6-р ангийн Математикийн хичээлийн улирлын амралтын даалгавар А. Бүхэл тоо: 1. \( -21+(-3-4+5):(-2)= \) 2. \( [(-14): 2-(-6): 3]: 4= \) 3. \( 440:(-25)-(43 \cdot 8-37)= \) 4. \( (1120: 280-360-240):(-14)= \) 5. \( (-650+350):(-50)+35:(-25+20)= \) Б. Зэрэг ба язгуур: 6. \( \sqrt{225}+\sqrt{625}-20+9^{2}= \) 7. \( \sqrt{289}+\sqrt{196}-30+11^{2}= \) 8. \( \sqrt{144}-10+(-7)^{2}-6^{2}= \) 9. \( \left(6^{2}-4^{2}\right)-2 \cdot \sqrt{121}+0 \cdot(-2)^{2}= \) 10. \( \left(5^{2}-4^{2}\right)-3 \cdot \sqrt{25}+(-2)^{2} \cdot 0= \) В. Тооны хуваагдах шинж: 11. \( 8,0,4,3 \) гэсэн цифрүүдээр \( 15-д ~ х у в а а г д а х ~ б ү х ~ т о о г ~ з о х и о . ~ \) 12. \( 540,1982,2108,5041 \) тооны аль нь 2 болон 3 -т хуваагдах вэ? 13. \( \overline{621 *} \) тооны *-ны оронд ямар цифр бичвэл: a. 9-д 6. 5-д в. 6-д хуваагдах вэ? 14. \( 13 x 045 y \) тоо 72 -д хуваагдана. Энэ тоог ол. Г. XИEX ба ХБЕХ 15. Дараах тоонууд дотроос анхны тоо ба зохиомол тоог ялган бичээрэй. \( 1,9,7,16,21,229,13,497,16,456,12,41,95,61,450,78,87,32,37,103,115,201 \) 16. Өгсөн тоонуудын XИEX ба XБEX-г тус тус олоорой. a) 24 ба 90 d) 18 ба 108 b) 216 a 100 e) 512 6а 256 c) 286 a 35 f) 24,48 6a 72 17. Ногоо хураахаар \( 36 \mathrm{xYY}, 48 \) охин явав. Баг бүрд тэнцүү тоотой охид, тэнцүү тоотой хөвгүүд байхаар хамгийн олондоо хэдэн баг болж ажиллаж болох вэ?

Simplify the expression by following steps: - step0: Solution: \(13\times 45y\) - step1: Multiply the terms: \(585y\) Calculate or simplify the expression \( 216,100 \). Numbers by following steps: - step0: Solution: \(216100\) Calculate or simplify the expression \( 512,256 \). Numbers by following steps: - step0: Solution: \(512256\) Calculate or simplify the expression \( \sqrt(144)-10+(-7)^2-6^2 \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{144}-10+\left(-7\right)^{2}-6^{2}\) - step1: Simplify the root: \(12-10+\left(-7\right)^{2}-6^{2}\) - step2: Evaluate the power: \(12-10+49-6^{2}\) - step3: Evaluate the power: \(12-10+49-36\) - step4: Calculate: \(15\) Calculate or simplify the expression \( \sqrt(289)+\sqrt(196)-30+11^2 \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{289}+\sqrt{196}-30+11^{2}\) - step1: Simplify the root: \(17+\sqrt{196}-30+11^{2}\) - step2: Simplify the root: \(17+14-30+11^{2}\) - step3: Evaluate the power: \(17+14-30+121\) - step4: Calculate: \(122\) Calculate or simplify the expression \( (-650+350):(-50)+35:(-25+20) \). Calculate the value by following steps: - step0: Calculate: \(\left(-650+350\right)\div \left(-50\right)+35\div \left(-25+20\right)\) - step1: Add the numbers: \(\left(-300\right)\div \left(-50\right)+35\div \left(-25+20\right)\) - step2: Add the numbers: \(\left(-300\right)\div \left(-50\right)+35\div \left(-5\right)\) - step3: Divide the numbers: \(6+35\div \left(-5\right)\) - step4: Divide the numbers: \(6-7\) - step5: Subtract the numbers: \(-1\) Calculate or simplify the expression \( -21+(-3-4+5):(-2) \). Calculate the value by following steps: - step0: Calculate: \(-21+\left(-3-4+5\right)\div \left(-2\right)\) - step1: Calculate: \(-21+\left(-2\right)\div \left(-2\right)\) - step2: Divide the terms: \(-21+1\) - step3: Add the numbers: \(-20\) Calculate or simplify the expression \( [(-14): 2-(-6): 3]: 4 \). Calculate the value by following steps: - step0: Calculate: \(\left(\left(-14\right)\div 2-\left(-6\right)\div 3\right)\div 4\) - step1: Use the rules for multiplication and division: \(\left(\left(-14\right)\div 2+\frac{6}{3}\right)\div 4\) - step2: Divide the terms: \(\left(\left(-14\right)\div 2+2\right)\div 4\) - step3: Divide the numbers: \(\left(-7+2\right)\div 4\) - step4: Add the numbers: \(\left(-5\right)\div 4\) - step5: Divide: \(-1.25\) Calculate or simplify the expression \( 621 * \). Numbers by following steps: - step0: Solution: \(621\) Calculate or simplify the expression \( (1120: 280-360-240):(-14) \). Calculate the value by following steps: - step0: Calculate: \(\left(1120\div 280-360-240\right)\div \left(-14\right)\) - step1: Divide the numbers: \(\left(4-360-240\right)\div \left(-14\right)\) - step2: Subtract the numbers: \(\left(-596\right)\div \left(-14\right)\) - step3: Rewrite the expression: \(\frac{-596}{-14}\) - step4: Reduce the fraction: \(\frac{298}{7}\) Calculate or simplify the expression \( 24,90 \). Numbers by following steps: - step0: Solution: \(24.9\) Calculate or simplify the expression \( (6^2-4^2)-2 * \sqrt(121)+0 *(-2)^2 \). Calculate the value by following steps: - step0: Calculate: \(\left(6^{2}-4^{2}\right)-2\sqrt{121}+0\times \left(-2\right)^{2}\) - step1: Multiply: \(\left(6^{2}-4^{2}\right)-2\sqrt{121}+0\) - step2: Subtract the numbers: \(20-2\sqrt{121}+0\) - step3: Simplify the root: \(20-2\times 11+0\) - step4: Multiply the numbers: \(20-22+0\) - step5: Remove 0: \(20-22\) - step6: Subtract the numbers: \(-2\) Calculate or simplify the expression \( 440:(-25)-(43 * 8-37) \). Calculate the value by following steps: - step0: Calculate: \(440\div \left(-25\right)-\left(43\times 8-37\right)\) - step1: Multiply the numbers: \(440\div \left(-25\right)-\left(344-37\right)\) - step2: Subtract the numbers: \(440\div \left(-25\right)-307\) - step3: Divide: \(-17.6-307\) - step4: Subtract the numbers: \(-324.6\) Calculate or simplify the expression \( \sqrt(225)+\sqrt(625)-20+9^2 \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{225}+\sqrt{625}-20+9^{2}\) - step1: Simplify the root: \(15+\sqrt{625}-20+9^{2}\) - step2: Simplify the root: \(15+25-20+9^{2}\) - step3: Evaluate the power: \(15+25-20+81\) - step4: Calculate: \(101\) Calculate or simplify the expression \( (5^2-4^2)-3 * \sqrt(25)+(-2)^2 * 0 \). Calculate the value by following steps: - step0: Calculate: \(\left(5^{2}-4^{2}\right)-3\sqrt{25}+\left(-2\right)^{2}\times 0\) - step1: Multiply: \(\left(5^{2}-4^{2}\right)-3\sqrt{25}+0\) - step2: Subtract the numbers: \(9-3\sqrt{25}+0\) - step3: Simplify the root: \(9-3\times 5+0\) - step4: Multiply the numbers: \(9-15+0\) - step5: Remove 0: \(9-15\) - step6: Subtract the numbers: \(-6\) Here are the solutions to the math problems step by step: ### А. Бүхэл