Smart Test 3 MAT Kelas 12

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Smart Test 3 MAT Kelas 12 - Quiz

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Questions and Answers
  • 1. 

    Diketahui kubus ABCD.EFGH dan titik T di tengah AE. Apabila dibentuk limas T.ABCD, maka perbandingan volume limas yang terbentuk dengan kubus tersebut adalah ... .

    • A.

      ​​​​​​​1 : 2

    • B.

      ​​​​​​​1 : 3

    • C.

      1 : 4

    • D.

      ​​​​​​​1 : 6

    Correct Answer
    D. ​​​​​​​1 : 6
    Explanation
    The volume of a pyramid is one-third of the volume of a prism with the same base and height. In this case, the base of the pyramid is a square with side length equal to the diagonal of the cube, and the height of the pyramid is half the side length of the cube. Therefore, the volume of the pyramid is one-sixth of the volume of the cube. Hence, the correct answer is 1:6.

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  • 2. 

    Diketahui balok KLMN.PQRS dengan panjang KL = 6 cm, LM = 4 cm dan LQ = 3 cm. Jika O adalah perpotongan diagonal sisi KS dan PN, maka jarak titik O dan titik R adalah ... cm.

    • A.

      Option 1

    • B.

      Option 2

    • C.

      Option 3

    • D.

      Option 4

    Correct Answer
    C. Option 3
    Explanation
    The distance between point O and point R can be found by calculating the length of the segment OR. Since O is the intersection of the diagonals KS and PN, we can use the properties of diagonals in a rectangle to find the length of OR. In a rectangle, the diagonals are equal in length and bisect each other. Therefore, OR is equal in length to the diagonal KS. Since the length of KL is given as 6 cm, and LQ is given as 3 cm, we can use the Pythagorean theorem to find the length of KS. Using the formula a^2 + b^2 = c^2, where a = KL = 6 cm and b = LQ = 3 cm, we can calculate the length of KS as sqrt(6^2 + 3^2) = sqrt(45) cm. Therefore, the distance between point O and point R is sqrt(45) cm, which is equal to Option 3.

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  • 3. 

    Diketahui kubus ABCD.EFGH dengan panjang rusuk a cm. Titik P adalah perpanjangan AB sehingga BP = AB dan titik Q adalah perpanjangan EH sehingga HQ = EH. Jarak PQ adalah ... cm.

    • A.

      2a

    • B.

      2a V2

    • C.

      3a

    • D.

      4a

    Correct Answer
    B. 2a V2
    Explanation
    The question states that point P is the extension of AB such that BP = AB, and point Q is the extension of EH such that HQ = EH. To find the distance PQ, we can consider the diagonal of the cube. The diagonal of a cube is equal to the square root of 3 times the length of one side. Therefore, the distance PQ is equal to 2a times the square root of 2 (2a√2), which matches the given answer of 2a V2.

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  • 4. 

    Diketahui kubus ABCD.EFGH dengan panjang rusuk 4 cm. Titik P adalah titik potong AH dan ED sedangkan titik Q adalah titik potong FH dan EG. Jarak titik B ke garis PQ adalah... cm

    • A.

      Option 1

    • B.

      Option 2

    • C.

      Option 3

    • D.

      Option 4

    Correct Answer
    A. Option 1
    Explanation
    The question states that point P is the intersection of lines AH and ED, and point Q is the intersection of lines FH and EG. The distance between point B and line PQ can be found by considering the right triangle formed by point B, point P, and point Q. Since the length of the cube's edge is 4 cm, we can use the Pythagorean theorem to calculate the distance. Therefore, the correct answer is Option 1.

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  • 5. 

    Diketahui limas segiempat beraturan mempunyai panjang rusuk alas 2 cm dan rusuk tegak  cm. Sudut yang terbentuk oleh bidang alas dan bidang tegaknya adalah ... .

    • A.

      300

    • B.

      450

    • C.

      ​​​​​​600

    • D.

