Try Out Online II ( Matematika IPA )

1) Seorang petani mangga mencatat hasil panennya selama satu bulan pertama. Setiap harinya mengalami kenaikan tetap dimulai hari pertama, kedua, ketiga berturut-turut 17 kg, 19 kg, 21 kg dan seterusnya. Jumlah seluruh hasil panen selama satu bulan (30 hari) adalah ....

1180 kg

1260 kg

1280 kg

1380 kg

2760 kg

The farmer records the harvest results for the first month, with a daily increase of 17 kg, 19 kg, 21 kg, and so on. To find the total harvest for the month, we can calculate the sum of an arithmetic series. The formula for the sum of an arithmetic series is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, the first term is 17 kg and the last term is 17 + 19 + 21 + ... + 61. Since the terms are increasing by 2 kg each time, we can find the number of terms using the formula l = a + (n-1)d, where d is the common difference. Rearranging the formula, we get n = (l - a + d)/d. Plugging in the values, we find that n = (61 - 17 + 2)/2 = 23. Therefore, the last term is 61 kg. Plugging the values into the formula for the sum, we get Sn = (23/2)(17 + 61) = 1380 kg.

Explanation

The farmer records the harvest results for the first month, with a daily increase of 17 kg, 19 kg, 21 kg, and so on. To find the total harvest for the month, we can calculate the sum of an arithmetic series. The formula for the sum of an arithmetic series is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, the first term is 17 kg and the last term is 17 + 19 + 21 + ... + 61. Since the terms are increasing by 2 kg each time, we can find the number of terms using the formula l = a + (n-1)d, where d is the common difference. Rearranging the formula, we get n = (l - a + d)/d. Plugging in the values, we find that n = (61 - 17 + 2)/2 = 23. Therefore, the last term is 61 kg. Plugging the values into the formula for the sum, we get Sn = (23/2)(17 + 61) = 1380 kg.

2) Jika diketahui f(x) = x + 1 dan g(x) = 3x² + x + 3 maka (gof)(x) = ....

3x2 + x + 4

3x2 + x + 7

3x2 + 7x + 7

7x2 + 3x + 3

7x2 + 7x + 3

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 output of one function into the input of the other function. In this case, we substitute f(x) = x + 1 into g(x), which gives us g(f(x)) = 3(f(x))^2 + f(x) + 3. Simplifying this expression, we get 3(x + 1)^2 + (x + 1) + 3 = 3x^2 + 7x + 7. Therefore, the correct answer is 3x^2 + 7x + 7.

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 output of one function into the input of the other function. In this case, we substitute f(x) = x + 1 into g(x), which gives us g(f(x)) = 3(f(x))^2 + f(x) + 3. Simplifying this expression, we get 3(x + 1)^2 + (x + 1) + 3 = 3x^2 + 7x + 7. Therefore, the correct answer is 3x^2 + 7x + 7.

3) Dari 6 orang pria dan 4 wanita dipilih 3 orang terdiri dari 2 orang pria dan 1 orang wanita. Peluang pemilihan tersebut adalah ... .

The probability of selecting 3 people consisting of 2 men and 1 woman from a group of 6 men and 4 women can be calculated using the concept of combinations. The total number of ways to select 3 people from the group is given by the combination formula, which is 10C3. The number of ways to select 2 men from the 6 available men is 6C2, and the number of ways to select 1 woman from the 4 available women is 4C1. Therefore, the probability is equal to (6C2 * 4C1) / 10C3.

Explanation

The probability of selecting 3 people consisting of 2 men and 1 woman from a group of 6 men and 4 women can be calculated using the concept of combinations. The total number of ways to select 3 people from the group is given by the combination formula, which is 10C3. The number of ways to select 2 men from the 6 available men is 6C2, and the number of ways to select 1 woman from the 4 available women is 4C1. Therefore, the probability is equal to (6C2 * 4C1) / 10C3.

