Kuiz Math : Penaakulan Matematik

1. Heksagon mempunyai 5 sisi

Pernyataan

Bukan Pernyataan

The given statement "Heksagon mempunyai 5 sisi" is incorrect. A hexagon is a polygon with six sides, so it has six sides, not five. Therefore, the correct answer is "Bukan Pernyataan" which means "Not a Statement" in English.

Explanation

The given statement "Heksagon mempunyai 5 sisi" is incorrect. A hexagon is a polygon with six sides, so it has six sides, not five. Therefore, the correct answer is "Bukan Pernyataan" which means "Not a Statement" in English.

2. Nyatakan sama ada setiap pernyataan berikut adalah benar atau palsu.
2 ialah nombor perdana dan 5 ialah nombor genap.

Benar

Palsu

The statement says that 2 is a prime number and 5 is an even number. However, 2 is indeed a prime number but 5 is not an even number, it is an odd number. Therefore, the statement is false.

Explanation

The statement says that 2 is a prime number and 5 is an even number. However, 2 is indeed a prime number but 5 is not an even number, it is an odd number. Therefore, the statement is false.

3. Nyatakan sama ada pernyataan berikut adalah benar atau palsu. 5 > 3 atau 2³ = 6

True

Palsu

The statement is true because the first part of the statement "5 > 3" is true. In mathematics, 5 is indeed greater than 3. The second part of the statement "23 = 6" is not relevant to determining the overall truth value of the statement. Therefore, since the first part is true, the whole statement is true.

Explanation

The statement is true because the first part of the statement "5 > 3" is true. In mathematics, 5 is indeed greater than 3. The second part of the statement "23 = 6" is not relevant to determining the overall truth value of the statement. Therefore, since the first part is true, the whole statement is true.

4. Nyatakan sama ada setiap pernyataan berikut adalah benar atau palsu. 17 ialah nombor perdana atau nombor genap.

Benar

Palsu

17 adalah nombor perdana kerana ia hanya boleh dibahagikan dengan 1 dan dirinya sendiri tanpa sisa. Walaupun 17 bukanlah nombor genap kerana ia tidak boleh dibahagikan dengan 2 tanpa sisa, tetapi pernyataan tersebut benar kerana ia adalah nombor perdana.

Explanation

17 adalah nombor perdana kerana ia hanya boleh dibahagikan dengan 1 dan dirinya sendiri tanpa sisa. Walaupun 17 bukanlah nombor genap kerana ia tidak boleh dibahagikan dengan 2 tanpa sisa, tetapi pernyataan tersebut benar kerana ia adalah nombor perdana.

5. Lengkapkan setiap pernyataan dengan menggunakan pengkuantiti 'semua' atau
'sebilangan' supaya menjadi suatu pernyataan benar. _____ pentagon mempunyai lima sisi.

The correct answer is "SEMUA, semua, Semua". The word "SEMUA" means "all" or "every" in Indonesian. The statement "SEMUA pentagon mempunyai lima sisi" translates to "All pentagons have five sides" in English. This is a correct statement because by definition, a pentagon is a polygon with five sides.

Explanation

The correct answer is "SEMUA, semua, Semua". The word "SEMUA" means "all" or "every" in Indonesian. The statement "SEMUA pentagon mempunyai lima sisi" translates to "All pentagons have five sides" in English. This is a correct statement because by definition, a pentagon is a polygon with five sides.

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6. Lengkapkan pernyataan, di ruang jawapan, untuk membentuk satu pernyataan yang benar dengan menggunakan pengkuantiti 'semua' atau 'sebilangan'. _____ gandaan bagi 3 adalah gandaan bagi 6.

The correct answer is "Sebilangan, SEBILANGAN, sebilangan" because the statement is asking for a correct completion using the quantifiers "semua" (all) or "sebilangan" (some). In this case, "sebilangan" is the correct quantifier to use because it means "some" or "a certain number". The repetition of "sebilangan" emphasizes that it is not specifying a specific quantity, but rather an indefinite number.

Explanation

The correct answer is "Sebilangan, SEBILANGAN, sebilangan" because the statement is asking for a correct completion using the quantifiers "semua" (all) or "sebilangan" (some). In this case, "sebilangan" is the correct quantifier to use because it means "some" or "a certain number". The repetition of "sebilangan" emphasizes that it is not specifying a specific quantity, but rather an indefinite number.

