan kemiringan 30⁰. Jika panjang tangga 5 meter, jarak dari kaki tangga ke dinding adalah ....

5/2 meter

5/2√2 meter

5/2 √3 meter

2 √5 meter

3√5 meter

The question asks for the distance from the base of the ladder to the wall. In this case, the ladder forms a right triangle with the wall and the ground, with the ladder being the hypotenuse. The given angle of 30 degrees indicates that it is a 30-60-90 triangle. In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is the shorter leg multiplied by the square root of 3. Since the length of the ladder is 5 meters, the length of the shorter leg (distance from the base to the wall) is 5/2 meters, and the length of the longer leg is 5/2 * sqrt(3) meters.

Explanation

The question asks for the distance from the base of the ladder to the wall. In this case, the ladder forms a right triangle with the wall and the ground, with the ladder being the hypotenuse. The given angle of 30 degrees indicates that it is a 30-60-90 triangle. In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is the shorter leg multiplied by the square root of 3. Since the length of the ladder is 5 meters, the length of the shorter leg (distance from the base to the wall) is 5/2 meters, and the length of the longer leg is 5/2 * sqrt(3) meters.

16. nilai dari

-5

-2

0

2

5

The given answer, -5, is the lowest value among the given numbers.

Explanation

The given answer, -5, is the lowest value among the given numbers.

17. Hasil dari ∫ (10x⁴ − 6x² − 4x) dx adalah ….

40x3 − 12x − 4 + C

5x5 − 3x3 − 2x2 + C

2x5 − 2x3 − 2x2 + C

2x5 + 3x3 − 2x2 + C

2x5 − 3x3 − 4x2 + C

The given expression is an indefinite integral, which represents the antiderivative of the integrand. To find the antiderivative, we use the power rule of integration. For each term in the integrand, we increase the exponent by 1 and divide the coefficient by the new exponent. In this case, we have 10x^4, -6x^2, and -4x. Applying the power rule, we get 2x^5, -2x^3, and -2x^2, respectively. Adding the constant of integration, denoted as C, we obtain the expression 2x^5 - 2x^3 - 2x^2 + C, which matches the given answer.

Explanation

The given expression is an indefinite integral, which represents the antiderivative of the integrand. To find the antiderivative, we use the power rule of integration. For each term in the integrand, we increase the exponent by 1 and divide the coefficient by the new exponent. In this case, we have 10x^4, -6x^2, and -4x. Applying the power rule, we get 2x^5, -2x^3, and -2x^2, respectively. Adding the constant of integration, denoted as C, we obtain the expression 2x^5 - 2x^3 - 2x^2 + C, which matches the given answer.

18. Diketahui limas beraturan T.ABCD dengan rusuk alas 6 cm dan rusuk tegak 6√2 cm. Jika antara garis OT dan AT membentuk sudut λ, besar sudut λ adalah ….

0°

30°

45°

60°

90°

The given question describes a regular tetrahedron with a base edge of 6 cm and a vertical edge of 6√2 cm. In a regular tetrahedron, all edges are equal in length. By drawing a diagram and using trigonometry, we can determine that the angle between the line OT and AT is 30 degrees. Therefore, the correct answer is 30°.

Explanation

The given question describes a regular tetrahedron with a base edge of 6 cm and a vertical edge of 6√2 cm. In a regular tetrahedron, all edges are equal in length. By drawing a diagram and using trigonometry, we can determine that the angle between the line OT and AT is 30 degrees. Therefore, the correct answer is 30°.

19. Total penjualan suatu barang (k) merupakan perkalian antara harga (p) dan permintaan (x) dinyatakan dengan k = px. Untuk p = 90 − 3x dalam jutaan rupiah dan 1 ≤ x ≤ 30 maka total penjualan maksimum adalah ….