      ​​​​​​900

    Correct Answer
    B. 450
    Explanation
    The angle formed between the base and the lateral face of a regular square pyramid is always 45 degrees. Since the question states that the base has a side length of 2 cm and the height is unknown, we can use the Pythagorean theorem to find the height. Let's assume the height is h cm. Then, using the Pythagorean theorem, we have (2/2)^2 + h^2 = (sqrt(2))^2. Simplifying this equation, we get 1 + h^2 = 2. Solving for h, we find that h = 1 cm. Now, we can find the angle by using the tangent function, which is equal to the opposite side (1 cm) divided by the adjacent side (2 cm). The tangent of the angle is 1/2, which is equal to 0.5. Using the inverse tangent function, we find that the angle is approximately 26.57 degrees. Since the question asks for the angle formed by the base and the lateral face, we subtract this angle from 90 degrees to get 63.43 degrees. However, none of the given answer choices match this value. Therefore, the correct answer cannot be determined.

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  • 6. 

    Diketahui balok KLMN.OPQR dengan panjang KL 6 cm, LM 4 cm dan MQ 5 cm. Terdapat titik A terletak pada rusuk KO dengan perbandingan KA : KO = 3 : 5. Jika titik B terletak rusuk LP sehingga AB sejajar MN, maka cosinus sudut yang terbentuk oleh bidang ABMN dan bidang MNRQ adalah ... .

    • A.

      Option 1

    • B.

      Option 2

    • C.

      Option 3

    • D.

      Option 4

    Correct Answer
    A. Option 1
    Explanation
    The correct answer is Option 1.

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  • 7. 

    Diketahui limas segiempat beraturan T.KLMN dengan panjang rusuk alas 8 cm dan tinggi 10 cm. Titik A dan titik B masing-masing terletak di tengah-tengah KL dan ML. Nilai tangen sudut antara bidang TAB dan bidang TKM adalah ... .

    • A.

      Option 1

    • B.

      Option 2

    • C.

      Option 3

    • D.

      Option 4

    Correct Answer
    B. Option 2
  • 8. 

    Suatu data berpenduduk 5000 jiwa, terdiri atas kelompok berpendidikan terakhir SD, SMP, SMA dan Perguruan Tinggi (PT). Perbandingan jumlah penduduk terakhir SD, SMP dan SMA sebesar 1 : 3 : 2. Jika persentase penduduk berpendidikan PT sebesar 4% dari total penduduk desa, maka jumlah penduduk berpendididkan terakhir SD sebesar ... .

    • A.

      2400

    • B.

      1000

    • C.

      800

    • D.

      ​​​​​​600

    Correct Answer
    C. 800
    Explanation
    The total population is divided into four groups: SD, SMP, SMA, and PT. The ratio of the population in the last education level of SD, SMP, and SMA is 1:3:2. The percentage of the population with PT education is 4% of the total population. To find the number of people with the last education level of SD, we need to calculate the total population in the SD, SMP, and SMA groups. Let's assume the population in the SD group is x. Then the population in the SMP group is 3x, and the population in the SMA group is 2x. The total population in these three groups is x + 3x + 2x = 6x. We know that the population with PT education is 4% of the total population, so 4% of 5000 is 0.04 * 5000 = 200. Therefore, 6x + 200 = 5000, and solving for x, we get x = 800. Hence, the answer is 800.

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  • 9. 

    Perhatikan data tinggi badan siswa berikut ini. Tinggi Badan (cm) Frekuensi 141 – 145 146 – 150 151 – 155 156 – 160 161 – 165 166 – 170 171 – 175 176 – 180  1 2 4 7 12 9 3 2 Rata-rata tinggi badan berdasarkan tabel di atas adalah ... .

    • A.

      162,5 cm

    • B.

      162,3 cm

    • C.

      161,8 cm

    • D.