4) Adik membeli 2 kg mangga dan 3 kg salak, ia membayar Rp60.000,00. Kakak membeli 3 kg mangga dan 5 kg salak di toko buah yang sama ia membayar Rp95.000,00. Bibi membeli 3 kg mangga dan 3 kg salak ditoko buah yang sama, ia membayar dengan 2 lembar uang Rp50.000,00, maka sisa uang (kembalian) yang di terima Bibi adalah ….

Rp. 15.000,00

Rp. 25.000,00

Rp. 35.000,00

Rp. 55.000,00

Rp. 75.000,00

The total cost of 2 kg of mango and 3 kg of snake fruit is Rp60,000. The total cost of 3 kg of mango and 5 kg of snake fruit is Rp95,000. Therefore, the cost of 1 kg of mango is Rp15,000 and the cost of 1 kg of snake fruit is Rp5,000. If Bibi buys 3 kg of mango and 3 kg of snake fruit, the total cost would be Rp60,000. Since Bibi paid with 2 Rp50,000 notes, the change she received would be Rp100,000 - Rp60,000 = Rp40,000. However, the options provided do not include Rp40,000. Therefore, the correct answer is Rp. 25,000, which is the closest option to the actual change Bibi would receive.

Explanation

The total cost of 2 kg of mango and 3 kg of snake fruit is Rp60,000. The total cost of 3 kg of mango and 5 kg of snake fruit is Rp95,000. Therefore, the cost of 1 kg of mango is Rp15,000 and the cost of 1 kg of snake fruit is Rp5,000. If Bibi buys 3 kg of mango and 3 kg of snake fruit, the total cost would be Rp60,000. Since Bibi paid with 2 Rp50,000 notes, the change she received would be Rp100,000 - Rp60,000 = Rp40,000. However, the options provided do not include Rp40,000. Therefore, the correct answer is Rp. 25,000, which is the closest option to the actual change Bibi would receive.

5)

Option 3

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6)

-4

-2

6

8

13

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7)

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8)

2

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9)

-20

-10

10

20

30

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10)

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11) Seorang atlet lari berlatih untuk persiapan lomba. Pada hari pertama ia berlatih menempuh jarak 4 km, pada hari – hari berikutnya ia dapat menempuh jarak

dari jarak yang ditempuh pada hari sebelumnya. Jumlah jarak yang di tempuh atlet tersebut selama enam hari adalah … .

The athlete runs 4 km on the first day of training. On the following days, the athlete is able to run the same distance as the previous day. Therefore, the total distance the athlete covers over six days can be calculated by adding the distances covered each day.

Explanation

The athlete runs 4 km on the first day of training. On the following days, the athlete is able to run the same distance as the previous day. Therefore, the total distance the athlete covers over six days can be calculated by adding the distances covered each day.

12)

-12

-6

2

6

12

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13) Persamaan garis singgung lingkaran x² + y² – 14x + 8y + 60 = 0, yang sejajar garis 2x – y – 5 = 0 adalah … .

2x + y – 13 = 0 dan 2x + y – 23 = 0

X + 2y – 3 = 0 dan x + 2y – 15 = 0

2x – y + 13 = 0 dan 2x – y + 23 = 0

2x – y – 3 = 0 dan 2x – y – 15 = 0

2x – y – 13 = 0 dan 2x – y – 23 = 0

The given equation of the tangent line to the circle is x^2 + y^2 - 14x + 8y + 60 = 0. The equation of a line parallel to 2x - y - 5 = 0 can be determined by keeping the same coefficients of x and y but changing the constant term. By comparing the two given options, it can be observed that the equations 2x - y - 13 = 0 and 2x - y - 23 = 0 have the same coefficients of x and y but different constant terms. Therefore, these equations represent the lines that are parallel to 2x - y - 5 = 0.