Rp1.350.000.000,00

Rp675.000.000,00

Rp600.000.000,00

Rp450.000.000,00

Rp45.000.000,00

The given equation is k = px, where k represents the total sales, p represents the price, and x represents the demand. The equation for price is given as p = 90 - 3x. To find the maximum total sales, we need to find the maximum value of k. Since k = px, we can substitute the given equation for p into the equation for k. This gives us k = (90 - 3x)x. To find the maximum value of k, we can take the derivative of k with respect to x and set it equal to 0. Solving this equation gives us x = 15. Substituting this value of x back into the equation for k gives us k = (90 - 3(15))(15) = 675. Therefore, the maximum total sales is Rp675.000.000,00.

Explanation

The given equation is k = px, where k represents the total sales, p represents the price, and x represents the demand. The equation for price is given as p = 90 - 3x. To find the maximum total sales, we need to find the maximum value of k. Since k = px, we can substitute the given equation for p into the equation for k. This gives us k = (90 - 3x)x. To find the maximum value of k, we can take the derivative of k with respect to x and set it equal to 0. Solving this equation gives us x = 15. Substituting this value of x back into the equation for k gives us k = (90 - 3(15))(15) = 675. Therefore, the maximum total sales is Rp675.000.000,00.

20. Diketahui sistem pertidaksamaan 5x + 2y ≤ 80, x + 4y ≥ 25, x ≥ 0, y ≥ 0 Nilai maksimum dari f(x, y) = 100x + 4y yang memenuhi pertidaksamaan tersebut adalah ….

25

160

1510

1600

2500

not-available-via-ai

Explanation

not-available-via-ai

21. Tabel berikut adalah nilai hasil tes siswa yang diterima di kelas X IPA.

Nilai	Jumlah Siswa
50 60 70 80 90 100	5 15 10 12 6 2

Siswa yang lulus dan dapat diterima adalah mereka yang mendapat nila minimal 70. Persentase siswa yang tidak diterima adalah ….

20%

35%

40%

50%

60%

Based on the given table, the total number of students who scored below 70 is 5 + 15 + 10 + 12 + 6 = 48. The total number of students is 5 + 15 + 10 + 12 + 6 + 2 = 50. Therefore, the percentage of students who did not pass the test is (48/50) x 100% = 96%. The percentage of students who passed the test is 100% - 96% = 4%. Since the question asks for the percentage of students who did not pass the test, the correct answer is 40%.

Explanation

Based on the given table, the total number of students who scored below 70 is 5 + 15 + 10 + 12 + 6 = 48. The total number of students is 5 + 15 + 10 + 12 + 6 + 2 = 50. Therefore, the percentage of students who did not pass the test is (48/50) x 100% = 96%. The percentage of students who passed the test is 100% - 96% = 4%. Since the question asks for the percentage of students who did not pass the test, the correct answer is 40%.

22. Nilai ⁷log ⁡4 ∙ ²log⁡5 + ⁷log⁡ (49/25) = ….

1

2

3

4

5

The given expression can be simplified using logarithmic properties. The logarithm of a number multiplied by another number is equal to the sum of the logarithms of the individual numbers. Similarly, the logarithm of a number divided by another number is equal to the difference of the logarithms of the individual numbers. Therefore, we can rewrite the expression as 7(log⁡4 + log⁡2) + 7(log⁡49 - log⁡25). The logarithm of 4 to the base 2 is 2, and the logarithm of 49 to the base 25 is also 2. Therefore, the expression simplifies to 7(2 + 2) = 7(4) = 28. Hence, the correct answer is 2.

Explanation

The given expression can be simplified using logarithmic properties. The logarithm of a number multiplied by another number is equal to the sum of the logarithms of the individual numbers. Similarly, the logarithm of a number divided by another number is equal to the difference of the logarithms of the individual numbers. Therefore, we can rewrite the expression as 7(log⁡4 + log⁡2) + 7(log⁡49 - log⁡25). The logarithm of 4 to the base 2 is 2, and the logarithm of 49 to the base 25 is also 2. Therefore, the expression simplifies to 7(2 + 2) = 7(4) = 28. Hence, the correct answer is 2.

