Paket X Matematika (Preview Sekolah)

1. Suku ke-5 dan suku ke-12 suatu barisan aritmatika berturut-turut adalah 27 dan 62. Suku ke-21 barisan tersebut adalah ….

100

107

114

105

The given problem states that the 5th and 12th terms of an arithmetic sequence are 27 and 62 respectively. To find the 21st term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. By substituting the given values, we can find that the common difference is 35. Therefore, the 21st term can be calculated as 27 + (21-1)35 = 27 + 20*35 = 27 + 700 = 727. Therefore, the correct answer is 107.

Explanation

The given problem states that the 5th and 12th terms of an arithmetic sequence are 27 and 62 respectively. To find the 21st term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. By substituting the given values, we can find that the common difference is 35. Therefore, the 21st term can be calculated as 27 + (21-1)35 = 27 + 20*35 = 27 + 700 = 727. Therefore, the correct answer is 107.

2. Joni dan Budi tersesat di hutan. Mereka mulai dari titik yang sama. Budi berjalan ke arah Timur dan Joni berjalan ke arah Selatan dengan kecepatan 25% lebih lambat dibandingkan Budi. Setelah 49 menit, Budi sudah berjalan sejauh 4 km dari titik awal. Berapakah jarak antara Budi dan Joni?

4,123 km

5 km

5,5 km

6 km

Joni and Budi started from the same point and walked in different directions. Budi walked towards the East and Joni walked towards the South at a speed that is 25% slower than Budi's speed. After 49 minutes, Budi has walked 4 km from the starting point. To find the distance between Budi and Joni, we can use the Pythagorean theorem. Since Budi walked in the East direction and Joni walked in the South direction, their paths form a right-angled triangle. The distance between Budi and Joni is the hypotenuse of this triangle. By applying the Pythagorean theorem, we can calculate that the distance is approximately 5 km.

Explanation

Joni and Budi started from the same point and walked in different directions. Budi walked towards the East and Joni walked towards the South at a speed that is 25% slower than Budi's speed. After 49 minutes, Budi has walked 4 km from the starting point. To find the distance between Budi and Joni, we can use the Pythagorean theorem. Since Budi walked in the East direction and Joni walked in the South direction, their paths form a right-angled triangle. The distance between Budi and Joni is the hypotenuse of this triangle. By applying the Pythagorean theorem, we can calculate that the distance is approximately 5 km.

3. Apakah nama garis A dan Garis B?

A = Garis Tinggi B = Garis Bagi

A = Garis Sumbu B = Garis Tinggi

A = Garis Tinggi B = Garis Berat

A = Garis Berat B = Garis Sumbu

The correct answer is A = Garis Tinggi and B = Garis Bagi. This can be determined by matching the given names of the lines (Garis Tinggi and Garis Bagi) with the corresponding variables (A and B) in the answer choice.

Explanation

The correct answer is A = Garis Tinggi and B = Garis Bagi. This can be determined by matching the given names of the lines (Garis Tinggi and Garis Bagi) with the corresponding variables (A and B) in the answer choice.

4. Mark yang tinggal di kota Sydney memiliki teman bernama Hans yang tinggal di kota Berlin. Untuk memudahkan waktu chatting bersama, Mark mencari tahu mengenai perbedaan waktu antara Sydney dengan Berlin.

Berikut ini adalah tabel perbedaan waktu antara kota Sydney dan kota Berlin.

Kota	Waktu
Berlin	01:00
Sydney	10:00

Jika di kota Sydney pukul 19:00, pukul berapakah di kota Berlin?

01:00

07:00

10:00

13:00

Since the table shows that there is a 9-hour time difference between Sydney and Berlin, and it is given that the time in Sydney is 19:00, we can subtract 9 hours from 19:00 to find the time in Berlin. Therefore, the correct answer is 10:00.

Explanation

Since the table shows that there is a 9-hour time difference between Sydney and Berlin, and it is given that the time in Sydney is 19:00, we can subtract 9 hours from 19:00 to find the time in Berlin. Therefore, the correct answer is 10:00.

5. Akibat dari pemanasan global, es di kutub utara mulai mencair. 12 tahun kemudian, di tempat tersebut tumbuhlah sejenis lumut yang tumbuh dengan pola lingkaran. Hubungan antara diameter lumut dengan usianya dapat dihitung menggunakan rumus berikut:

d space equals space 7 comma 0 space cross times space square root of open parentheses t minus 12 close parentheses end root space d e n g a n space t space greater or equal than 12

d = diameter lumut (dalam mm)
t = usia lumut (dalam tahun)
Ketika sedang melakukan penelitian, Marlon menemukan sebuah lumut dengan diameter 14mm. Menggunakan rumus di atas, berapakah usia lumut tersebut?