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7. Lengkapkan premis dalam hujah berikut:

Premis 1: Semua heksagon mempunyai enam sisi Premis 2: _____________________ Kesimpulan: ABCDEF mempunyai enam sisi.

Heksagon mempunyai enam sisi

ABCDEF mempunyai enam sisi

ABCDEF ialah suatu heksagon

Heksagon bukan mempunyai enam sisi

Since the first premise states that all hexagons have six sides, and the conclusion states that ABCDEF has six sides, we can infer that ABCDEF is a hexagon. Therefore, the missing premise is "ABCDEF is a hexagon."

Explanation

Since the first premise states that all hexagons have six sides, and the conclusion states that ABCDEF has six sides, we can infer that ABCDEF is a hexagon. Therefore, the missing premise is "ABCDEF is a hexagon."

8. Lengkapkan setiap pernyataan dengan menggunakan pengkuantiti 'semua' atau
'sebilangan' supaya menjadi suatu pernyataan benar.

_____ nombor perdana adalah nombor ganjil

The correct answer is "sebilangan, Sebilangan, SEBILANGAN" because not all prime numbers are odd. There is only one prime number that is even, which is 2. Therefore, the statement "sebilangan nombor perdana adalah nombor ganjil" is true.

Explanation

The correct answer is "sebilangan, Sebilangan, SEBILANGAN" because not all prime numbers are odd. There is only one prime number that is even, which is 2. Therefore, the statement "sebilangan nombor perdana adalah nombor ganjil" is true.

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9. Lengkapkan premis dalam hujah berikut : Premis 1 : ………………………………………………………………… Premis 2 : 𝑚 ≠ 3 Kesimpulan : Garisan 𝑦 = 3𝑥 + 7 dan 𝑦 = 𝑚𝑥 + 12 adalah tidak selari.

Semua garisan 𝑦 = 3𝑥 + 7 dan 𝑦 = 𝑚𝑥 + 12 adalah tidak selari

Garisan 𝑦 = 3𝑥 + 7 dan 𝑦 = 𝑚𝑥 + 12 adalah selari, maka 𝑚 = 3

𝑚 ≠ 3

𝑚 = 3

The given answer states that the conclusion is "Garisan y = 3x + 7 dan y = mx + 12 adalah selari, maka m = 3" which means that the lines y = 3x + 7 and y = mx + 12 are parallel if m = 3. However, premise 2 states that m is not equal to 3 (m ≠ 3). Therefore, the conclusion is not supported by the premises and the lines are not parallel.

Explanation

The given answer states that the conclusion is "Garisan y = 3x + 7 dan y = mx + 12 adalah selari, maka m = 3" which means that the lines y = 3x + 7 and y = mx + 12 are parallel if m = 3. However, premise 2 states that m is not equal to 3 (m ≠ 3). Therefore, the conclusion is not supported by the premises and the lines are not parallel.

10. 3.5 < 4 dan -5 > -10

Benar

Palsu

The given statement is comparing two inequalities. The first inequality, 3.5 -10, is also true because -5 is greater than -10. Therefore, both inequalities are true, and the overall statement is true.

Explanation

The given statement is comparing two inequalities. The first inequality, 3.5 -10, is also true because -5 is greater than -10. Therefore, both inequalities are true, and the overall statement is true.

11. Tentukan antejadian bagi hujah yang berikut: Jika sebuah poligon mempunyai 6 sisi, maka poligon itu adalah sebuah heksagon.

poligon adalah sebuah heksagon

Semua poligon mempunyai 6 sisi

poligon mempunyai 6 sisi

Semua poligon adalah heksagon

The given correct answer states that "poligon mempunyai 6 sisi" which means "a polygon has 6 sides". This statement is a valid explanation for the argument because it directly supports the claim that "Jika sebuah poligon mempunyai 6 sisi, maka poligon itu adalah sebuah heksagon" which translates to "If a polygon has 6 sides, then it is a hexagon". Therefore, the fact that a polygon has 6 sides provides evidence to support the conclusion that the polygon is a hexagon.

Explanation

The given correct answer states that "poligon mempunyai 6 sisi" which means "a polygon has 6 sides". This statement is a valid explanation for the argument because it directly supports the claim that "Jika sebuah poligon mempunyai 6 sisi, maka poligon itu adalah sebuah heksagon" which translates to "If a polygon has 6 sides, then it is a hexagon". Therefore, the fact that a polygon has 6 sides provides evidence to support the conclusion that the polygon is a hexagon.

