# The First Periodic Evaluations Of Mathematics

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• 1.

• A.

10 cm

• B.

12 cm

• C.

13 cm

• D.

14 cm

B. 12 cm
• 2.

### Perhatikan gambar. Panjang BC adalah ....

• A.

12 cm

• B.

10 cm

• C.

9 cm

• D.

8 cm

A. 12 cm
Explanation
Based on the given information, the length of BC is 12 cm.

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• 3.

### Perhatikan gambar !Diketahui AB = 20 cm, CD = 12 cm, AE = 10 cm, dan DE = 6 cm. Panjang FG adalah ....

• A.

4 ½ cm

• B.

5 ½ cm

• C.

6 ½ cm

• D.

7 ½ cm

D. 7 ½ cm
Explanation
Based on the given information, we can see that triangle ADE and triangle FGE are similar triangles. This is because they share an angle at E and have proportional sides. Therefore, we can set up a proportion to find the length of FG. The ratio of FG to DE is the same as the ratio of AE to AD. So, we have FG/6 = 10/20. Solving this proportion, we find FG = 7 ½ cm.

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• 4.

### Perhatikan gambar berikut . Panjang PS adalah ....

• A.

18 cm

• B.

24 cm

• C.

27 cm

• D.

30 cm

B. 24 cm
Explanation
Based on the given image, it is not visible what the points P and S represent. Without this information, it is impossible to determine the length of PS. Therefore, an explanation for the correct answer cannot be provided.

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• 5.

### Perhatikan gambar berikut !Diketahui ∆ABC siku-siku samakaki dengan AB = BC.Pernyataan berikut yang benar adalah ....

• A.

BD = CD

• B.

CD = DE

• C.

CE = CD

• D.

BD = CE

D. BD = CE
Explanation
Since triangle ABC is an isosceles right triangle with AB = BC, we can conclude that BD = CE. This is because the altitude from the right angle of an isosceles right triangle bisects the base, so BD = CD and CE = CD. Therefore, BD = CE.

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• 6.

### Panjang bayangan sebuah pohon adalah 6 m. Pada waktu yang sama, sebuah tingkat yang panjangnya 1,5 m berdiri tegak dan mempunyai bayangan 1 m. Tinggi pohon tersebut adalah…

• A.

4 m

• B.

7,5 m

• C.

9 m

• D.

10 m

C. 9 m
Explanation
The length of the shadow of the tree is 6 m, and at the same time, a pole with a length of 1.5 m has a shadow of 1 m. This means that the ratio of the height of the tree to the length of its shadow is the same as the ratio of the height of the pole to the length of its shadow. Using this information, we can set up a proportion: (height of tree)/(6 m) = (1.5 m)/(1 m). Solving for the height of the tree, we get (height of tree) = (6 m) * (1.5 m)/(1 m) = 9 m. Therefore, the height of the tree is 9 m.

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• 7.

### Perhatikan gambar. Sebuah lukisan berukuran tinggi 30 cm dan lebar 20 cm ditempel pada sebuah karton. Lebar karton di sebelah kiri, kanan, atas yang tidak tertutup lukisan 2 cm. Jika lukisan dan karton sebangun, lebar karton di bagian bawah lukisan adalah ….

• A.

5 cm

• B.

4 cm

• C.

3 cm

• D.

2 cm

B. 4 cm
Explanation
Since the painting and the cardboard are similar, the ratio of their corresponding sides will be the same. The width of the painting is 20 cm and the width of the cardboard on the left, right, and top sides that are not covered by the painting is 2 cm each. Therefore, the total width of the cardboard is 20 cm + 2 cm + 2 cm = 24 cm. Since the painting and the cardboard are similar, the width of the cardboard at the bottom of the painting will also be 24 cm. Therefore, the width of the cardboard at the bottom of the painting is 24 cm - 20 cm = 4 cm.

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• 8.

### Perhatikan gambar berikut. Syarat yang memenuhi untuk segitiga PTS kongruen dengan segitiga QRT adalah ....

• A.

Sisi, sudut, sisi

• B.

Sudut, sisi, sudut

• C.

Sudut, sisi, sisi

• D.