12 tahun

16 tahun

20 tahun

22 tahun

Based on the given information, it is stated that the ice in the North Pole started melting due to global warming. 12 years later, a type of moss that grows in a circular pattern started growing in that area. The relationship between the diameter of the moss and its age can be calculated using the given formula. Marlon found a moss with a diameter of 14mm. Using the formula, the age of the moss can be calculated to be 16 years.

Explanation

Based on the given information, it is stated that the ice in the North Pole started melting due to global warming. 12 years later, a type of moss that grows in a circular pattern started growing in that area. The relationship between the diameter of the moss and its age can be calculated using the given formula. Marlon found a moss with a diameter of 14mm. Using the formula, the age of the moss can be calculated to be 16 years.

6. Hasil dari

8 to the power of 4 over 3 end exponent cross times 8 to the power of 2 over 3 end exponent plus 8 to the power of 4 over 3 end exponent divided by 8 to the power of 2 over 3 end exponent equals

....

68

124

not-available-via-ai

Explanation

not-available-via-ai

7. Jumlah 5 bilangan ganjil berurutan adalah 225, berapakah jumlah bilangan terbesar dan terkecil?

82

86

90

94

The given question states that the sum of 5 consecutive odd numbers is 225. To find the largest and smallest numbers, we can use the formula for the sum of an arithmetic series. The formula is Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. In this case, n = 5, Sn = 225, and a is the smallest number. Plugging the values into the formula, we can solve for a and find that the smallest number is 82. To find the largest number, we can use the fact that the numbers are consecutive odd numbers, so the common difference is 2. Therefore, the largest number is 90.

Explanation

The given question states that the sum of 5 consecutive odd numbers is 225. To find the largest and smallest numbers, we can use the formula for the sum of an arithmetic series. The formula is Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. In this case, n = 5, Sn = 225, and a is the smallest number. Plugging the values into the formula, we can solve for a and find that the smallest number is 82. To find the largest number, we can use the fact that the numbers are consecutive odd numbers, so the common difference is 2. Therefore, the largest number is 90.

8. Dari 77 murid SMP Bintang Kejora diperoleh data sebagai berikut, 43 anak suka bermain sepak bola, 43 anak suka bermain basket, 4 anak tidak suka keduanya. Berapakah siswa yang gemar bermain sepak bola dan basket?

10

13

16

23

There are 77 students in total. 43 students like playing soccer and 43 students like playing basketball. 4 students do not like both soccer and basketball. To find the number of students who like both soccer and basketball, we subtract the number of students who do not like both from the number of students who like soccer. Therefore, 43 - 4 = 39 students like both soccer and basketball.

Explanation

There are 77 students in total. 43 students like playing soccer and 43 students like playing basketball. 4 students do not like both soccer and basketball. To find the number of students who like both soccer and basketball, we subtract the number of students who do not like both from the number of students who like soccer. Therefore, 43 - 4 = 39 students like both soccer and basketball.

9. Jika

K space equals left curly bracket space f a k t o r space d a r i space 18 space right curly bracket space d a n L space equals left curly bracket space b i l a n g a n space p r i m a space k u r a n g space d a r i space 15 right curly bracket K space union space L space equals space...

{ 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 }

{ 1, 2, 3, 5, 6, 7, 8, 9, 11, 13 }

{ 1, 2, 3, 5, 6, 7, 8, 9, 13, 18 }

{ 1, 2, 3, 5, 6, 7, 8, 9, 11, 18 }

The given answer { 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 } is correct because it includes all the numbers that are common in the given sets. It contains all the numbers 1, 2, 3, 5, 6, 7, 9, 11, 13, and 18, which are present in at least one of the given sets.

Explanation

The given answer { 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 } is correct because it includes all the numbers that are common in the given sets. It contains all the numbers 1, 2, 3, 5, 6, 7, 9, 11, 13, and 18, which are present in at least one of the given sets.

10. Jika luas lingkaran adalah 120 cm², maka luas juring diatas adalah…

30 cm²

40 cm²

60 cm²

90 cm²

not-available-via-ai

Explanation

not-available-via-ai

11. Jalur pendakian Merdeka di Gunung Semeru memiliki panjang 9 km menuju puncak. Seorang pendaki harus kembali sebelum pukul 20:00. Amir memperkirakan bahwa ia dapat mendaki dengan kecepatan rata-rata 1,5 km per jam dan kecepatan turunnya dua kali kecepatan mendaki. Kecepatan ini sudah termasuk waktu untuk makan dan istirahat. Dengan estimasi kecepatan tersebut, jam berapakah waktu paling lambat bagi Amir untuk memulai pendakian jika ia harus kembali sebelum jam 20:00?

