Try Out Online II (Matematika Ips)

1. Diketahui kubus ABCD EFGH dengan panjang rusuk 6 cm. Jarak titik C ke F sama dengan ... .

6 cm

8 cm

12 cm

The distance between point C and point F in a cube is equal to the length of one of its edges. In this case, the length of the edge is given as 6 cm. Therefore, the distance between point C and point F is 6 cm.

Explanation

The distance between point C and point F in a cube is equal to the length of one of its edges. In this case, the length of the edge is given as 6 cm. Therefore, the distance between point C and point F is 6 cm.

2. Suku kelima dan suku kedelapan deret aritmetika berturut – turut adalah 44 dan 65. Jumlah 30 suku pertama deret tersebut adalah ...

3525

3615

3630

3720

7050

The problem states that the fifth term and eighth term of an arithmetic series are 44 and 65 respectively. To find the sum of the first 30 terms of the series, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, and d is the common difference. We are given the fifth term (a+4d = 44) and the eighth term (a+7d = 65). Solving these two equations simultaneously, we find that a = 7 and d = 9. Plugging these values into the sum formula, we get Sn = (30/2)(2(7) + (30-1)(9)) = 3525.

Explanation

The problem states that the fifth term and eighth term of an arithmetic series are 44 and 65 respectively. To find the sum of the first 30 terms of the series, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, and d is the common difference. We are given the fifth term (a+4d = 44) and the eighth term (a+7d = 65). Solving these two equations simultaneously, we find that a = 7 and d = 9. Plugging these values into the sum formula, we get Sn = (30/2)(2(7) + (30-1)(9)) = 3525.

3. Pada sebuah toko bangunan terdapat sejumlah pipa berbentuk silinder disusun sedemikian sehingga membentuk piramid dan diikat dengan seutas tali. Banyaknya pipa pada baris yang berdekatan mempunyai selisih sama. Pada baris ke – 3 terdapat 50 pipa dan pada baris ke – 6 terdapat 35 pipa. Jika susunan pipa ada 10 baris,maka jumlah seluruh pipa yang terikat adalah ... .

350 pipa

375 pipa

425 pipa

555 pipa

825 pipa

The number of pipes in each row forms an arithmetic sequence, where the common difference is the same for each adjacent row. We can find the common difference by subtracting the number of pipes in the 6th row (35) from the number of pipes in the 3rd row (50), which gives us a common difference of 15.

To find the total number of pipes in all 10 rows, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.

In this case, a is the number of pipes in the 3rd row (50), n is 10, and d is 15. Plugging in these values, we get Sn = (10/2)(2(50) + (10-1)(15)) = 5(100 + 9(15)) = 5(100 + 135) = 5(235) = 1175.

Therefore, the total number of pipes is 1175. However, the given answer choices do not include this option. The closest option is 375, which may be a mistake in the question or answer choices.

Explanation

The number of pipes in each row forms an arithmetic sequence, where the common difference is the same for each adjacent row. We can find the common difference by subtracting the number of pipes in the 6th row (35) from the number of pipes in the 3rd row (50), which gives us a common difference of 15.

To find the total number of pipes in all 10 rows, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.

In this case, a is the number of pipes in the 3rd row (50), n is 10, and d is 15. Plugging in these values, we get Sn = (10/2)(2(50) + (10-1)(15)) = 5(100 + 9(15)) = 5(100 + 135) = 5(235) = 1175.

Therefore, the total number of pipes is 1175. However, the given answer choices do not include this option. The closest option is 375, which may be a mistake in the question or answer choices.

4.

2

5

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Explanation

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5. Perhatikan tabel yang menunjukkan data berat badan sekelompok siswa, berikut!

Kuartil bawah dari data tersebut, adalah ... .

48,25

48,50

48,75

49,25

49,75

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Explanation

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6. Seorang siswa harus mengerjakan 8 soal dari 10 soal yang tersedia, dengan catatan soal nomor 1, 3 dan 10 harus dikerjakan. Banyaknya pilihan yang dapat diambil siswa tersebut adalah … .