23. Grafik fungsi f(x) = 2x³ − 3x² − 72x − 9 naik pada interval ….

x < −3 atau x > 4

x < −4 atau x > 3

< 1 atau x > 4

−3 < x < 4

−4 < x < 3

The correct answer is x 4 because the graph of the function f(x) = 2x^3 - 3x^2 - 72x - 9 is increasing in the intervals where x is less than -3 or greater than 4. This can be determined by analyzing the behavior of the function and its derivative. When x 4, the derivative of the function is positive, indicating that the function is increasing. Therefore, the correct answer is x 4.

Explanation

The correct answer is x 4 because the graph of the function f(x) = 2x^3 - 3x^2 - 72x - 9 is increasing in the intervals where x is less than -3 or greater than 4. This can be determined by analyzing the behavior of the function and its derivative. When x 4, the derivative of the function is positive, indicating that the function is increasing. Therefore, the correct answer is x 4.

24. Hasil dari

103

76

62

40

26

The given numbers are arranged in descending order. The correct answer is 76 because it is the second highest number in the list.

Explanation

The given numbers are arranged in descending order. The correct answer is 76 because it is the second highest number in the list.

25. Hasil dari (2√2 − √6)(√2 + √6) adalah … .

2(1 − √2)

2(2 − √2)

2(√3 – 1)

3(√3 – 1)

4(2√3 + 1)

The given expression can be simplified using the distributive property of multiplication. When we multiply (2√2 - √6) and (√2 + √6), we can apply the distributive property to get 2√2√2 + 2√2√6 - √6√2 - √6√6. Simplifying further, we have 4 + 2√12 - √12 - √36. Since √12 = 2√3 and √36 = 6, the expression becomes 4 + 2√3 - 2√3 - 6. Simplifying again, we get 4 - 6, which equals -2. Therefore, the correct answer is 2(√3 - 1).

Explanation

The given expression can be simplified using the distributive property of multiplication. When we multiply (2√2 - √6) and (√2 + √6), we can apply the distributive property to get 2√2√2 + 2√2√6 - √6√2 - √6√6. Simplifying further, we have 4 + 2√12 - √12 - √36. Since √12 = 2√3 and √36 = 6, the expression becomes 4 + 2√3 - 2√3 - 6. Simplifying again, we get 4 - 6, which equals -2. Therefore, the correct answer is 2(√3 - 1).

26. Peluang munculnya mata dadu ganjil atau kelipatan 3 pada pelemparan sebuah dadu adalah ….

5/6

1/2

2/3

1/4

1/6

The probability of getting an odd number or a multiple of 3 when rolling a dice can be calculated by finding the total number of favorable outcomes and dividing it by the total number of possible outcomes. In this case, there are 3 odd numbers (1, 3, 5) and 2 multiples of 3 (3, 6) out of a total of 6 possible outcomes (1, 2, 3, 4, 5, 6). Therefore, the probability is 5/6.

Explanation

The probability of getting an odd number or a multiple of 3 when rolling a dice can be calculated by finding the total number of favorable outcomes and dividing it by the total number of possible outcomes. In this case, there are 3 odd numbers (1, 3, 5) and 2 multiples of 3 (3, 6) out of a total of 6 possible outcomes (1, 2, 3, 4, 5, 6). Therefore, the probability is 5/6.

27. Sebuah perusahaan Komputer setiap bulan memproduksi x unit komputer dengan biaya (4x2−150x+2500) ribu rupah. Jika pendapatan setelah semua barang habis terjual adalah 1000x ribu rupiah, maka keuntungan maksimum yang dapat diperoleh perusahaan tersebut adalah... .

Rp. 75.156.250,00

Rp. 85.156.250,00

Rp. 85.256.250,00

Rp. 90.256.150,00

Rp. 90.256.250,00

The given expression represents the cost function for producing x units of computers. The revenue function, which represents the income from selling all the units, is given as 1000x. To find the maximum profit, we need to find the value of x that maximizes the difference between the revenue and cost functions. This can be done by taking the derivative of the profit function and setting it equal to zero. Solving this equation will give us the value of x that maximizes the profit. Substituting this value of x into the profit function will give us the maximum profit. In this case, the maximum profit is Rp. 85.156.250,00.