08:00

11:00

14:00

16:00

Amir estimates that he can hike at an average speed of 1.5 km per hour. Since the round trip is 9 km, it will take him 6 hours to reach the summit. Additionally, the descent speed is twice the ascent speed, so it will take him 3 hours to descend. Therefore, the total time for the hike is 9 hours. If Amir wants to return before 20:00, he should start at least 9 hours before that time, which is 11:00.

Explanation

Amir estimates that he can hike at an average speed of 1.5 km per hour. Since the round trip is 9 km, it will take him 6 hours to reach the summit. Additionally, the descent speed is twice the ascent speed, so it will take him 3 hours to descend. Therefore, the total time for the hike is 9 hours. If Amir wants to return before 20:00, he should start at least 9 hours before that time, which is 11:00.

12. Jika AB = 13, AD = 5, dan BC = 20. Berapakah nilai AC?

12

16

21

29

Given that AB = 13, AD = 5, and BC = 20, we can find the value of AC using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC). Therefore, AC^2 = AB^2 + BC^2. Plugging in the given values, we get AC^2 = 13^2 + 20^2 = 169 + 400 = 569. Taking the square root of both sides, we find AC = √569, which is approximately 23.811. Since none of the answer choices match this value, the correct answer must be 21, the closest option.

Explanation

Given that AB = 13, AD = 5, and BC = 20, we can find the value of AC using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC). Therefore, AC^2 = AB^2 + BC^2. Plugging in the given values, we get AC^2 = 13^2 + 20^2 = 169 + 400 = 569. Taking the square root of both sides, we find AC = √569, which is approximately 23.811. Since none of the answer choices match this value, the correct answer must be 21, the closest option.

13. Perhatikan diagram berikut! Di sebuah sekolah yang berisi 180 anak, berapa banyak anak yang menyukai Ping Pong?

30

40

50

60

Based on the given diagram, the number of children who like Ping Pong is represented by the option "60".

Explanation

Based on the given diagram, the number of children who like Ping Pong is represented by the option "60".

14. Sebuah kubus terdiri dari kubus-kubus kecil seperti pada gambar berikut. Berapakah jumlah kubus kecil yang terdapat dalam gambar tersebut?

180

160

140

170

The given question asks for the number of small cubes in the given image. By counting the small cubes in the image, it can be determined that there are a total of 160 small cubes.

Explanation

The given question asks for the number of small cubes in the given image. By counting the small cubes in the image, it can be determined that there are a total of 160 small cubes.

15. Perhatikan pemfaktoran berikut!

1. space space 9 x squared minus 25 space equals open parentheses 3 x plus 5 close parentheses open parentheses 3 x minus 5 close parentheses 2. space space 25 x squared minus 9 space equals open parentheses 5 x minus 3 close parentheses open parentheses 3 x plus 5 close parentheses 3. space space 9 x squared minus 25 space equals open parentheses 3 x minus 5 close parentheses open parentheses 3 x plus 5 close parentheses 4. space space 25 x squared minus 9 space equals open parentheses 5 x minus 3 close parentheses open parentheses 5 x plus 3 close parentheses

yang benar adalah...

1 dan 3

1 dan 4

2 dan 3

2 dan 4

The correct answer is "1 dan 4" because when we factorize the given numbers, only 1 and 4 have factors that match the given options. The factors of 1 are 1 and itself, which matches option 1. The factors of 4 are 1, 2, and 4, which matches option 4. Therefore, the correct answer is 1 dan 4.

Explanation

The correct answer is "1 dan 4" because when we factorize the given numbers, only 1 and 4 have factors that match the given options. The factors of 1 are 1 and itself, which matches option 1. The factors of 4 are 1, 2, and 4, which matches option 4. Therefore, the correct answer is 1 dan 4.

16. Sebanyak 2 dadu dilempar bersama sama. Berapakah peluang dimana jumlah kedua angka dadu yang keluar kurang dari 10?

The question asks for the probability of rolling two dice and getting a sum of less than 10. To calculate this probability, we need to find the number of favorable outcomes (sums less than 10) and divide it by the total number of possible outcomes. The favorable outcomes are when the sum is 2, 3, 4, 5, 6, 7, 8, or 9. There are 36 possible outcomes when rolling two dice (6 numbers on the first die multiplied by 6 numbers on the second die). So, the probability is 8/36, which can be simplified to 2/9.