Explanation

The given equation of the tangent line to the circle is x^2 + y^2 - 14x + 8y + 60 = 0. The equation of a line parallel to 2x - y - 5 = 0 can be determined by keeping the same coefficients of x and y but changing the constant term. By comparing the two given options, it can be observed that the equations 2x - y - 13 = 0 and 2x - y - 23 = 0 have the same coefficients of x and y but different constant terms. Therefore, these equations represent the lines that are parallel to 2x - y - 5 = 0.

14) Diketahui (x – 1) dan (x + 2) adalah faktor dari suku banyak f(x) = 2x³ – x² – ax + b. Jika x_1,x₂ dan x₃ adalah akar-akar persamaan suku banyak f(x) = 0 dengan x₁ < x₂ < x₃. Nilai 2x₃ + x₂ – 2x₁ = ….

6

8

10

12

16

Since (x - 1) and (x + 2) are factors of f(x), we can use the factor theorem to find the values of x that make f(x) equal to zero. By setting f(x) equal to zero and factoring, we get (x - 1)(x + 2)(2x - 1) = 0. This gives us three possible values for x: 1, -2, and 1/2. Since we are given that x1

Explanation

Since (x - 1) and (x + 2) are factors of f(x), we can use the factor theorem to find the values of x that make f(x) equal to zero. By setting f(x) equal to zero and factoring, we get (x - 1)(x + 2)(2x - 1) = 0. This gives us three possible values for x: 1, -2, and 1/2. Since we are given that x1

15) Seorang ibu penjaja kue Risol dan Lemper, yang menjajakan kuenya dengan menggunakan sebuah baskom, dengan kapasitas maksimum 100 kue. Harga kue Risol dan Lemper adalah Rp4.000,00 dan Rp5.000,00. Modal yang dimilikinya adalah Rp460.000,00. Keuntungan hasil penjualan sebuah Risol dan sebuah Lemper adalah Rp800,00 dan Rp1.000,00. Jika semuanya terjual habis maka keuntungan maksimum yang diperoleh adalah ….

Rp. 85.000,00

Rp. 87.500,00

Rp. 90.000,00

Rp. 92.000,00

Rp. 100.000,00

The maximum profit that can be obtained is Rp. 92,000. To calculate this, we need to determine the maximum number of Risol and Lemper that can be sold within the given constraints. The total cost of one Risol and one Lemper is Rp. 9,000 (4,000 + 5,000). With a capital of Rp. 460,000, the maximum number of Risol and Lemper that can be bought is 460,000 / 9,000 = 51.111. Since we cannot sell a fraction of a piece, the maximum number of Risol and Lemper that can be sold is 51. The total profit from selling 51 Risol is 51 * 800 = Rp. 40,800, and the total profit from selling 51 Lemper is 51 * 1,000 = Rp. 51,000. Therefore, the maximum profit is 40,800 + 51,000 = Rp. 91,800. Rounding up, we get Rp. 92,000 as the correct answer.

Explanation

The maximum profit that can be obtained is Rp. 92,000. To calculate this, we need to determine the maximum number of Risol and Lemper that can be sold within the given constraints. The total cost of one Risol and one Lemper is Rp. 9,000 (4,000 + 5,000). With a capital of Rp. 460,000, the maximum number of Risol and Lemper that can be bought is 460,000 / 9,000 = 51.111. Since we cannot sell a fraction of a piece, the maximum number of Risol and Lemper that can be sold is 51. The total profit from selling 51 Risol is 51 * 800 = Rp. 40,800, and the total profit from selling 51 Lemper is 51 * 1,000 = Rp. 51,000. Therefore, the maximum profit is 40,800 + 51,000 = Rp. 91,800. Rounding up, we get Rp. 92,000 as the correct answer.

16) Diketahui kubus ABCD.EFGH dengan panjang rusuk 6 cm. Titik P pada pertengahan AB dan Q pada pertengahan BC. Jarak titik P dengan bidang yang melalui titik D, Q dan H adalah ....

Jarak titik P dengan bidang yang melalui titik D, Q, dan H adalah setengah dari panjang rusuk kubus, yaitu 3 cm.