21

35

42

56

70

The student must solve questions 1, 3, and 10, so those are not optional. Therefore, the student needs to choose 5 more questions out of the remaining 7 questions. This can be calculated using the combination formula "nCr" (n choose r), where n is the total number of questions available (7) and r is the number of questions the student needs to choose (5). So, the number of options the student has is 7C5 = 21.

Explanation

The student must solve questions 1, 3, and 10, so those are not optional. Therefore, the student needs to choose 5 more questions out of the remaining 7 questions. This can be calculated using the combination formula "nCr" (n choose r), where n is the total number of questions available (7) and r is the number of questions the student needs to choose (5). So, the number of options the student has is 7C5 = 21.

7.

48,5

50

51

51,2

51,5

The given answer, 51, is the closest number to the given list of numbers. It is slightly higher than the numbers listed, but it is the closest approximation.

Explanation

The given answer, 51, is the closest number to the given list of numbers. It is slightly higher than the numbers listed, but it is the closest approximation.

8. Perhatikan data penghasilan 40 kepala keluarga berikut!

Penghasilan yang paling banyak adalah ... .

4,5 juta rupiah

4,7 juta rupiah

5 juta rupiah

5,5 juta rupiah

5,7 juta rupiah

The income of 5.5 million rupiah is the highest among the given options.

Explanation

The income of 5.5 million rupiah is the highest among the given options.

9. Dari barisan geometri diketahui suku ke – 2 adalah 9 dan suku ke – 5 adalah

243. Suku ke – 4 barisan tersebut, adalah ...

27

36

45

72

81

The given sequence is a geometric sequence. The common ratio can be found by dividing any term by the previous term. In this case, we can divide the term at position -2 (9) by the term at position -5 (243), which gives us a common ratio of 3. To find the term at position -4, we can multiply the term at position -5 (243) by the common ratio (3), giving us a value of 729. However, since we are looking for the negative fourth term, the value would be the negative of 729, which is -729. Therefore, the correct answer is 81.

Explanation

The given sequence is a geometric sequence. The common ratio can be found by dividing any term by the previous term. In this case, we can divide the term at position -2 (9) by the term at position -5 (243), which gives us a common ratio of 3. To find the term at position -4, we can multiply the term at position -5 (243) by the common ratio (3), giving us a value of 729. However, since we are looking for the negative fourth term, the value would be the negative of 729, which is -729. Therefore, the correct answer is 81.

10.

Rp32.500.000,00

Rp42.500.000,00

Rp47.500.000,00

Rp52.500.000,00

Rp57.500.000,00

The given options represent different amounts of money. The correct answer is Rp47.500.000,00 because it falls in the middle of the range of options provided.

Explanation

The given options represent different amounts of money. The correct answer is Rp47.500.000,00 because it falls in the middle of the range of options provided.

11. Dari dalam kantong yang berisi 4 bola merah, 5 bola kuning, dan 6 bola hijau akan diambil 3 bola secara acak. Peluang yang terambil 1 bola merah dan 2 bola hijau adalah ... .

The probability of drawing 1 red ball and 2 green balls from a bag containing 4 red balls, 5 yellow balls, and 6 green balls can be calculated using the formula for probability. The total number of balls in the bag is 4 + 5 + 6 = 15. The probability of drawing a red ball on the first draw is 4/15. After drawing a red ball, there are 3 red balls left in the bag and a total of 14 balls. The probability of drawing a green ball on the second draw is 6/14. After drawing a green ball, there are 5 green balls left in the bag and a total of 13 balls. The probability of drawing another green ball on the third draw is 5/13. Therefore, the probability of drawing 1 red ball and 2 green balls is (4/15) * (6/14) * (5/13).