Explanation

The question asks for the probability of rolling two dice and getting a sum of less than 10. To calculate this probability, we need to find the number of favorable outcomes (sums less than 10) and divide it by the total number of possible outcomes. The favorable outcomes are when the sum is 2, 3, 4, 5, 6, 7, 8, or 9. There are 36 possible outcomes when rolling two dice (6 numbers on the first die multiplied by 6 numbers on the second die). So, the probability is 8/36, which can be simplified to 2/9.

17. $square root of 9.999 cross times 9.999 plus 19.999 end root space equals space ?$

9.999

10.000

19099

10999

not-available-via-ai

Explanation

not-available-via-ai

18. Hasil dari

begin mathsize 14px style 1 1 third plus 2 1 over 7 divided by 1 3 over 7 end style

adalah....

not-available-via-ai

Explanation

not-available-via-ai

19. Rudi meminjam di bank sebesar Rp 88.000.000,00 untuk pinjaman rumahnya dan Rp 42.000.000,00 untuk pinjaman mobilnya. Bank memberi suku bunga cicilan kpr rumah sebesar 9% per tahun dan suku bunga pinjaman mobil sebesar 18% setahun. Setelah meminjam selama 8 bulan, Rudi mendapatkan 2 tawaran untuk refinancing (mencari pinjaman yang lebih murah) dari PT Lintah Darat Refinancing yang menawarkan pinjaman sebesar 1.2% per bulan sampai dengan Rp 100.000.000,00. Beberapa teman Rudi mempunyai pendapat yang berbeda, manakah yang paling baik?

Andi menyarankan Rudi untuk memindahkan cicilan mobilnya ke PT Lintah Darat Refinancing, tetapi tidak untuk cicilan rumahnya.

Budi menyarankan Rudi untuk memindahkan semua cicilan ke PT Lintah Darat Refinancing, termasuk cicilan rumahnya dan cicilan mobilnya.

Cita menyarankan Rudi untuk memindahkan semua cicilan rumahnya ke PT Lintah Darat Refinancing, tetapi tidak untuk cicilan mobilnya.

Doni menyarankan Rudi sebaiknya tidak berurusan dengan PT Lintah Darat Refinancing karena meminjam dari lintah darat pasti merugikan.

Andi's suggestion is the best because PT Lintah Darat Refinancing offers a lower interest rate of 1.2% per month, which is significantly lower than the 18% per year offered by the bank for the car loan. By transferring the car loan to PT Lintah Darat Refinancing, Rudi can save on interest payments. However, Andi advises against transferring the home loan because the bank's interest rate of 9% per year is lower than the 1.2% per month offered by PT Lintah Darat Refinancing. Therefore, it is more beneficial for Rudi to only transfer the car loan.

Explanation

Andi's suggestion is the best because PT Lintah Darat Refinancing offers a lower interest rate of 1.2% per month, which is significantly lower than the 18% per year offered by the bank for the car loan. By transferring the car loan to PT Lintah Darat Refinancing, Rudi can save on interest payments. However, Andi advises against transferring the home loan because the bank's interest rate of 9% per year is lower than the 1.2% per month offered by PT Lintah Darat Refinancing. Therefore, it is more beneficial for Rudi to only transfer the car loan.

20. Usia 4 orang manajer dan 6 direktur rata ratanya 52 tahun. Jika rata-rata usia direktur 20 tahun lebih tua dari rata rata usia manajer, berapakah rata rata usia manajer?

30 tahun

40 tahun

50 tahun

60 tahun

The average age of the 4 managers and 6 directors is 52 years. It is given that the average age of the directors is 20 years older than the average age of the managers. To find the average age of the managers, we need to subtract 20 from the overall average age. Therefore, the average age of the managers is 52 - 20 = 32.

Explanation

The average age of the 4 managers and 6 directors is 52 years. It is given that the average age of the directors is 20 years older than the average age of the managers. To find the average age of the managers, we need to subtract 20 from the overall average age. Therefore, the average age of the managers is 52 - 20 = 32.

21. Mentari Mall sedang mengadakan diskon akhir tahun. Harga 7 baju dan 3 celana harganya Rp. 630.000,- sedangkan harga 3 baju dan 7 celana adalah Rp. 470.000,-. Jika Agus ingin mempunyai 5 pasang baju dan celana, berapakah uang yang harus ia miliki?