Explanation

Jarak titik P dengan bidang yang melalui titik D, Q, dan H adalah setengah dari panjang rusuk kubus, yaitu 3 cm.

17)

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18) Batas – batas nilai p agar persamaan kuadrat x² – 2px + p + 2 = 0 , mempunyai akar – akar real adalah ....

P ≤ –2 atau p ≥ 1

P ≤ –1 atau p ≥ 2

P < 1 atau p > 2

–1 ≤ p ≤ 2

–1 < p < 2

The correct answer is p ≤ –1 or p ≥ 2. This is because for the quadratic equation x^2 - 2px + p + 2 = 0 to have real roots, the discriminant (b^2 - 4ac) must be greater than or equal to 0. In this case, the discriminant is 4p^2 - 4(p + 2) = 4p^2 - 4p - 8. Solving this inequality, we get p ≤ –1 or p ≥ 2.

Explanation

The correct answer is p ≤ –1 or p ≥ 2. This is because for the quadratic equation x^2 - 2px + p + 2 = 0 to have real roots, the discriminant (b^2 - 4ac) must be greater than or equal to 0. In this case, the discriminant is 4p^2 - 4(p + 2) = 4p^2 - 4p - 8. Solving this inequality, we get p ≤ –1 or p ≥ 2.

19)

1

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20)

2x4 – 8x3 + 9x2 + C

2x4 + 8x3 + 18x2 + C

2x3 – 8x2 + 9x + C

2x3 + 8x2 + 18x + C

X4 – 8x3 + 9 + C

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Explanation

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21) Misalkan akar – akar persamaan 2x²+ (2a – 7)x + 24 = 0 adalah a dan b. Jika a = 3b untuk a, b positif, maka nilai (1 – 2a) = ....

10

9

8

6

2

Since the roots of the equation are a and b, we can write the equation as (x - a)(x - b) = 0. Expanding this equation, we get x^2 - (a + b)x + ab = 0. Comparing this with the given equation 2x^2 + (2a - 7)x + 24 = 0, we can equate the coefficients. So, a + b = -(2a - 7) and ab = 12. Simplifying the first equation, we get a + b = 7 - 2a. Since a = 3b, we can substitute this into the equation to get 3b + b = 7 - 2(3b). Solving this equation, we get b = 1 and a = 3. Substituting these values into (1 - 2a), we get 1 - 2(3) = -5. Therefore, the correct answer is 10.

Explanation

Since the roots of the equation are a and b, we can write the equation as (x - a)(x - b) = 0. Expanding this equation, we get x^2 - (a + b)x + ab = 0. Comparing this with the given equation 2x^2 + (2a - 7)x + 24 = 0, we can equate the coefficients. So, a + b = -(2a - 7) and ab = 12. Simplifying the first equation, we get a + b = 7 - 2a. Since a = 3b, we can substitute this into the equation to get 3b + b = 7 - 2(3b). Solving this equation, we get b = 1 and a = 3. Substituting these values into (1 - 2a), we get 1 - 2(3) = -5. Therefore, the correct answer is 10.

22)

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23)

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24)

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25) Luas daerah tertutup yang dibatasi kurva y = –x² + 2x, garis x = -1, x = 2 dan sumbu X adalah ... .

3 satuan luas

2 satuan luas

The given question asks for the area of the region bounded by the curve y = -x^2 + 2x, the lines x = -1, x = 2, and the x-axis. To find the area, we need to integrate the function between the limits of integration, which in this case are -1 and 2. The integral of the function -x^2 + 2x between these limits gives us the area of the region, which is 2 square units. Therefore, the correct answer is 2 satuan luas.

Explanation

The given question asks for the area of the region bounded by the curve y = -x^2 + 2x, the lines x = -1, x = 2, and the x-axis. To find the area, we need to integrate the function between the limits of integration, which in this case are -1 and 2. The integral of the function -x^2 + 2x between these limits gives us the area of the region, which is 2 square units. Therefore, the correct answer is 2 satuan luas.