12. Buat satu kesimpulan umum secara aruhan bagi urutan nombor 10, 35, 70, … yang mengikut pola berikut. 10 = 5 (2)² – 10 35 = 5 (3)² – 10 70 = 5 (4)² – 10 …. = ………..

5 (n + 1)2 – 10, n = 1,2,3 ...

5 (n)2 – 10, n=2,3,4...

n (2)2 – 10, n=5,10,15...

5 (2)n – 10, n=1,2,3...

The given sequence follows the pattern of 5 (n + 1)2 - 10, where n represents the position of the number in the sequence. The pattern is derived by observing that each number in the sequence is obtained by multiplying (n + 1) by itself and then multiplying the result by 5. Finally, 10 is subtracted from the product to obtain the number in the sequence. This pattern holds true for all values of n starting from 1, and therefore, the general conclusion for the sequence is 5 (n + 1)2 - 10.

Explanation

The given sequence follows the pattern of 5 (n + 1)2 - 10, where n represents the position of the number in the sequence. The pattern is derived by observing that each number in the sequence is obtained by multiplying (n + 1) by itself and then multiplying the result by 5. Finally, 10 is subtracted from the product to obtain the number in the sequence. This pattern holds true for all values of n starting from 1, and therefore, the general conclusion for the sequence is 5 (n + 1)2 - 10.

13. Lengkapkan premis dalam hujah berikut:

Premis 1: Jika suatu nombor ialah faktor bagi 24, maka nombor itu ialah faktor bagi 48. Premis 2: 12 ialah faktor bagi 24. Kesimpulan: _____

Based on the given premises, if a number is a factor of 24, then it is also a factor of 48. The second premise states that 12 is a factor of 24. Therefore, we can conclude that 12 is a factor of 48.

Explanation

Based on the given premises, if a number is a factor of 24, then it is also a factor of 48. The second premise states that 12 is a factor of 24. Therefore, we can conclude that 12 is a factor of 48.

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14. Nyatakan akas untuk implikasi berikut. Seterusnya, nyatakan sama ada akas tersebut adalah benar atau palsu.

Jika x adalah gandaan bagi 12, maka x adalah gandaan bagi 3.

Jika x adalah gandaan bagi 3, maka x adalah gandaan bagi 12, BENAR

Jika x adalah bukan gandaan bagi 3, maka x adalah gandaan bagi 12, PALSU

Jika x adalah gandaan bagi 3, maka x adalah bukan gandaan bagi 12. BENAR

Jika x adalah gandaan bagi 3, maka x adalah gandaan bagi 12, PALSU.

The correct answer is "Jika x adalah gandaan bagi 3, maka x adalah gandaan bagi 12, PALSU." This means that if x is a multiple of 3, then x is a multiple of 12, which is false. Just because a number is a multiple of 3 does not guarantee that it is also a multiple of 12.

Explanation

The correct answer is "Jika x adalah gandaan bagi 3, maka x adalah gandaan bagi 12, PALSU." This means that if x is a multiple of 3, then x is a multiple of 12, which is false. Just because a number is a multiple of 3 does not guarantee that it is also a multiple of 12.

15. Diberi luas, 𝐿 sebuah segi tiga dengan panjang dan lebar masing – masing 𝑥 cm dan 𝑦 cm ialah 𝐿 = ½ (𝑥)(𝑦). Buat satu kesimpulan bagi sebuah segitiga yang mempunyai panjang dan lebar masing-masing 12 cm dan 15 cm. _____

The given answer is incorrect. The formula for the area of a triangle is L = 1/2 (x)(y), where x and y are the length and width of the triangle. Therefore, for a triangle with length and width of 12 cm and 15 cm, the area would be L = 1/2 (12)(15) = 90 cm^2. The correct conclusion for this triangle would be that its area is 90 square centimeters.

Explanation

The given answer is incorrect. The formula for the area of a triangle is L = 1/2 (x)(y), where x and y are the length and width of the triangle. Therefore, for a triangle with length and width of 12 cm and 15 cm, the area would be L = 1/2 (12)(15) = 90 cm^2. The correct conclusion for this triangle would be that its area is 90 square centimeters.

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