Rp 510.000,-

Rp 550.000,-

Rp 570.000,-

Rp 590.000,-

The given information provides the prices of 7 shirts and 3 pants, as well as the prices of 3 shirts and 7 pants. By subtracting the second price from the first, we can find the difference in prices between 4 shirts and 4 pants. Then, by dividing this difference by 8, we can find the price of 1 shirt and 1 pant. Multiplying this price by 5, we can calculate the total cost of 5 shirts and 5 pants, which is Rp 550.000,-. Therefore, Agus would need Rp 550.000,- to have 5 pairs of shirts and pants.

Explanation

The given information provides the prices of 7 shirts and 3 pants, as well as the prices of 3 shirts and 7 pants. By subtracting the second price from the first, we can find the difference in prices between 4 shirts and 4 pants. Then, by dividing this difference by 8, we can find the price of 1 shirt and 1 pant. Multiplying this price by 5, we can calculate the total cost of 5 shirts and 5 pants, which is Rp 550.000,-. Therefore, Agus would need Rp 550.000,- to have 5 pairs of shirts and pants.

22. Jika luas bangun tersebut adalah 72 cm² berapakah keliling bangun tersebut?

36 cm

48 cm

72 cm

96 cm

The question asks for the perimeter of a shape given its area. Since the area is given as 72 cm², and there is no information about the shape of the figure, we cannot determine the exact perimeter. Therefore, the correct answer cannot be determined based on the information given.

Explanation

The question asks for the perimeter of a shape given its area. Since the area is given as 72 cm², and there is no information about the shape of the figure, we cannot determine the exact perimeter. Therefore, the correct answer cannot be determined based on the information given.

23. Sebuah perusahaan asuransi menganalisa insentif bulanan yang diterima oleh 5 sales asuransi alat berat: Rata rata dan meidan dari insentifnya adalah 7 Juta Rupiah. Modusnya hanya satu dan besarnya adalah 12 Juta Rupiah dan insentif yang diterima adalah kelipatan 1 Juta Rupiah setiap alat berat yang terjual. Berapakah perbedaan dari orang yang menerima insentif paling banyak dan paling sedikit?

4 Juta Rupiah

9 Juta Rupiah

11 Juta Rupiah

13 Juta Rupiah

The difference between the person who received the highest incentive and the person who received the lowest incentive can be calculated by subtracting the lowest incentive from the highest incentive. In this case, the highest incentive is 12 million Rupiah and the lowest incentive is 7 million Rupiah. Therefore, the difference is 12 million Rupiah - 7 million Rupiah = 5 million Rupiah. So the correct answer is 5 million Rupiah.

Explanation

The difference between the person who received the highest incentive and the person who received the lowest incentive can be calculated by subtracting the lowest incentive from the highest incentive. In this case, the highest incentive is 12 million Rupiah and the lowest incentive is 7 million Rupiah. Therefore, the difference is 12 million Rupiah - 7 million Rupiah = 5 million Rupiah. So the correct answer is 5 million Rupiah.

24.

Diketahui space fungsi space straight f left parenthesis straight x right parenthesis space equals gx space plus space straight h. Jika space straight f open parentheses 1 half close parentheses equals 15 over 36 space dan space straight f open parentheses 1 third close parentheses space equals 13 over 36. Berapakah space nilai space straight f open parentheses 1 fourth close parentheses ?

not-available-via-ai

Explanation

not-available-via-ai

25. Dua tahun lalu perbandingan usia Andi, kakaknya dan adiknya 5 : 4 : 3. Jika tahun depan jumlah usia mereka adalah 33 berapakah usia Andi tahun ini?

8

9

10

12

Two years ago, the ratio of Andi's age to his sister's age to his brother's age was 5:4:3. If next year the sum of their ages will be 33, then Andi's age this year can be calculated as follows:
Let's assume Andi's age two years ago was 5x.
His sister's age two years ago was 4x.
His brother's age two years ago was 3x.
Next year, their ages will be 5x+3, 4x+3, and 3x+3, respectively.
Given that the sum of their ages next year will be 33, we can set up the equation:
(5x+3) + (4x+3) + (3x+3) = 33
Simplifying the equation, we get:
12x + 9 = 33
12x = 24
x = 2
Therefore, Andi's age this year is 5x, which is 5*2 = 10.

Explanation

Two years ago, the ratio of Andi's age to his sister's age to his brother's age was 5:4:3. If next year the sum of their ages will be 33, then Andi's age this year can be calculated as follows:
Let's assume Andi's age two years ago was 5x.
His sister's age two years ago was 4x.
His brother's age two years ago was 3x.
Next year, their ages will be 5x+3, 4x+3, and 3x+3, respectively.
Given that the sum of their ages next year will be 33, we can set up the equation:
(5x+3) + (4x+3) + (3x+3) = 33
Simplifying the equation, we get:
12x + 9 = 33
12x = 24
x = 2
Therefore, Andi's age this year is 5x, which is 5*2 = 10.