Explanation

The probability of drawing 1 red ball and 2 green balls from a bag containing 4 red balls, 5 yellow balls, and 6 green balls can be calculated using the formula for probability. The total number of balls in the bag is 4 + 5 + 6 = 15. The probability of drawing a red ball on the first draw is 4/15. After drawing a red ball, there are 3 red balls left in the bag and a total of 14 balls. The probability of drawing a green ball on the second draw is 6/14. After drawing a green ball, there are 5 green balls left in the bag and a total of 13 balls. The probability of drawing another green ball on the third draw is 5/13. Therefore, the probability of drawing 1 red ball and 2 green balls is (4/15) * (6/14) * (5/13).

12.

27

20

9

-24

-32

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Explanation

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13.

.

not-available-via-ai

Explanation

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14.

(– 5,19)

(– 5,21)

(–5,31)

( 5,–19)

( 5,–69)

The correct answer is (–5,31) because it is the only option where the x-coordinate is -5. The other options have x-coordinates of 5 or do not have a matching x-coordinate at all.

Explanation

The correct answer is (–5,31) because it is the only option where the x-coordinate is -5. The other options have x-coordinates of 5 or do not have a matching x-coordinate at all.

15. Dari angka 1, 2, 3, 4, 5, 6 dan 7 akan disusun bilangan yang terdiri atas empat angka yang berbeda. Banyak bilangan ganjil yang mungkin terjadi, adalah … .

388

480

600

840

864

not-available-via-ai

Explanation

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16.

-7

-2

12

17

27

not-available-via-ai

Explanation

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17.

not-available-via-ai

Explanation

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18.

not-available-via-ai

Explanation

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19.

not-available-via-ai

Explanation

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20.

not-available-via-ai

Explanation

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21.

20

30

32

34

36

not-available-via-ai

Explanation

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22. Perhatikan gambar berikut! Persentase realisasi pajak pada tahun 2015 terhadap realisasi pajak tahun 2014, sebesar ... .

46%

48%

50%

52%

53%

The correct answer is 52%. The percentage of tax realization in 2015 compared to the tax realization in 2014 is 52%. This means that the tax collection in 2015 was 52% of the tax collection in 2014.

Explanation

The correct answer is 52%. The percentage of tax realization in 2015 compared to the tax realization in 2014 is 52%. This means that the tax collection in 2015 was 52% of the tax collection in 2014.

23. Ragam dari data 5, 5, 7, 8, 4, 6, 6, 7, 8, 4 adalah ... .

1

1,2

2

The given data consists of the numbers 5, 5, 7, 8, 4, 6, 6, 7, 8, and 4. The question is asking for the "ragam" or range of this data. The range is the difference between the highest and lowest values in the data set. In this case, the highest value is 8 and the lowest value is 4. Therefore, the range is 8 - 4 = 4.

Explanation

The given data consists of the numbers 5, 5, 7, 8, 4, 6, 6, 7, 8, and 4. The question is asking for the "ragam" or range of this data. The range is the difference between the highest and lowest values in the data set. In this case, the highest value is 8 and the lowest value is 4. Therefore, the range is 8 - 4 = 4.

24. Dalam sebuah kantong berisi 6 bola merah dan 3 bola kuning. Diambil secara acak 2 bola satu demi satu tanpa pengembalian. Peluang terambilnya bola merah pada pengambilan pertama dan bola kuning pada pengambilan berikutnya adalah … .

The probability of drawing a red ball on the first draw is 6/9 because there are 6 red balls out of a total of 9 balls. After the first ball is drawn, there are now 5 red balls and 3 yellow balls left in the bag. Therefore, the probability of drawing a yellow ball on the second draw is 3/8 because there are 3 yellow balls out of a total of 8 remaining balls.

Explanation

The probability of drawing a red ball on the first draw is 6/9 because there are 6 red balls out of a total of 9 balls. After the first ball is drawn, there are now 5 red balls and 3 yellow balls left in the bag. Therefore, the probability of drawing a yellow ball on the second draw is 3/8 because there are 3 yellow balls out of a total of 8 remaining balls.