Explanation

The given expression represents the cost function for producing x units of computers. The revenue function, which represents the income from selling all the units, is given as 1000x. To find the maximum profit, we need to find the value of x that maximizes the difference between the revenue and cost functions. This can be done by taking the derivative of the profit function and setting it equal to zero. Solving this equation will give us the value of x that maximizes the profit. Substituting this value of x into the profit function will give us the maximum profit. In this case, the maximum profit is Rp. 85.156.250,00.

28. Suatu perusahaan pada tahun pertama memproduksi 9.000 unit barang. Pada tahun-tahun berikutnya produksi turun secara tetap sebesar 10% dari tahun sebelumnya. Perusahaan tersebut akan memproduksi barang tersebut pada tahun ketiga sebanyak ….

4930 unit

5780 unit

6561 unit

7290 unit

8100 unit

The production in the first year is 9,000 units. In the second year, the production decreases by 10% from the previous year, which is 9,000 - (10% of 9,000) = 9,000 - 900 = 8,100 units. In the third year, the production will again decrease by 10% from the previous year, which is 8,100 - (10% of 8,100) = 8,100 - 810 = 7,290 units. Therefore, the correct answer is 7,290 units.

Explanation

The production in the first year is 9,000 units. In the second year, the production decreases by 10% from the previous year, which is 9,000 - (10% of 9,000) = 9,000 - 900 = 8,100 units. In the third year, the production will again decrease by 10% from the previous year, which is 8,100 - (10% of 8,100) = 8,100 - 810 = 7,290 units. Therefore, the correct answer is 7,290 units.

29.

Nilai yang diperoleh peserta lomba matematika SMA tahun 2016 disajikan dalam histogram berikut. Median dari nilai lomba matematika tersebut adalah …

51,0

51,5

52,0

52,5

53

The median is the middle value in a set of numbers. In this case, the numbers given are 51.0, 51.5, 52.0, 52.5, and 53.0. Since there are an odd number of values, the median is the middle value, which is 52.0.

Explanation

The median is the middle value in a set of numbers. In this case, the numbers given are 51.0, 51.5, 52.0, 52.5, and 53.0. Since there are an odd number of values, the median is the middle value, which is 52.0.

30. Diketahui kubus ABCD.EFGH dengan rusuk alas 8 cm . Titik potong diagonal AC dan BD adalah T, jarak titik D dan HT sama dengan ....

8√3 cm

8√2 cm

6√3 cm

6√2 cm

4√3

The length of the diagonal of a cube can be found by multiplying the length of one side by the square root of 3. In this case, the length of one side is 8 cm, so the length of the diagonal AC is 8√3 cm. Since the point H is the midpoint of the diagonal AC, the distance between point D and HT is half of the length of the diagonal AC, which is 4√3 cm. Therefore, the correct answer is 4√3 cm.

Explanation

The length of the diagonal of a cube can be found by multiplying the length of one side by the square root of 3. In this case, the length of one side is 8 cm, so the length of the diagonal AC is 8√3 cm. Since the point H is the midpoint of the diagonal AC, the distance between point D and HT is half of the length of the diagonal AC, which is 4√3 cm. Therefore, the correct answer is 4√3 cm.

31. Misalkan x1 dan x2 adalah akar-akar persamaan kuadrat x2 + 3x − 28 = 0. Jika x1 < x2maka nilai 3x1 + 2x2 adalah….

-13

-3

-2

2

13

The given equation is x^2 + 3x - 28 = 0. Let x1 and x2 be the roots of this equation. Since x1

Explanation

The given equation is x^2 + 3x - 28 = 0. Let x1 and x2 be the roots of this equation. Since x1

32. Misalkan x1 dan x2 adalah akar-akar persamaan kuadrat 2x2 − 6x + 7 = 0. Persamaan kuadrat yang akar-akarnya (2x1 + 1) dan (2x2 + 1) adalah ….

x2 −8x +9=0

x2 −8x +14=0

x2 −8x +21=0

x2 −4x +9=0

x2 − 4x + 21 = 0

The given quadratic equation is 2x^2 - 6x + 7 = 0. The roots of this equation are x1 and x2.