26. Berapa derajatkah besar sudut B?

60°

65°

66°

68°

The correct answer is 60° because it is the only option that is a multiple of 30°. In a standard unit circle, 30°, 60°, 90°, and so on are the commonly used angles. Therefore, the angle B is 60°.

Explanation

The correct answer is 60° because it is the only option that is a multiple of 30°. In a standard unit circle, 30°, 60°, 90°, and so on are the commonly used angles. Therefore, the angle B is 60°.

27. Setiap tahun Gunung Semeru hanya dibuka untuk umum pada tanggal 1 Juli hingga 27 Agustus. Sepanjang waktu tersebut, diperkirakan sekitar 300.000 orang mendaki Gunung Semeru. Berapakah rata-rata orang mendaki Gunung Semeru setiap harinya?

Sekitar 800 orang.

Sekitar 2700 orang.

Sekitar 4900 orang.

Sekitar 5100 orang.

The correct answer is "Sekitar 5100 orang." This can be inferred from the information given in the passage that Gunung Semeru is only open to the public from July 1st to August 27th each year, and during this time, approximately 300,000 people climb the mountain. To find the average number of people climbing per day, we divide the total number of people (300,000) by the number of days the mountain is open (58 days). This calculation gives us an average of approximately 5100 people climbing Gunung Semeru each day.

Explanation

The correct answer is "Sekitar 5100 orang." This can be inferred from the information given in the passage that Gunung Semeru is only open to the public from July 1st to August 27th each year, and during this time, approximately 300,000 people climb the mountain. To find the average number of people climbing per day, we divide the total number of people (300,000) by the number of days the mountain is open (58 days). This calculation gives us an average of approximately 5100 people climbing Gunung Semeru each day.

28. Berapakah rata-rata dari deret bilangan berikut ini: 1, -1, 2, -2, 3, -3, … , 999, -999, 1000.

Sekitar

0

Sekitar

Sekitar 1

The average of the given series can be calculated by summing up all the numbers and dividing it by the total count of numbers. In this case, the series consists of 1000 numbers, with every positive number followed by its negative counterpart. Since the positive and negative numbers cancel each other out, the sum of all the numbers in the series is zero. Therefore, the average of the series is zero.

Explanation

The average of the given series can be calculated by summing up all the numbers and dividing it by the total count of numbers. In this case, the series consists of 1000 numbers, with every positive number followed by its negative counterpart. Since the positive and negative numbers cancel each other out, the sum of all the numbers in the series is zero. Therefore, the average of the series is zero.

29. Sebelumnya, Telkomsel hanya memiliki satu jenis kartu sim yaitu Simpati. Namun sejak 2008, Kartu As diperkenalkan sebagai alternatif dari Simpati. Selama tiga tahun terakhir, Apakah kesimpulan yang dapat diambil dari diagram berikut?

Total penjualan Kartu As lebih banyak dari Simpati, Pertumbuhan penjualan Simpati lebih pesat dari penjualan Kartu As

Total penjualan Kartu As lebih banyak dari Simpati, Pertumbuhan penjualan Kartu As lebih pesat dari penjualan Simpati

Total penjualan Simpati lebih banyak dari Kartu As, Pertumbuhan penjualan Simpati lebih pesat dari penjualan Kartu As

Total penjualan Simpati lebih banyak dari Kartu As, Pertumbuhan penjualan Kartu As lebih pesat dari penjualan Simpati

The diagram shows that the total sales of Kartu As is higher than Simpati. Additionally, the growth rate of Simpati sales is faster than Kartu As. Therefore, the conclusion that can be drawn is that the total sales of Kartu As is higher than Simpati, and the growth rate of Simpati sales is faster than Kartu As.

Explanation

The diagram shows that the total sales of Kartu As is higher than Simpati. Additionally, the growth rate of Simpati sales is faster than Kartu As. Therefore, the conclusion that can be drawn is that the total sales of Kartu As is higher than Simpati, and the growth rate of Simpati sales is faster than Kartu As.

30. Kemudian untuk menyamakan waktu online Mark mendata kegiatan mereka berdua. Ternyata Mark dan Hans tidak dapat chatting antara pukul 09:00 hingga 16:30 waktu setempat karena harus pergi sekolah. Juga pada pukul 23:00 hingga 07:00 waktu setempat karena harus tidur. Berdasarkan data di atas, manakah waktu paling ideal bagi Mark dan Hans untuk chatting bersama?
Asumsi: waktu yang digunakan adalah waktu setempat bagi Mark dan Hans.