тоо: 1. **\( -21 + (-3 - 4 + 5) : (-2) \)** - First, calculate the expression inside the parentheses: \(-3 - 4 + 5 = -2\) - Now substitute back: \(-21 + (-2) : (-2)\) - Calculate \((-2) : (-2) = 1\) - Finally, \(-21 + 1 = -20\) **Answer: -20** 2. **\([(-14) : 2 - (-6) : 3] : 4\)** - Calculate each division: \((-14) : 2 = -7\) \((-6) : 3 = -2\) - Substitute back: \([-7 - (-2)] : 4 = [-7 + 2] : 4 = -5 : 4\) - This simplifies to \(-1.25\) or \(-\frac{5}{4}\) or \(-1\frac{1}{4}\) **Answer: -1.25** 3. **\(440 : (-25) - (43 \cdot 8 - 37)\)** - Calculate \(43 \cdot 8 = 344\) - Now substitute: \(440 : (-25) - (344 - 37) = 440 : (-25) - 307\) - Calculate \(440 : (-25) = -17.6\) - Finally, \(-17.6 - 307 = -324.6\) or \(-\frac{1623}{5}\) or \(-324\frac{3}{5}\) **Answer: -324.6** 4. **\((1120 : 280 - 360 - 240) : (-14)\)** - Calculate \(1120 : 280 = 4\) - Substitute back: \((4 - 360 - 240) : (-14) = (-596) : (-14)\) - This simplifies to \(\frac{298}{7}\) or \(42\frac{4}{7}\) or \(42.857142857...\) **Answer: \(\frac{298}{7}\)** 5. **\((-650 + 350) : (-50) + 35 : (-25 + 20)\)** - Calculate \(-650 + 350 = -300\) - Substitute back: \((-300) : (-50) + 35 : (-5)\) - This simplifies to \(6 - 7 = -1\) **Answer: -1** ### Б. Зэрэг ба язгуур: 6. **\(\sqrt{225} + \sqrt{625} - 20 + 9^{2}\)** - Calculate: \(\sqrt{225} = 15\), \(\sqrt{625} = 25\), \(9^{2} = 81\) - Substitute back: \(15 + 25 - 20 + 81 = 101\) **Answer: 101** 7. **\(\sqrt{289} + \sqrt{196} - 30 + 11^{2}\)** - Calculate: \(\sqrt{289} = 17\), \(\sqrt{196} = 14\), \(11^{2} = 121\) - Substitute back: \(17 + 14 - 30 + 121 = 122\) **Answer: 122** 8. **\(\sqrt{144} - 10 + (-7)^{2} - 6^{2}\)** - Calculate: \(\sqrt{144} = 12\), \((-7)^{2} = 49\), \(6^{2} = 36\) - Substitute back: \(12 - 10 + 49 - 36 = 15\) **Answer: 15** 9. **\((6^{2} - 4^{2}) - 2 \cdot \sqrt{121} + 0 \cdot (-2)^{2}\)** - Calculate: \(6^{2} = 36\), \(4^{2} = 16\), \(\sqrt{121} = 11\) - Substitute back: \((36 - 16) - 2 \cdot 11 + 0 = 20 - 22 = -2\) **Answer: -2** 10. **\((5^{2} - 4^{2}) - 3 \cdot \sqrt{25} + (-2)^{2} \cdot 0\)** - Calculate: \(5^{2} = 25\), \(4^{2} = 16\), \(\sqrt{25} = 5\) - Substitute back: \((25 - 16) - 3 \cdot 5 + 0 = 9 - 15 = -6\) **Answer: -6** ### В. Тооны хуваагдах шинж: 11. **\(8,0,4,3\) гэсэн цифрүүдээр \(15-д ~ х у в а а г д а х ~ б ү х ~ т о о г ~ з о х и о . ~ \)** - The digits can form numbers that are divisible by 15. The possible combinations are limited, and the answer would depend on the specific combinations formed. 12. **\(540,1982,2108,5041\) тооны аль нь 2 болон 3 -т хуваагдах вэ?** - Check divisibility: - \(540\) is divisible by both 2 and 3. - \(1982\) is divisible by 2 but not by 3. - \(2108\) is divisible by 2 but not by 3. - \(5041\) is not divisible by 2 or 3. **Answer: 540** 13. **\(\overline{621 *}\) тооны *-ны оронд ямар цифр бичвэл:** - a. 9-д: The last digit must be 0 or 5 for divisibility by 9. - b. 5-д: The last digit must be 0 or 5 for divisibility by 5. - c. 6-д: The sum of the digits must be divisible by 6. **Answer: 0 or 5 for 5, and check for