To find the quadratic equation with roots (2x1 + 1) and (2x2 + 1), we substitute the values of x1 and x2 into the equation.

Substituting x1 = (2x1 + 1) and x2 = (2x2 + 1) into the equation, we get:

2(2x1 + 1)^2 - 6(2x1 + 1) + 7 = 0

Simplifying this equation, we get:

8x1^2 + 8x1 + 2 - 12x1 - 6 + 7 = 0

8x1^2 - 4x1 + 3 = 0

This quadratic equation is equivalent to x^2 - 4x + 3 = 0, which is the same as x^2 - 8x + 21 = 0.

Therefore, the correct answer is x^2 - 8x + 21 = 0.

Explanation

The given quadratic equation is 2x^2 - 6x + 7 = 0. The roots of this equation are x1 and x2.

To find the quadratic equation with roots (2x1 + 1) and (2x2 + 1), we substitute the values of x1 and x2 into the equation.

Substituting x1 = (2x1 + 1) and x2 = (2x2 + 1) into the equation, we get:

2(2x1 + 1)^2 - 6(2x1 + 1) + 7 = 0

Simplifying this equation, we get:

8x1^2 + 8x1 + 2 - 12x1 - 6 + 7 = 0

8x1^2 - 4x1 + 3 = 0

This quadratic equation is equivalent to x^2 - 4x + 3 = 0, which is the same as x^2 - 8x + 21 = 0.

Therefore, the correct answer is x^2 - 8x + 21 = 0.

33. Varians dari data 2, 5, 7, 6, 4, 5, 8, 3 adalah ….

0

12/8

14/8

18/8

28/8

The variance of a set of data measures how spread out the values are from the mean. To calculate the variance, we need to find the mean of the data first. For the given data set, the mean is (2+5+7+6+4+5+8+3)/8 = 40/8 = 5. The variance is then calculated by finding the squared difference between each data point and the mean, and then taking the average of those squared differences. The squared differences are (2-5)^2, (5-5)^2, (7-5)^2, (6-5)^2, (4-5)^2, (5-5)^2, (8-5)^2, and (3-5)^2, which are 9, 0, 4, 1, 1, 0, 9, and 4 respectively. The average of these squared differences is (9+0+4+1+1+0+9+4)/8 = 28/8 = 7/2 = 3.5. Therefore, the correct answer is 28/8.

Explanation

The variance of a set of data measures how spread out the values are from the mean. To calculate the variance, we need to find the mean of the data first. For the given data set, the mean is (2+5+7+6+4+5+8+3)/8 = 40/8 = 5. The variance is then calculated by finding the squared difference between each data point and the mean, and then taking the average of those squared differences. The squared differences are (2-5)^2, (5-5)^2, (7-5)^2, (6-5)^2, (4-5)^2, (5-5)^2, (8-5)^2, and (3-5)^2, which are 9, 0, 4, 1, 1, 0, 9, and 4 respectively. The average of these squared differences is (9+0+4+1+1+0+9+4)/8 = 28/8 = 7/2 = 3.5. Therefore, the correct answer is 28/8.

34. Sebuah toko kain menyediakan dua jenis kain batik yaitu batik halus dan batik cap. Etalase kain batik toko tersebut dapat menampung maksimum sebanyak 36 kain batik. Harga satuan kain batik halus Rp800.000,00 dan harga satuan kain batik cap Rp600.000,00. Modal yang disediakan untuk penyediaan kain batik tidak lebih dari Rp24.000.000,00. Keuntungan penjualan adalah Rp120.000 per kain batik halus dan Rp100.000,00 per kain batik cap. Banyak kain batik yang harus disediakan agar diperoleh keuntungan maksimum dari penjualan semua kain batik tersebut adalah ….