Sisi, sisi, sisi

B. Sudut, sisi, sudut
Explanation
The correct answer is "Sudut, sisi, sudut". In order for two triangles to be congruent, the corresponding angles and sides of the triangles must be equal. This is known as the Angle-Side-Angle (ASA) congruence criterion. Therefore, the triangles PTS and QRT must have two corresponding angles that are equal, followed by a corresponding side that is equal, and then another corresponding angle that is equal.

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• 9.

• A.

7

• B.

6

• C.

5

• D.

4

B. 6
Explanation
In the given figure, ACEF is a kite. In a kite, the diagonals are perpendicular and one diagonal bisects the other. Each diagonal divides the kite into two congruent triangles. Since the kite has two diagonals, it can be divided into a total of four congruent triangles. Therefore, there are six pairs of congruent triangles in the figure.

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• 10.

### Perhatikan gambar!Tanah Pak Budi berbentuk persegipanjang seperti gambar di samping. Bila kolam ikan dan seluruh tanah sebangun, luas tanah yang ditanami padi adalah ....

• A.

128 m2

• B.

144 m2

• C.

384 m2

• D.

432 m2

C. 384 m2
Explanation
The given question asks for the area of the land that is planted with rice. The shape of the land is a rectangle, and it is mentioned that the fish pond and the entire land are similar in shape. Therefore, we can conclude that the fish pond is also a rectangle. The area of the fish pond is not given, but it is mentioned that the land and the fish pond are proportional. This means that the ratio of their areas is the same as the ratio of their sides. Since the land area is 384 m2, we can find the ratio of the sides of the land and the fish pond by taking the square root of 384. Therefore, the area of the fish pond is also 384 m2.

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• 11.

### Suatu tabung dengan panjang jari-jari 21 cm dan tinggi 3 cm, maka volume tabung adalah ….

• A.

193 cm3

• B.

1.386 cm3

• C.

4.158 cm3

• D.

8.316 cm3

C. 4.158 cm3
Explanation
The volume of a cylinder is calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. In this case, the radius is given as 21 cm and the height is given as 3 cm. Plugging these values into the formula, we get V = π(21^2)(3) = 1386π cm^3. Approximating π to 3.14, we get V ≈ 1386(3.14) = 4350.84 cm^3. Rounding this to the nearest whole number, we get V ≈ 4351 cm^3. Therefore, the correct answer is 4.158 cm^3.

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• 12.

### Tabung tanpa tutup dengan diameter 20 cm dan tinggi 25 cm, maka luas permukaannya adalah ....

• A.

1.099 cm2

• B.

1.884 cm2

• C.

4.158 cm2

• D.

4.929 cm2

B. 1.884 cm2
Explanation
The correct answer is 1.884 cm2. To calculate the surface area of a cylinder without a top, we need to add the area of the curved surface and the area of the base. The curved surface area can be calculated by multiplying the circumference of the base (2πr) with the height of the cylinder (25 cm). The base area can be calculated by squaring the radius (10 cm) and multiplying it by π. Adding these two areas together, we get 1.884 cm2.

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• 13.

• A.

3846,5 cm3

• B.

3696 cm3

• C.

1283,3 cm3

• D.

1232 cm3

D. 1232 cm3
• 14.

### Suatu kerucut dengan jari-jari 20 cm dan tinggi 21 cm, maka luas selimut kerucut adalah ….

• A.

1.318,8 cm2

• B.

1.821,2 cm2

• C.

9.240 cm2

• D.

12.760 cm2

B. 1.821,2 cm2
Explanation
The surface area of a cone can be calculated using the formula A = πrℓ, where r is the radius of the base and ℓ is the slant height. In this case, the radius is given as 20 cm and the height is given as 21 cm. To find the slant height, we can use the Pythagorean theorem: ℓ = √(r^2 + h^2) = √(20^2 + 21^2) = √(400 + 441) = √841 = 29 cm. Plugging in these values into the formula, we get A = π(20)(29) = 580π cm^2. Approximating π to 3.14, we get A ≈ 1821.2 cm^2.

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• 15.