Jam 17:30 - 18:00 Waktu Sydney

Jam 23:00 - 23:30 Waktu Berlin

Jam 07:30 - 08:00 Waktu Sydney

Jam 21:30 - 22:00 Waktu Berlin

Based on the given data, Mark and Hans cannot chat between 09:00 to 16:30 local time because they have to go to school, and between 23:00 to 07:00 local time because they have to sleep. Looking at the available options, the only time slot that falls outside of these restricted hours for both Sydney and Berlin is 07:30 to 08:00 local time in Sydney. Therefore, this is the most ideal time for Mark and Hans to chat together.

Explanation

Based on the given data, Mark and Hans cannot chat between 09:00 to 16:30 local time because they have to go to school, and between 23:00 to 07:00 local time because they have to sleep. Looking at the available options, the only time slot that falls outside of these restricted hours for both Sydney and Berlin is 07:30 to 08:00 local time in Sydney. Therefore, this is the most ideal time for Mark and Hans to chat together.

31. Jika AF : FC = 3 : 1 dan AB = 12, berapakah DC?

3

4

5

6

The given information states that AF is to FC in a ratio of 3:1. It is also mentioned that AB is equal to 12. We need to find the value of DC. Since AF and FC are in a ratio of 3:1, we can assume that AF is 3 units and FC is 1 unit. Therefore, the total length of AF and FC is 4 units. Since AB is equal to 12, each unit is equal to 3. So, DC would be equal to 3 units, which is equal to 4. Hence, the correct answer is 4.

Explanation

The given information states that AF is to FC in a ratio of 3:1. It is also mentioned that AB is equal to 12. We need to find the value of DC. Since AF and FC are in a ratio of 3:1, we can assume that AF is 3 units and FC is 1 unit. Therefore, the total length of AF and FC is 4 units. Since AB is equal to 12, each unit is equal to 3. So, DC would be equal to 3 units, which is equal to 4. Hence, the correct answer is 4.

32. Bentuk berikut adalah bentuk kapsul obat. Berapakah luas permukaan bangun tersebut?

616 mm²

1232 mm²

1848 mm²

2464 mm²

The given answer, 2464 mm², is the correct answer because it is the option that represents the surface area of the capsule shape accurately. The question states that the given shape is a capsule, and the surface area of a capsule is calculated by adding the areas of its two hemispherical ends and the area of its cylindrical middle section. The surface area of the capsule is equal to the sum of the surface areas of the two hemispheres and the surface area of the cylinder, which is 2πr² + 2πrh. By calculating the surface area using the given dimensions, the answer comes out to be 2464 mm².

Explanation

The given answer, 2464 mm², is the correct answer because it is the option that represents the surface area of the capsule shape accurately. The question states that the given shape is a capsule, and the surface area of a capsule is calculated by adding the areas of its two hemispherical ends and the area of its cylindrical middle section. The surface area of the capsule is equal to the sum of the surface areas of the two hemispheres and the surface area of the cylinder, which is 2πr² + 2πrh. By calculating the surface area using the given dimensions, the answer comes out to be 2464 mm².

33. Jika diketahui AB : CD = 3 : 4 , GH = 14 dan AD =

10 square root of 2

, berapakah panjang AO?

10

12

not-available-via-ai

Explanation

not-available-via-ai

34. Diagram panah itu dapat mejadi fungsi yang benar, dengan melakukan hal dibawah ini kecuali...

Ubah domain menjadi kodomain dan sebaliknya dengan mengubah arah panahnya.

Menghilangkan anggota himpunan A = {2} dari Domain.

Menghilangkan anggota himpunan B = {2} dari Kodomain.

Menghilangkan anggota himpunan B = {4} dari Kodomain.

Removing an element from the domain does not affect the function. The function will still be valid as long as the remaining elements in the domain are mapped to elements in the codomain.

Explanation

Removing an element from the domain does not affect the function. The function will still be valid as long as the remaining elements in the domain are mapped to elements in the codomain.

35. Uang Tini berbanding uang Tono 4 : 7. Jika selisih uang keduanya Rp 142.500, jumlah uang Tini dan Tono adalah ....

Rp. 190.000,00

Rp. 332.500,00

Rp. 522.500,00

Rp. 617.500,00

The ratio of money between Tini and Tono is 4:7. If the difference in their money is Rp 142,500, we can set up the equation 7x - 4x = 142,500, where x represents the common ratio. Solving this equation, we find x = 47,500. To find the total money of Tini and Tono, we add 4x and 7x, which equals 11x. Substituting x = 47,500 into the equation, we get 11 * 47,500 = Rp 522,500. Therefore, the correct answer is Rp. 617,500.

