id int64 1 735k | topic stringclasses 11
values | difficulty stringclasses 2
values | question stringlengths 12 91 | answer stringlengths 1 11 | reasoning stringlengths 20 98 | category stringclasses 19
values |
|---|---|---|---|---|---|---|
731,801 | number_theory | medium | What is the GCD (greatest common divisor) of 51 and 34? | 17 | Find greatest number dividing both 51 and 34. Divisors common, greatest is 17. | gcd |
731,802 | arithmetic | easy | What is 27 * 90? | 2430 | Multiply: 27 * 90 = 2430. | basic_operations |
731,803 | calculus | medium | What is the indefinite integral of x^2 dx? | x^3/3 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^2 = x^3/3 + C. | integral |
731,804 | algebra | medium | Solve for x: x^2 + 12x + 27 = 0 | x = -3, -9 | Factor: (x - -3)(x - -9) = x^2 -(-12)x + 27 = 0. So x = -3 or -9. Check sum = -12, product = 27. | quadratic |
731,805 | calculus | medium | What is the indefinite integral of x^5 dx? | x^6/6 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^5 = x^6/6 + C. | integral |
731,806 | calculus | medium | What is the indefinite integral of x^5 dx? | x^6/6 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^5 = x^6/6 + C. | integral |
731,807 | fractions | medium | What is 18/5 - 13/11? Give as simplified fraction. | 133/55 | Common denominator 55. Numerator 198-65=133. So 133/55 simplifies to 133/55. | fraction_operations |
731,808 | calculus | medium | What is the indefinite integral of x^6 dx? | x^7/7 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^6 = x^7/7 + C. | integral |
731,809 | calculus | medium | What is the derivative of 1x^4 with respect to x? | 4x^3 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [1x^4] = 1*4*x^3 = 4x^3. | derivative |
731,810 | geometry | easy | Find the area of a rectangle with length 72 and width 3. | 216 | Area = length * width = 72*3 = 216. | rectangle_area |
731,811 | fractions | medium | What is 11/12 - 9/14? Give as simplified fraction. | 23/84 | Common denominator 168. Numerator 154-108=46. So 46/168 simplifies to 23/84. | fraction_operations |
731,812 | number_theory | medium | What is the LCM (least common multiple) of 70 and 70? | 70 | LCM = |70*70| / GCD(70,70). GCD=70, so LCM=4900/70=70. | lcm |
731,813 | exponents | easy | What is 9^3? | 729 | 9^3 means multiply 9 by itself 3 times: 9*9*9 = 729. | exponents |
731,814 | calculus | medium | What is the indefinite integral of x^7 dx? | x^8/8 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^7 = x^8/8 + C. | integral |
731,815 | calculus | medium | What is the derivative of 9x^2 with respect to x? | 18x | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [9x^2] = 9*2*x^1 = 18x. | derivative |
731,816 | calculus | medium | What is the derivative of 1x^8 with respect to x? | 8x^7 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [1x^8] = 1*8*x^7 = 8x^7. | derivative |
731,817 | algebra | medium | Solve for x: x^2 - 4x - 12 = 0 | x = -2, 6 | Factor: (x - -2)(x - 6) = x^2 -(4)x + -12 = 0. So x = -2 or 6. Check sum = 4, product = -12. | quadratic |
731,818 | statistics | easy | What is the mean (average) of 4, 40, 27? | 23.67 | Mean = sum/count. Sum = 4+40+27=71. Count=3. Mean=71/3=23.67. | mean |
731,819 | arithmetic | easy | What is 773 + 872? | 1645 | Add the two numbers: 773 + 872 = 1645. | basic_operations |
731,820 | arithmetic | easy | What is 629 + 413 * 48? Remember order of operations. | 20453 | Order of operations (PEMDAS): first 413*48=19824, then 629+19824=20453. | basic_operations |
731,821 | percentages | easy | What is 34% of 851? | 289.34 | Calculate 34/100 * 851 = 0.34*851 = 289.34. | percentages |
731,822 | arithmetic | easy | What is 562 - 30? | 532 | Subtract: 562 - 30 = 532. | basic_operations |
731,823 | calculus | medium | What is the derivative of 10x^3 with respect to x? | 30x^2 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [10x^3] = 10*3*x^2 = 30x^2. | derivative |
731,824 | arithmetic | easy | What is 616 + 932 * 53? Remember order of operations. | 50012 | Order of operations (PEMDAS): first 932*53=49396, then 616+49396=50012. | basic_operations |
731,825 | fractions | medium | What is 5/2 * 19/8? Give as simplified fraction. | 95/16 | Multiply numerators: 5*19=95. Denominators: 2*8=16. Simplify by gcd 1 to get 95/16. | fraction_operations |
731,826 | calculus | medium | What is the derivative of 3x^3 with respect to x? | 9x^2 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [3x^3] = 3*3*x^2 = 9x^2. | derivative |
731,827 | geometry | easy | Find the area of a rectangle with length 84 and width 17. | 1428 | Area = length * width = 84*17 = 1428. | rectangle_area |
731,828 | fractions | medium | What is 10/12 + 3/14? Give as simplified fraction. | 22/21 | Common denominator 12*14=168. 10/12=140/168, 3/14=36/168. Sum = 176/168 = 22/21 simplified. | fraction_operations |