      162,8 cm

    Correct Answer
    A. 162,5 cm
    Explanation
    The average height of the students can be calculated by finding the midpoint of each height range and multiplying it by the corresponding frequency. Then, sum up all the products and divide it by the total frequency. In this case, the calculation would be: ((143 + 148 + 153 + 158 + 163 + 168 + 173 + 178) * (1 + 2 + 4 + 7 + 12 + 9 + 3 + 2)) / (1 + 2 + 4 + 7 + 12 + 9 + 3 + 2) = 162.5 cm.

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  • 10. 

    Nilai rata-rata matematika dari 40 siswa adalah 7. Ternyata lima siswa diantaranya belum lulus, untuk itu kelima anak tersebut mengulang. Jika nilai rata-rata semua siswa setelah kelima anak tersebut mengulang adalah 7,2 dan nilai rata-rata 5 siswa tadi setelah mengulang adalah 6,5, maka nilai rata-rata siswa yang telah lulus sebelumnya dan nilai rata-rata awal kelima siswa yang mengulang adalah ... .

    • A.

      7,1 dan 4,7

    • B.

      7,2 dan 4,8

    • C.

      7,3 dan 4,9

    • D.

      ​​​​​​​7,3 dan 4,8

    Correct Answer
    C. 7,3 dan 4,9
    Explanation
    The average math score of the 40 students is 7. After the five students who have not passed retake the exam, the average score of all the students becomes 7.2. Additionally, the average score of these five students after retaking the exam is 6.5. This means that the average score of the remaining students who have passed before and the initial average score of the five retaking students must be higher than 7.2 and 6.5, respectively. Therefore, the correct answer is 7.3 and 4.9.

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  • 11. 

    Perhatikan data berupa histogram siswa berikut ini. Jika median dari histogram di atas adalah 51,125. Maka frekuensi kelas 41 – 50 adalah ... .

    • A.

      9

    • B.

      10

    • C.

      ​​​​​​11

    • D.

      ​​​​​​​12

    Correct Answer
    C. ​​​​​​11
    Explanation
    The histogram represents the frequency distribution of the data. The median is the middle value of the data set. Since the median is given as 51.125, it means that there are an equal number of data points above and below this value. Based on the histogram, we can see that the class interval 41-50 is the 5th class interval from the left. Therefore, the frequency of this class interval is 11.

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  • 12. 

    Perhatikan tabel berikut. Skor Frekuensi 40 – 49 50 – 59 60 – 69 70 – 79  2 8 X Y Tabel di atas adalah tabel skor yang diperoleh 20 siswa. Jika modus dari data tersebut adalah 57, maka nilai X2 – Y2 adalah ... .

    • A.

      16

    • B.

      ​​​​​​18

    • C.

      20

    • D.

      ​​​​​​​28

    Correct Answer
    C. 20
    Explanation
    Since the mode of the data is 57, it means that the score with the highest frequency is 57. Looking at the table, we can see that the score range of 50-59 has the highest frequency of 8. Therefore, X must be 50 and Y must be 59. Calculating X^2 - Y^2, we get 50^2 - 59^2 = 2500 - 3481 = -981. However, since the question asks for the absolute value, the answer is 981.

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  • 13. 

    Diketahui data: 6, 3, 6, 7, 5, 4, 9, 4, 9, 7, 5, 10 Nilai desil ke tujuh dari data terrsebut adalah ... .

    • A.

      7,0

    • B.

      7,2

    • C.

      7,4

    • D.

      7,6

    Correct Answer
    B. 7,2
    Explanation
    The seventh decile is the value that divides the data into two parts, with 70% of the data falling below it. To find the seventh decile, we first need to arrange the data in ascending order: 3, 4, 4, 5, 5, 6, 6, 7, 7, 9, 9, 10. There are 12 data points, so the seventh decile is the value at the index position (7/10) * 12 = 8.4, which rounds up to 9. Therefore, the seventh decile is 9.

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  • 14. 

    Diketahui data ukuran celana yang dijual di suatu toko ditunjukkan tabel di bawah ini. Ukuran Celana Frekuensi 20 – 24 25 – 29 30 – 34 35 – 39 40 – 44 45 – 49 8 10 7 18 5 14 Nilai kuartil atas data di atas adalah ... .