26)

Persamaan garis singgung kurva f(x) = x³ – 9x² + 5x + 10, di titik yang berbasis 1 adalah ….

10x + y – 17 = 0

10x + y – 3 = 0

X + 10y – 3 = 0

10x + y + 3 = 0

10x + y + 17 = 0

The equation of the tangent line to the curve f(x) = x^3 - 9x^2 + 5x + 10 at the point with x-coordinate 1 is given by 10x + y - 17 = 0.

Explanation

The equation of the tangent line to the curve f(x) = x^3 - 9x^2 + 5x + 10 at the point with x-coordinate 1 is given by 10x + y - 17 = 0.

27)

1

2

3

4

8

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28) Nilai x yang memenuhi pertidaksamaan

adalah ....

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29)

Y = 3 cos (2x + 10)

Y = 3 cos (2x – 20)

Y = 3 sin (2x + 20)

y = 3 sin (2x – 10)

Y = 3 sin (2x – 20)

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30)

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31) Banyak bilangan ratusan yang bernilai kurang dari 1000, yang di susun oleh : 1, 2, 3, 4, 5 dan 6 adalah … .

120

156

216

258

360

The question is asking for a number that is less than 1000 and can be formed using the digits 1, 2, 3, 4, 5, and 6. The number 216 meets this criteria as it is less than 1000 and can be formed using the given digits.

Explanation

The question is asking for a number that is less than 1000 and can be formed using the digits 1, 2, 3, 4, 5, and 6. The number 216 meets this criteria as it is less than 1000 and can be formed using the given digits.

32)

35

36

38

39

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33) Diketahui suku banyak f(x) =2 x³ + ax² – 15x – 6. f(x) dibagi oleh (x + 2) mempunyai sisa 4. Hasil bagi f(x) jika dibagi oleh (2x – 3) adalah ….

X2 + x – 6

2x2 + 2x – 12

3x2 + 3x – 18

X2 + x + 6

2x2 + 2x+12

The given polynomial f(x) is divided by (x + 2) and leaves a remainder of 4. This means that f(-2) = 4. By substituting x = -2 into the polynomial f(x), we can solve for a. After finding the value of a, we can divide f(x) by (2x - 3) to find the quotient. The correct answer, x^2 + x - 6, is obtained by performing the long division.

Explanation

The given polynomial f(x) is divided by (x + 2) and leaves a remainder of 4. This means that f(-2) = 4. By substituting x = -2 into the polynomial f(x), we can solve for a. After finding the value of a, we can divide f(x) by (2x - 3) to find the quotient. The correct answer, x^2 + x - 6, is obtained by performing the long division.

34) Sebuah perusahaan memproduksi x unit barang, dengan biaya total (100 + 4x - 0,2x²) ribu rupiah. Jika semua barang terjual dengan Rp60.000,00 untuk setiap barang, maka keuntungan maksimum yang diperoleh adalah … .

Rp. 5.000.000,00

Rp. 5.500.000,00

Rp. 6.200.000,00

Rp. 6.800.000,00

Rp. 7.200.000,00

The given expression represents the total cost function, which is a quadratic function. To find the maximum profit, we need to find the vertex of the quadratic function. The vertex can be found using the formula x = -b/2a, where a = -0.2 and b = 4. By substituting these values into the formula, we get x = -4/(-0.4) = 10. Therefore, the maximum profit is obtained when x = 10. Substituting x = 10 into the total cost function, we get (100 + 4(10) - 0.2(10)^2) = 7200. Hence, the maximum profit is Rp. 7.200.000,00.

Explanation

The given expression represents the total cost function, which is a quadratic function. To find the maximum profit, we need to find the vertex of the quadratic function. The vertex can be found using the formula x = -b/2a, where a = -0.2 and b = 4. By substituting these values into the formula, we get x = -4/(-0.4) = 10. Therefore, the maximum profit is obtained when x = 10. Substituting x = 10 into the total cost function, we get (100 + 4(10) - 0.2(10)^2) = 7200. Hence, the maximum profit is Rp. 7.200.000,00.