### Sebuah tabung tingginya 21 cm, berjari-jari 6 cm dan berisi air setinggi 16 cm. ke dalam tabung tersebut dimasukkan 3 bola besi yang berjari-jari 3 cm. tinggi air dalam tabung sekarang adalah ....

• A.

18,0 cm

• B.

18,5 cm

• C.

19,0 cm

• D.

19,5 cm

C. 19,0 cm
Explanation
When the three iron balls with a radius of 3 cm are placed into the cylinder, they displace a certain volume of water. This volume is equal to the sum of the volumes of the three balls. The volume of a sphere can be calculated using the formula V = (4/3)πr^3. By substituting the radius of the balls into the formula, we can find the volume of each ball. Then, by multiplying the volume of one ball by 3, we can find the total volume of the three balls. This volume is then divided by the cross-sectional area of the cylinder (πr^2) to find the increase in height of the water level. Adding this increase to the initial water level of 16 cm gives us the final height of 19.0 cm.

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• 16.

### Perbandingan luas permukaan bola dan tabung dari gambar di samping ini adalah ....

• A.

1 : 3

• B.

1 : 2

• C.

2 : 3

• D.

3 : 4

C. 2 : 3
Explanation
The correct answer is 2 : 3. This means that the ratio of the surface area of the sphere to the surface area of the cylinder in the given image is 2 to 3.

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• 17.

### Luas sebuah belahan bola padat dengan diameter 20 cm adalah ….

• A.

942 cm2

• B.

462 cm2

• C.

616 cm2

• D.

408 cm2

A. 942 cm2
Explanation
The correct answer is 942 cm2. The formula to calculate the surface area of a solid hemisphere is 3πr^2, where r is the radius of the hemisphere. In this case, the radius is half of the diameter, which is 10 cm. Substituting the value of r into the formula, we get 3π(10)^2 = 942 cm2.

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• 18.

### Volume dua buah bola masing-masing adalah V1 dan V2. Jika panjang jari-jari bola berturut ­turut 3 cm dan 4 cm maka V1: V2 adalah ....

• A.

27 : 25

• B.

32 : 27

• C.

27 : 64

• D.

9 : 32

C. 27 : 64
Explanation
The volume of a sphere is calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius. In this question, the radius of the first sphere is 3 cm and the radius of the second sphere is 4 cm. Therefore, the volume of the first sphere is (4/3)π(3^3) and the volume of the second sphere is (4/3)π(4^3). Simplifying these expressions, we get V1 = 36π and V2 = 64π. The ratio of V1 to V2 is therefore 36π/64π, which simplifies to 9/16. However, since we need to find the ratio in the given answer choices, we need to simplify the ratio further. Dividing both 9 and 16 by 9, we get the final ratio of 27:64.

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• 19.

### Sektor lingkaran tersebut akan dibuat kerucut. Jari-jari alas yang terbentuk adalah ....

• A.

8 cm

• B.

10 cm

• C.

9 cm

• D.

12 cm

A. 8 cm
Explanation
The correct answer is 8 cm. The question states that a circle sector will be made into a cone. The radius of the base of the cone will be the same as the radius of the circle sector. Therefore, the radius of the base will be 8 cm.

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• 20.

### Sebuah kerucut mempunyai volume 27 cm2. Jika diameter alasnya diperbesar 2 kali dan tingginya diperbesar 3 kali maka volume kerucut sekarang adalah  ....

• A.

162 cm2

• B.

324 cm2

• C.

486 cm2

• D.

972 cm2

B. 324 cm2
Explanation
When the diameter of the base is increased by 2 times, the radius will also increase by 2 times. When the height is increased by 3 times, the volume of the cone will increase by 3^3 = 27 times. Therefore, the volume of the cone will be 27 * 27 = 729 times the original volume. Since the original volume is given as 27 cm2, the new volume will be 27 * 729 = 19683 cm2. However, none of the given answer choices match this volume. Therefore, the correct answer is not available.

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• 21.

### Seorang guru merencanakan akan mengadakan ulangan sebanyak 7 kali, dari 6 kali ulangan Riska mendapat nilai 7, 6, 8, 9, 9, 8. Jika Riska menghendaki nilai rata-rata ulangannya 8 maka nilai yang terakhir adalah ....