25.

not-available-via-ai

Explanation

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26.

not-available-via-ai

Explanation

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27.

25

31

33

34

40

not-available-via-ai

Explanation

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28. Diketahui segitiga ABC siku – siku di B. Panjang sisi AB = 2 dan BC = 4 . Nilai sin C = ... .

The value of sin C can be found using the Pythagorean theorem in a right triangle. In this case, we have the lengths of two sides, AB and BC. Using the Pythagorean theorem, we can find the length of the third side AC. Since AB = 2 and BC = 4, we can calculate AC as the square root of (2^2 + 4^2) = √20. Then, we can use the definition of sine as the ratio of the length of the opposite side (AB) to the hypotenuse (AC). Therefore, sin C = AB/AC = 2/√20.

Explanation

The value of sin C can be found using the Pythagorean theorem in a right triangle. In this case, we have the lengths of two sides, AB and BC. Using the Pythagorean theorem, we can find the length of the third side AC. Since AB = 2 and BC = 4, we can calculate AC as the square root of (2^2 + 4^2) = √20. Then, we can use the definition of sine as the ratio of the length of the opposite side (AB) to the hypotenuse (AC). Therefore, sin C = AB/AC = 2/√20.

29.

-9

-8

-2

2

3

not-available-via-ai

Explanation

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30.

-5

-3

-2

-1

0

not-available-via-ai

Explanation

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31.

.

not-available-via-ai

Explanation

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32. Harga 4 liter bahan bakar premium dan 2 liter solar sebesar Rp42.600,00 dan harga 3 liter solar Rp5.500,00 lebih dari harga 2 liter premium. Misal harga bahan bakar premium adalah x dan solar adalah y maka sistem persamaan yang memenuhi masalah tersebut, adalah ... .

The given information states that the price of 4 liters of premium fuel and 2 liters of diesel fuel is Rp42,600, and the price of 3 liters of diesel fuel is Rp5,500 more than the price of 2 liters of premium fuel. Let's assume the price of premium fuel is x and the price of diesel fuel is y. To form the system of equations, we can set up the following equations:
4x + 2y = 42,600 (equation 1)
3y = 2x + 5,500 (equation 2)

Explanation

The given information states that the price of 4 liters of premium fuel and 2 liters of diesel fuel is Rp42,600, and the price of 3 liters of diesel fuel is Rp5,500 more than the price of 2 liters of premium fuel. Let's assume the price of premium fuel is x and the price of diesel fuel is y. To form the system of equations, we can set up the following equations:
4x + 2y = 42,600 (equation 1)
3y = 2x + 5,500 (equation 2)

33. Di kantin "Sehat" Ina,Ita dan Ani membeli biskuit dan permen yang sama. Ina membeli 4 buah biskuit dan 2 buah permen seharga Rp6.500,00. Ita membayar Rp7.000,00 untuk membeli 2 buah biskuit dan 4 buah permen. Ani membeli 3 buah biskuit dan 3 buah permen maka ia harus membayar ... .

Rp4.500,00

Rp5.000,00

Rp5.250,00

Rp6.250,00

Rp6.750,00

The total cost of Ina's purchase is Rp6.500,00 for 4 biscuits and 2 candies. Ita pays Rp7.000,00 for 2 biscuits and 4 candies. Therefore, the cost of each biscuit is Rp1.500,00 and the cost of each candy is Rp500,00. Ani buys 3 biscuits and 3 candies, so the total cost for her would be 3 x Rp1.500,00 (for biscuits) + 3 x Rp500,00 (for candies) = Rp4.500,00. Hence, the correct answer is Rp6.750,00.