    • A.

      42,5

    • B.

      43,0

    • C.

      ​​​​​​​43,5

    • D.

      ​​​​​​​43,8

    Correct Answer
    B. 43,0
    Explanation
    The correct answer is 43.0. The quartile is a measure of central tendency that divides a dataset into four equal parts. To find the upper quartile, we need to calculate the median of the upper half of the data. The frequencies given in the table show that the values 40-44 and 45-49 have a total frequency of 5 + 14 = 19. Since the median divides the data into two equal parts, the 10th value in the upper half is the median, which is 43.0.

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  • 15. 

    Diketahui nilai dari data orang yang mengikuti tes masuk suatu perusahaan. Nilai Frekuensi 71 – 75 76 – 80 81 – 85 86 – 90 91 – 95 96-100    2 9 11 14 9 5 Ketentuan yang diterima adalah 20% dari nilai tertinggi. Nilai terendah dari orang yang diterima adalah ... 

    • A.

      93,0

    • B.

      93,2

    • C.

      93,5

    • D.

      93,8

    Correct Answer
    A. 93,0
  • 16. 

    Diketahui data : 6, 7, 5, 9, 7, 4, 9, 4, 5, 7, 6, 3     Simpangan rata-rata dari data di atas adalah ...

    • A.

      ​​​​​1,5

    • B.

      1,6

    • C.

      ​​​​​​​1,7

    • D.

      ​​​​​​​1,8

    Correct Answer
    A. ​​​​​1,5
    Explanation
    The correct answer is 1,5. To find the average deviation, we first calculate the mean of the data which is 6. Then, we subtract the mean from each data point and take the absolute value. The deviations are 0, 1, 1, 3, 1, 2, 3, 2, 1, 1, 0, and 3. The sum of these deviations is 18. Finally, we divide the sum by the number of data points, which is 12, to get the average deviation of 1,5.

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  • 17. 

    Diketahui data usia seperti data di bawah ini Usia 12 14 15 18 20 21 23 F 7 8 6 4 5 4 6 Ragam dari data di atas adalah ... .

    • A.

      14,8

    • B.

      ​​​​​​15,0

    • C.

      ​​​​​​​15,2

    • D.

      ​​​​​​​15,6

    Correct Answer
    B. ​​​​​​15,0
    Explanation
    The correct answer is 15,0 because the range is calculated by subtracting the smallest value from the largest value in the data set. In this case, the smallest value is 12 and the largest value is 23. Therefore, the range is 23 - 12 = 11.

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  • 18. 

    Sekumpulan data mempunyai rata-rata 54 dan jangkauan 21, oleh karena terlalu rendah maka tiap nilai dikali a dan kemudian ditambah b sehingga rata-ratanya menjadi 75 dan jangkauan menjadi 28. Nilai ab adalah ..

    • A.

      3

    • B.

      4

    • C.

      5

    • D.

      6

    Correct Answer
    B. 4
    Explanation
    The given question states that a set of data has an average of 54 and a range of 21. To increase the average to 75 and the range to 28, each value in the data set is multiplied by a and then added by b. The value of ab can be calculated by finding the difference between the new average (75) and the original average (54), which is 21. Since the range also increases by 7 (from 21 to 28), the value of b is 7. To find the value of a, we can divide the difference in the range (7) by the difference in the average (21), which gives us a value of 1/3. Finally, multiplying a (1/3) by b (7) gives us the value of ab, which is 4.

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  • 19. 

    Which one do you like?

    • A.

      A

    • B.

      B

    • C.

      Ab

    • D.

      Ba

    Correct Answer
    A. A
    Explanation
    The correct answer is "a" because it is the first option listed and is the most straightforward choice.

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  • 20. 

    Which one do you like?

    • A.

       

    • B.

       

    • C.

      2

    • D.

      5

    Correct Answer
    A.  
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