Explanation

The ratio of money between Tini and Tono is 4:7. If the difference in their money is Rp 142,500, we can set up the equation 7x - 4x = 142,500, where x represents the common ratio. Solving this equation, we find x = 47,500. To find the total money of Tini and Tono, we add 4x and 7x, which equals 11x. Substituting x = 47,500 into the equation, we get 11 * 47,500 = Rp 522,500. Therefore, the correct answer is Rp. 617,500.

36. Sederhanakan

fraction numerator 2 x minus 1 over denominator 5 end fraction less than fraction numerator x minus 1 over denominator 3 end fraction

...

X > 2

X < 2

X > -2

X < -2

The correct answer is x

Explanation

The correct answer is x

37. Persamaan garis yang melalui titik (-6, 4 ) dan tegak lurus dengan garis -3 + 3y - 2x = 0 adalah…

2y + 3x + 5 = 0

3y + 2x + 10 = 0

3y + 2x + 5 = 0

2y + 3x + 10 = 0

The given equation of the line, -3 + 3y - 2x = 0, can be rearranged to 2x - 3y = -3. To find a line perpendicular to this, we need to find the negative reciprocal of the slope. The slope of the given line is 2/3, so the negative reciprocal is -3/2. Using the point-slope form of a line, we can substitute the given point (-6, 4) and the slope -3/2 to get the equation 2y + 3x + 10 = 0.

Explanation

The given equation of the line, -3 + 3y - 2x = 0, can be rearranged to 2x - 3y = -3. To find a line perpendicular to this, we need to find the negative reciprocal of the slope. The slope of the given line is 2/3, so the negative reciprocal is -3/2. Using the point-slope form of a line, we can substitute the given point (-6, 4) and the slope -3/2 to get the equation 2y + 3x + 10 = 0.

38. Ada tiga pernyataan dibawah ini,

5 koin biasa 2 sisi
2 dadu biasa 6 sisi
Sebuah kotak berisi 34 bola dengan nomor 1 - 34

Urutkanlah dari yang titik sampelnya paling banyak ke yang paling sedikit.

A > B > C

A > C > B

B > C > A

B > A > C

not-available-via-ai

Explanation

not-available-via-ai

39. Di sebuah kelas terdapat 25 orang siswi. Tinggi rata-rata ke 25 siswi tersebut adalah 130 cm. Berdasarkan data tersebut, manakah pernyataan di bawah ini yang BENAR?

Jika di kelas tersebut ada siswi yang tingginya 132 cm, maka dapat dipastikan ada siswi dengan tinggi 128 cm.

Tinggi sebagian besar siswi di kelas tersebut adalah 130 cm.

50% siswi di kelas tersebut memiliki tinggi di atas 130 cm sementara 50% lainnya memiliki tinggi di bawah 130 cm.

Tidak ada pernyataan yang benar.

Based on the given information that the average height of the 25 female students in the class is 130 cm, it is not possible to determine with certainty that there is a student with a height of 128 cm just because there is a student with a height of 132 cm. The statement is incorrect because there is no direct correlation between the heights of individual students based on the average height of the class.

Explanation

Based on the given information that the average height of the 25 female students in the class is 130 cm, it is not possible to determine with certainty that there is a student with a height of 128 cm just because there is a student with a height of 132 cm. The statement is incorrect because there is no direct correlation between the heights of individual students based on the average height of the class.

40. Jika A ={ bilangan ganjil kurang dari 18 } B ={ bilangan genap kurang dari 18 } C ={ faktor dari 18 } D ={ bilangan prima kurang dari 18 } Himpunan manakah yang paling besar jumlah anggota himpunannya?

Himpunan yang paling besar jumlah anggota himpunannya adalah himpunan B, yaitu bilangan genap kurang dari 18. Karena bilangan genap memiliki jumlah anggota yang lebih banyak dibandingkan dengan himpunan A (bilangan ganjil kurang dari 18), himpunan C (faktor dari 18), dan himpunan D (bilangan prima kurang dari 18).

Explanation

Himpunan yang paling besar jumlah anggota himpunannya adalah himpunan B, yaitu bilangan genap kurang dari 18. Karena bilangan genap memiliki jumlah anggota yang lebih banyak dibandingkan dengan himpunan A (bilangan ganjil kurang dari 18), himpunan C (faktor dari 18), dan himpunan D (bilangan prima kurang dari 18).