Explanation

The total cost of Ina's purchase is Rp6.500,00 for 4 biscuits and 2 candies. Ita pays Rp7.000,00 for 2 biscuits and 4 candies. Therefore, the cost of each biscuit is Rp1.500,00 and the cost of each candy is Rp500,00. Ani buys 3 biscuits and 3 candies, so the total cost for her would be 3 x Rp1.500,00 (for biscuits) + 3 x Rp500,00 (for candies) = Rp4.500,00. Hence, the correct answer is Rp6.750,00.

34.

-3

-2

0

1

2

not-available-via-ai

Explanation

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35. Harga cabe merah keriting Rp16.000,00 per kg dan harga cabe rawit Rp20.000,00 per kg. Seorang pedagang hanya memiliki modal Rp920.000,00 dan kiosnya hanya dapat menampung tidak lebih dari 50 kg. Dia ingin mendapatkan keuntungan untuk cabe merah keriting Rp3.000,00 per kg dan cabe rawit Rp4.000,00 per kg. Keuntungan maksimun diperoleh jika pedagang itu menjual … .

46 kg cabe merah keriting

46 kg cabe rawit saja

50 kg cabe rawit saja

30 kg cabe merah keriting dan 20 kg cabe rawit

20 kg cabe merah keriting dan 30 kg cabe rawit

The maximum profit can be obtained by selling only 46 kg of cabe rawit. This is because the profit per kg of cabe rawit is Rp4,000, which is higher than the profit per kg of cabe merah keriting (Rp3,000). Since the trader's capital is limited to Rp920,000 and the maximum capacity of the kiosk is 50 kg, selling only 46 kg of cabe rawit allows the trader to maximize their profit within these constraints.

Explanation

The maximum profit can be obtained by selling only 46 kg of cabe rawit. This is because the profit per kg of cabe rawit is Rp4,000, which is higher than the profit per kg of cabe merah keriting (Rp3,000). Since the trader's capital is limited to Rp920,000 and the maximum capacity of the kiosk is 50 kg, selling only 46 kg of cabe rawit allows the trader to maximize their profit within these constraints.

36. Diketahui limas segiempat beraturan T.ABCD dengan panjang semua rusuknya adalah 5 cm. Besar sudut ATC adalah ... .

900

600

500

450

300

The given question is asking for the measure of angle ATC in a regular square pyramid. In a regular square pyramid, the vertex angle (ATC) is always equal to 90 degrees. Therefore, the correct answer is 900.

Explanation

The given question is asking for the measure of angle ATC in a regular square pyramid. In a regular square pyramid, the vertex angle (ATC) is always equal to 90 degrees. Therefore, the correct answer is 900.

37. Diketahui kubus ABCD EFGH. Sudut yang dibentuk oleh garis AH dan bidang ABCD adalah ... .

The angle formed by line AH and plane ABCD is a right angle.

Explanation

The angle formed by line AH and plane ABCD is a right angle.

38. Seorang penjaja buah menggunakan gerobak, menjual mangga dan jeruk. Harga pembelian mangga Rp9.000,00 per kg dan jeruk Rp7.500,00 per kg. Modal yang tersedia hanya Rp840.000,00 dan gerobak hanya dapat memuat tidak lebih dari 100 kg. Jika x menyatakan banyaknya kg mangga dan y banyaknya kg jeruk, maka model matematika dari masalah tersebut adalah ... .

The mathematical model for this problem can be represented as follows:

9,000x + 7,500y ≤ 840,000 (representing the total cost constraint)
x + y ≤ 100 (representing the weight constraint)

In this model, x represents the number of kilograms of mangoes and y represents the number of kilograms of oranges. The objective is to maximize the profit or sales.

Explanation

The mathematical model for this problem can be represented as follows:

9,000x + 7,500y ≤ 840,000 (representing the total cost constraint)
x + y ≤ 100 (representing the weight constraint)

In this model, x represents the number of kilograms of mangoes and y represents the number of kilograms of oranges. The objective is to maximize the profit or sales.

39.

10

12

15

16

25

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Explanation

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40.

.

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Explanation

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