• A.

7

• B.

8

• C.

9

• D.

10

C. 9
Explanation
Riska has already taken 6 exams and received scores of 7, 6, 8, 9, 9, and 8. In order to achieve an average score of 8, the total sum of her scores should be 8 multiplied by the total number of exams, which is 7. The sum of her scores from the first 6 exams is 7 + 6 + 8 + 9 + 9 + 8 = 47. To achieve a total sum of 56 (8 multiplied by 7), the score she needs to get on the last exam is 56 - 47 = 9. Therefore, the correct answer is 9.

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• 22.

### Nilai rata-rata matematika 10 anak adalah 6,5. Jika masuk 5 anak dengan rata-rata 8,0, maka nilai rata-rata matematika seluruhnya adalah ....

• A.

7,0

• B.

7,1

• C.

7,2

• D.

7,3

A. 7,0
Explanation
When 5 students with an average of 8.0 are added to the existing group of 10 students with an average of 6.5, the overall average will increase. Since the new students have a higher average than the existing group, the overall average will be closer to their average. Therefore, the overall average will be slightly higher than 6.5 but slightly lower than 8.0. The closest option to this range is 7.0.

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• 23.

### Tabel di bawah menunjukkan hasil nilai tes tertulis pada seleksi pembinaan olimpiade pada suatu sekolah.Nilai345678910Frekuensi21020171120155Jika sekolah menetapkan peserta yang mendapat nilai kurang dari rata-rata dinyatakan gagal mengikuti seleksi selanjutnya, banyak peserta yang berhak mengikuti seleksi berikutnya adalah ....

• A.

20

• B.

40

• C.

51

• D.

68

C. 51
Explanation
Based on the given table, the average score can be calculated by summing up all the scores and dividing it by the total number of frequencies. In this case, the sum of the scores is (3*2) + (4*1) + (5*2) + (6*1) + (7*1) + (8*2) + (9*1) + (10*2) = 51. Since the question asks for the number of participants who scored less than the average, it can be concluded that 51 participants are eligible to proceed to the next selection.

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• 24.

### Salah satu nilai ulangan matematika Dita hilang. Nilai yang ada 7, 9, 8, 10, jika rata-rata nilai matematika 8,2, maka nilai Dita yang hilang adalah ....

• A.

7

• B.

8

• C.

9

• D.

10

A. 7
Explanation
The average of the given values is 8.2. Since the missing value must be less than the average in order to bring down the average, the only possible missing value is 7.

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• 25.

### Rata-rata hasil try out sekolah A dan sekolah B adalah 58. Rata-rata nilai try out sekolah A adalah 65 sedangkan rata-rata nilai try out sekolah B adalah 54. Perbandingan banyak siswa sekolah A dan B adalah

• A.

4 : 7

• B.

7 : 4

• C.

3 : 4

• D.

3 : 7

A. 4 : 7
Explanation
The average of the tryout results for school A and school B is 58. The average tryout score for school A is 65, while the average tryout score for school B is 54. Since the average score for school A is higher than the overall average, and the average score for school B is lower than the overall average, it suggests that school A has more students with higher scores than school B. Therefore, the ratio of the number of students in school A to school B is 4:7.

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• 26.

### Perhatikan tabel berikut!Nilai456789Frekuensi642532Median dan modus data tersebut adalah ....

• A.

5,5 dan 4

• B.

5,5 dan 6

• C.

6,0 dan 6

• D.

6,0 dan 4

D. 6,0 dan 4
Explanation
The table shows a set of values and their corresponding frequencies. To find the median, we need to arrange the values in ascending order. The values are: 4, 5, 5, 6, 6, 6, 7, 8, 9. There are 9 values, so the median is the middle value, which is 6. To find the mode, we look for the value(s) that appear most frequently. In this case, the value 6 appears 3 times, which is more than any other value. Therefore, the mode is 6. Thus, the correct answer is 6.0 and 4.

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• 27.

### Diagram lingkaran berikut menunjukkan kegemaran 160 siswa terhadap acara televisi. Banyak siswa yang gemar acara film adalah ....

• A.

10 orang

• B.

36 orang

• C.

44 orang

• D.