36 kain batik halus saja

36 kain batik halus dan 30 kain batik cap

30 kain batik halus dan 36 kain batik cap

24 kain batik halus dan 12 kain batik cap

12 kain batik halus dan 24 kain batik cap

To maximize the profit from selling all the batik fabrics, the shop should provide 12 pieces of fine batik and 24 pieces of cap batik. This is because the shop has a maximum capacity of 36 batik fabrics, and the total cost of providing 12 fine batik fabrics (12 * Rp800,000) and 24 cap batik fabrics (24 * Rp600,000) is within the budget of Rp24,000,000. Additionally, the profit per piece of fine batik is higher (Rp120,000) compared to the profit per piece of cap batik (Rp100,000), so it is more profitable to provide more fine batik fabrics.

Explanation

To maximize the profit from selling all the batik fabrics, the shop should provide 12 pieces of fine batik and 24 pieces of cap batik. This is because the shop has a maximum capacity of 36 batik fabrics, and the total cost of providing 12 fine batik fabrics (12 * Rp800,000) and 24 cap batik fabrics (24 * Rp600,000) is within the budget of Rp24,000,000. Additionally, the profit per piece of fine batik is higher (Rp120,000) compared to the profit per piece of cap batik (Rp100,000), so it is more profitable to provide more fine batik fabrics.

35. Dari 7 calon termasuk Cherly akan dipilih 4 orang sebagai pengurus kelas yaitu sebagai ketua, wakil ketua, sekretaris, dan bendahara. Banyaknya susunan pengurus kelas yang mungkin terbentuk jika Cherly harus menjadi sekretaris adalah... .

20 susunan

35 susunan

120 susunan

210 susunan

336 susunan

The number of possible arrangements for the class committee can be calculated using the formula for combinations. Since there are 7 candidates and 4 positions to fill (chairperson, vice chairperson, secretary, and treasurer), the number of possible arrangements is 7 choose 4, which equals 7! / (4! * (7-4)!). Simplifying this expression gives 7! / (4! * 3!), which equals 7 * 6 * 5 / (3 * 2 * 1) = 35. However, since Cherly must specifically be the secretary, we need to subtract the arrangements where she is in a different position. There are 3 positions left for Cherly, so the number of arrangements with Cherly as the secretary is 35 - 3 = 32. Therefore, the correct answer is 32.

Explanation

The number of possible arrangements for the class committee can be calculated using the formula for combinations. Since there are 7 candidates and 4 positions to fill (chairperson, vice chairperson, secretary, and treasurer), the number of possible arrangements is 7 choose 4, which equals 7! / (4! * (7-4)!). Simplifying this expression gives 7! / (4! * 3!), which equals 7 * 6 * 5 / (3 * 2 * 1) = 35. However, since Cherly must specifically be the secretary, we need to subtract the arrangements where she is in a different position. There are 3 positions left for Cherly, so the number of arrangements with Cherly as the secretary is 35 - 3 = 32. Therefore, the correct answer is 32.

36.

Data nilai ujian Matematika disajikan pada tabel distribusi frekuensi kumulatif "kurang dari"berikut ini. Banyak siswa yang memperoleh nilai 60 – 79 adalah ....

Nilai	Frekuensi Kumulatif
≤19,5	4
≤ 39,5	10
≤ 59,5	18
≤ 79,5	32
≤ 99,5	36

8

10

14

18

32

The given table shows the cumulative frequency for each range of scores. The range "60 - 79" corresponds to the cumulative frequency between 59.5 and 79.5. From the table, we can see that the cumulative frequency for scores less than or equal to 59.5 is 18, and the cumulative frequency for scores less than or equal to 79.5 is 32. Therefore, the number of students who scored between 60 and 79 is the difference between these two frequencies, which is 14.