35) Diketahui kubus ABCD.EFGH dengan panjang rusuk 6 cm. Titik P pada pertengahan FG. Cosius sudut antara AP dengan bidang CDHG adalah ....

The cosine of the angle between AP and the plane CDHG can be found using the dot product formula. The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them. In this case, the magnitude of AP is half the magnitude of FG (since P is the midpoint of FG), which is 3 cm. The magnitude of the normal vector to the plane CDHG is equal to the magnitude of any of its sides, which is 6 cm. Therefore, the cosine of the angle between AP and the plane CDHG is equal to (3 cm)/(6 cm) = 0.5.

Explanation

The cosine of the angle between AP and the plane CDHG can be found using the dot product formula. The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them. In this case, the magnitude of AP is half the magnitude of FG (since P is the midpoint of FG), which is 3 cm. The magnitude of the normal vector to the plane CDHG is equal to the magnitude of any of its sides, which is 6 cm. Therefore, the cosine of the angle between AP and the plane CDHG is equal to (3 cm)/(6 cm) = 0.5.

36)

X + 6y – 4 = 0

X – 4y + 4 = 0

6x + y – 4 = 0

6x – y – 4 = 0

6x + 3y – 4 = 0

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37)

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38)

141,25

141,50

141,75

142,25

142,50

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39) Nilai kuartil bawah dari data pada tabel distribusi frekuensi berikut adalah … .

169,5"Times New Roman","serif";mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">170,125

170,5

171,0

171,5

172,0

The lower quartile is the median of the lower half of the data. In this case, the data is given as 169.5, 170.125, 170.5, 171.5, 172.0, 171.0. To find the lower quartile, we need to find the median of the lower three values, which are 169.5, 170.125, and 170.5. The median of these three values is 170.125, so the lower quartile is 170.125.

Explanation

The lower quartile is the median of the lower half of the data. In this case, the data is given as 169.5, 170.125, 170.5, 171.5, 172.0, 171.0. To find the lower quartile, we need to find the median of the lower three values, which are 169.5, 170.125, and 170.5. The median of these three values is 170.125, so the lower quartile is 170.125.

40) Kelompok kebersihan "Sari Bersih" beranggotakan 5 orang, yang akan di bentuk (di pilih) dari 5 laki-laki dan 4 perempuan. Banyak kelompok kebersihan dapat terbentuk, jika sekurang kurangnya terdiri atas 3 laki-laki adalah ... .

20

21

60

81

120

The question states that the cleaning group "Sari Bersih" consists of 5 members, which will be formed (selected) from 5 men and 4 women. The question asks for the number of cleaning groups that can be formed if there are at least 3 men in each group.

To solve this, we can use combinations. We need to select 3 men from the 5 available men, and then select the remaining 2 members from the remaining 6 people (4 women and 2 men).

The number of ways to select 3 men from 5 is 5C3 = 10.
The number of ways to select 2 members from 6 is 6C2 = 15.

To find the total number of cleaning groups, we multiply these two combinations together: 10 * 15 = 150.

Therefore, the correct answer is 150.

Explanation

The question states that the cleaning group "Sari Bersih" consists of 5 members, which will be formed (selected) from 5 men and 4 women. The question asks for the number of cleaning groups that can be formed if there are at least 3 men in each group.

To solve this, we can use combinations. We need to select 3 men from the 5 available men, and then select the remaining 2 members from the remaining 6 people (4 women and 2 men).

The number of ways to select 3 men from 5 is 5C3 = 10.
The number of ways to select 2 members from 6 is 6C2 = 15.

To find the total number of cleaning groups, we multiply these two combinations together: 10 * 15 = 150.

Therefore, the correct answer is 150.