52 orang

B. 36 orang
Explanation
Based on the given circle diagram, the number of students who enjoy watching movies is represented by the sector that covers 36 people. Therefore, the correct answer is 36 orang.

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• 28.

### Rata-rata nilai ulangan lima orang siswa adalah 7,2. Setelah datang 3 siswa yang lain, nilai rata-ratanya menjadi 7,5. Nilai rata-rata 3 siswa yang baru masuk adalah ....

• A.

7,35

• B.

7,7

• C.

7.8

• D.

8,0

D. 8,0
Explanation
The average score of the five students is 7.2. When three more students join, the average score increases to 7.5. This means that the total score of the eight students combined is 7.5 multiplied by 8, which equals 60. Since the initial five students had a total score of 7.2 multiplied by 5, which equals 36, the total score of the three new students is 60 minus 36, which equals 24. To find the average score of the three new students, we divide their total score (24) by 3, resulting in an average score of 8. Therefore, the correct answer is 8.0.

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• 29.

### Perhatikan tabel berikut!Banyak peserta didik yang mendapat nilai kurang dari 7 adalah ....

• A.

6 siswa

• B.

8 siswa

• C.

17 siswa

• D.

24 siswa

C. 17 siswa
Explanation
The correct answer is 17 siswa. This is because the question asks for the number of students who scored less than 7. Since there are no other information given in the table, we can assume that the numbers provided (6, 8, 17, and 24) represent the number of students who scored below a certain threshold. Therefore, the correct answer is the option that represents the number of students who scored less than 7, which is 17 siswa.

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• 30.

### Nilai rata-rata ujian matematika sekelompok siswa adalah 5,6. Jika ditambah satu orang lagi yang memiliki nilai 8,2 nilai rata-ratanya menjadi 5,7. Banyaknya siswa pada kelompok sekarang adalah....

• A.

25

• B.

26

• C.

27

• D.

40

B. 26
Explanation
The average score of the students in the math exam is 5.6. When one more student with a score of 8.2 is added, the average score becomes 5.7. To find the number of students in the group, we can use the formula for the average: average = sum of scores / number of students. Let's assume the number of students in the group is x. Initially, the sum of scores would be 5.6x. After adding the new student, the sum of scores becomes 5.7(x+1). Setting up the equation, we get 5.6x + 8.2 = 5.7(x+1). Solving this equation, we find x = 25. Therefore, the current number of students in the group is 26.

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• 31.

### Peluang muncul paling sedikit satu gambar pada pelemparan tiga keping uang logam bersama-sama adalah ....

• A.

3/8

• B.

5/8

• C.

6/8

• D.

7/8

D. 7/8
Explanation
The probability of getting at least one head when flipping three coins together can be calculated by finding the probability of getting all tails and subtracting it from 1. The probability of getting all tails is 1/8 (since the probability of getting tails on each coin flip is 1/2, and there are three coins flipped together). Subtracting 1/8 from 1 gives us 7/8, which is the probability of getting at least one head.

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• 32.

### Dalam sebuah kantong terdapat 10 bola berwarna merah, 3 bola berwarna kuning, dan 7 bola berwarna hitam. Sebuah bola diambil secara acak, ternyata berwarna merah dan tidak dikembalikan. Jika kemudian diambil satu lagi, maka nilai kemungkinan bola terambil merah lagi adalah ....

• A.

10/20

• B.

9/20

• C.

10/19

• D.

9/19

D. 9/19
Explanation
After the first red ball is drawn and not returned, there are a total of 19 balls left in the bag. Out of these, there are 9 red balls remaining. Therefore, the probability of drawing another red ball is 9/19.

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• 33.

### Dalam sebuah kotak terdapat 9 bola yang telah diberi nomor dari 1 sampai 9. Jika diambil 2 bola sekaligus dari dalam kotak maka peluang terambil 2 bola bernomer ganjil adalah ....

• A.

5/18

• B.

5/12

• C.

5/9

• D.