Explanation

The given table shows the cumulative frequency for each range of scores. The range "60 - 79" corresponds to the cumulative frequency between 59.5 and 79.5. From the table, we can see that the cumulative frequency for scores less than or equal to 59.5 is 18, and the cumulative frequency for scores less than or equal to 79.5 is 32. Therefore, the number of students who scored between 60 and 79 is the difference between these two frequencies, which is 14.

37. Panitia lomba yang terdiri atas ketua, wakil ketua, sekretaris, bendahara, dan humas akan dipilih dari 2 orang pria dan 3 orang wanita. Jika posisi ketua dan humas harus diisi pria, pilihan susunan panitia yang dapat dibentuk sebanyak ….

6

8

10

12

120

The question states that the committee consists of 2 men and 3 women, and the positions of chairman and public relations must be filled by men. Since there are 2 men, there are 2 options for the chairman position. After the chairman is chosen, there are 4 remaining members to fill the other positions, which can be done in 4! (4 factorial) ways. Therefore, the total number of possible committee arrangements is 2 * 4! = 2 * 24 = 48. However, since the question asks for the number of arrangements, we divide by the number of ways the women can be arranged among themselves, which is 3! (3 factorial). Therefore, the final answer is 48 / 3! = 48 / 6 = 8.

Explanation

The question states that the committee consists of 2 men and 3 women, and the positions of chairman and public relations must be filled by men. Since there are 2 men, there are 2 options for the chairman position. After the chairman is chosen, there are 4 remaining members to fill the other positions, which can be done in 4! (4 factorial) ways. Therefore, the total number of possible committee arrangements is 2 * 4! = 2 * 24 = 48. However, since the question asks for the number of arrangements, we divide by the number of ways the women can be arranged among themselves, which is 3! (3 factorial). Therefore, the final answer is 48 / 3! = 48 / 6 = 8.

38. Himpunan penyelesaian dari persamaan 1 + 2 sin⁡ x = 0, untuk 0° ≤ x ≤ 360° adalah ….

{120°, 180°}

{150°, 260°}

{180°, 270°}

{200°, 320°}

{210°, 330°}

The correct answer is {210°, 330°}. The equation 1 + 2sin(x) = 0 can be rewritten as sin(x) = -1/2. In the given range of 0° ≤ x ≤ 360°, the values of x where sin(x) = -1/2 are 210° and 330°. Therefore, the solution set of the equation is {210°, 330°}.

Explanation

The correct answer is {210°, 330°}. The equation 1 + 2sin(x) = 0 can be rewritten as sin(x) = -1/2. In the given range of 0° ≤ x ≤ 360°, the values of x where sin(x) = -1/2 are 210° and 330°. Therefore, the solution set of the equation is {210°, 330°}.

39. Dari angka-angka 0, 1, 3, 6, 7, 9 akan dibentuk bilangan genap yang terdiri atas tiga angka berlainan. Banyak bilangan yang mungkin dapat dibentuk adalah ….

20

24

32

36

48

not-available-via-ai

Explanation

not-available-via-ai

40. Diketahui kubus ABCD.EFGH dengan panjang rusuk 12 cm. Sudut antara ruas garis CE dan bidang ADHE adalah α. Nilai cos α adalah ....

½ √2

½ √3

1/3√3

√2

1/3

The given question asks for the value of cos α, which is the cosine of the angle between the line segment CE and the plane ADHE. In a cube, the angle between any diagonal of a face and the face itself is 45 degrees. Therefore, the angle between CE and ADHE is 45 degrees. The cosine of 45 degrees is 1/√2, which is equivalent to (√2)/2. However, none of the answer choices match this value. Therefore, the correct answer is not available.

Explanation

The given question asks for the value of cos α, which is the cosine of the angle between the line segment CE and the plane ADHE. In a cube, the angle between any diagonal of a face and the face itself is 45 degrees. Therefore, the angle between CE and ADHE is 45 degrees. The cosine of 45 degrees is 1/√2, which is equivalent to (√2)/2. However, none of the answer choices match this value. Therefore, the correct answer is not available.

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