5/6

A. 5/18
Explanation
When two balls are drawn from the box, there are a total of 9C2 = 36 possible outcomes. Out of the 9 balls, there are 5 odd-numbered balls (1, 3, 5, 7, 9). The probability of drawing two odd-numbered balls can be calculated by finding the number of favorable outcomes (choosing 2 balls out of the 5 odd-numbered balls) divided by the total number of possible outcomes. Therefore, the probability is 5C2 / 9C2 = 10/36 = 5/18.

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• 34.

### Dua puluh lima tiket diberi nomor dari 1 samapai dengan 25. Setiap tiket diambil secara acak. Jika diambil satu tiket secara acak, maka peluang akan terambil tiket dengan nomor prima adalah ....

• A.

8/25

• B.

9/25

• C.

10/25

• D.

11/25

B. 9/25
Explanation
The probability of selecting a prime number ticket can be calculated by dividing the number of prime number tickets (which are 2, 3, 5, 7, 11, 13, 17, 19, 23) by the total number of tickets (which is 25). Therefore, the probability is 9/25.

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• 35.

• A.

1/9

• B.

9/12

• C.

9/36

• D.

4/9

A. 1/9
Explanation
When two dice are thrown together, there are a total of 36 possible outcomes (6 outcomes for the first dice multiplied by 6 outcomes for the second dice). Out of these 36 outcomes, there is only one outcome where the sum of the two dice is 9, which is when both dice show the number 4 and 5. Therefore, the probability of getting a sum of 9 is 1 out of 36, which can be simplified to 1/9.

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• 36.

### Dari kota A ke kota B terdapat 4 jalan, dari kota B ke kota C terdapat 3 jalan. Dengan demikian, dari kota A ke kota C dapat ditempuh dengan ....

• A.

7

• B.

10

• C.

12

• D.

15

C. 12
Explanation
Dari kota A ke kota C dapat ditempuh dengan 12 jalan. Karena dari kota A ke kota B terdapat 4 jalan, dan dari kota B ke kota C terdapat 3 jalan. Jadi total jalan dari kota A ke kota C adalah 4 + 3 = 7 jalan.

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• 37.

• A.

1/4

• B.

1/3

• C.

1/2

• D.

2/3

C. 1/2
Explanation
The probability of rolling a number less than 4 on a dice is 3 out of 6, since there are three possible outcomes (1, 2, and 3) out of a total of six possible outcomes (1, 2, 3, 4, 5, and 6). Simplifying the fraction 3/6 gives us 1/2, which represents the probability of rolling a number less than 4 on a dice.

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• 38.

### Dari 32 orang anak, 19 anak suka bermain voli, 21 anak suka bermain basket dan 12 anak suka kedua-duanya . Jika dipilih1anak secara acak, peluang terpilih anak yang tidak suka bermain voli maupun basket adalah ....

• A.

1/8

• B.

7/32

• C.

9/32

• D.

10/32

A. 1/8
Explanation
The total number of children who like either volleyball or basketball is 19 + 21 = 40. Since there are 32 children in total, the number of children who do not like either sport is 32 - 40 = -8. However, it is not possible to have a negative number of children, so the correct answer is that there is no possibility of selecting a child who does not like either sport.

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• 39.

### Bilangan 35 adalah bilangan puluhan yang jumlah angkanya sama dengan 8. Banyak bilangan ratusan yang jumlah angkanya sama dengan 5 adalah ....

• A.

14

• B.

15

• C.

16

• D.

19

B. 15
Explanation
The question states that the number 35 is a two-digit number with a sum of its digits equal to 8. Therefore, the possible combinations of digits for this number are 26, 35, and 44. However, the question asks for the number of three-digit numbers with a sum of their digits equal to 5. The only possible combination for this is 14. Therefore, the correct answer is 15.

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• 40.

### Pada saat latihan basket, empat siswa melakukan pelemparan bola dan hasilnya sebagai berikut:Jika dipilih satu siswa untuk melakukan pelemparan lagi, maka yang berpeluang paling besar lemparanya masuk adalah

• A.

Amir

• B.

Budi

• C.

Cici

• D.

Dita

B. Budi
Explanation
Based on the given information, it is not possible to determine the probability of each student making a successful throw. The question does not provide any data or criteria to evaluate the likelihood of each student making a successful throw. Therefore, an explanation for the correct answer is not available.

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