731,829 | arithmetic | easy | What is 26 * 9? | 234 | Multiply: 26 * 9 = 234. | basic_operations |
731,830 | word_problems | easy | If you have 82 candies and you buy 37 more candies, how many candies do you have in total? | 119 | Add initial 82 plus bought 37: 82+37=119. | addition_word |
731,831 | geometry | easy | Find the area of a rectangle with length 31 and width 38. | 1178 | Area = length * width = 31*38 = 1178. | rectangle_area |
731,832 | percentages | easy | What is 35% of 973? | 340.55 | Calculate 35/100 * 973 = 0.35*973 = 340.55. | percentages |
731,833 | arithmetic | easy | What is 3 * 93? | 279 | Multiply: 3 * 93 = 279. | basic_operations |
731,834 | number_theory | medium | What is the LCM (least common multiple) of 19 and 9? | 171 | LCM = |19*9| / GCD(19,9). GCD=1, so LCM=171/1=171. | lcm |
731,835 | algebra | easy | Solve for x: 2x - 20 = -18 | 1 | Add 20 to both sides: 2x = -18+20=2. Then x = 2/2 = 1. | linear_equation |
731,836 | algebra | medium | Solve for x: x^2 - 3x - 54 = 0 | x = -6, 9 | Factor: (x - -6)(x - 9) = x^2 -(3)x + -54 = 0. So x = -6 or 9. Check sum = 3, product = -54. | quadratic |
731,837 | algebra | easy | Solve for x: 19x + 8 = 369 | 19 | Subtract 8 from both sides: 19x = 369-8=361. Then divide by 19: x = 361/19 = 19. | linear_equation |
731,838 | fractions | medium | What is 19/6 - 13/9? Give as simplified fraction. | 31/18 | Common denominator 54. Numerator 171-78=93. So 93/54 simplifies to 31/18. | fraction_operations |
731,839 | arithmetic | easy | What is 872 + 747 * 20? Remember order of operations. | 15812 | Order of operations (PEMDAS): first 747*20=14940, then 872+14940=15812. | basic_operations |
731,840 | arithmetic | easy | What is 36 * 56? | 2016 | Multiply: 36 * 56 = 2016. | basic_operations |
731,841 | calculus | medium | What is the indefinite integral of x^6 dx? | x^7/7 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^6 = x^7/7 + C. | integral |
731,842 | arithmetic | easy | What is 39 + 62 * 20? Remember order of operations. | 1279 | Order of operations (PEMDAS): first 62*20=1240, then 39+1240=1279. | basic_operations |
731,843 | calculus | medium | What is the indefinite integral of x^7 dx? | x^8/8 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^7 = x^8/8 + C. | integral |
731,844 | calculus | medium | What is the indefinite integral of x^3 dx? | x^4/4 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^3 = x^4/4 + C. | integral |
731,845 | fractions | medium | What is 15/12 * 8/7? Give as simplified fraction. | 10/7 | Multiply numerators: 15*8=120. Denominators: 12*7=84. Simplify by gcd 12 to get 10/7. | fraction_operations |
731,846 | roots | easy | What is the square root of 1681? | 41 | Find number that when squared gives 1681. 41*41=1681, so sqrt(1681)=41. | square_roots |
731,847 | number_theory | medium | What is the GCD (greatest common divisor) of 92 and 50? | 2 | Find greatest number dividing both 92 and 50. Divisors common, greatest is 2. | gcd |
731,848 | algebra | easy | Solve for x: 17x - 37 = 150 | 11 | Add 37 to both sides: 17x = 150+37=187. Then x = 187/17 = 11. | linear_equation |
731,849 | statistics | easy | What is the mean (average) of 52, 42, 22? | 38.67 | Mean = sum/count. Sum = 52+42+22=116. Count=3. Mean=116/3=38.67. | mean |
731,850 | number_theory | medium | What is the LCM (least common multiple) of 62 and 67? | 4154 | LCM = |62*67| / GCD(62,67). GCD=1, so LCM=4154/1=4154. | lcm |
731,851 | percentages | easy | What is 12% of 986? | 118.32 | Calculate 12/100 * 986 = 0.12*986 = 118.32. | percentages |
731,852 | roots | easy | What is the square root of 529? | 23 | Find number that when squared gives 529. 23*23=529, so sqrt(529)=23. | square_roots |
731,853 | word_problems | easy | If you have 11 dollars and you buy 35 more dollars, how many dollars do you have in total? | 46 | Add initial 11 plus bought 35: 11+35=46. | addition_word |
731,854 | statistics | easy | What is the mean (average) of 52, 30, 60, 2? | 36 | Mean = sum/count. Sum = 52+30+60+2=144. Count=4. Mean=144/4=36.0. | mean |
731,855 | exponents | easy | What is 12^2? | 144 | 12^2 means multiply 12 by itself 2 times: 12*12 = 144. | exponents |
731,856 | calculus | medium | What is the indefinite integral of x^5 dx? | x^6/6 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^5 = x^6/6 + C. | integral |
731,857 | arithmetic | easy | What is 6 + 129? | 135 | Add the two numbers: 6 + 129 = 135. | basic_operations |
731,858 | statistics | easy | What is the mean (average) of 19, 68, 36, 91, 21? | 47 | Mean = sum/count. Sum = 19+68+36+91+21=235. Count=5. Mean=235/5=47.0. | mean |
731,859 | calculus | medium | What is the derivative of 6x^3 with respect to x? | 18x^2 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [6x^3] = 6*3*x^2 = 18x^2. | derivative |
731,860 | algebra | easy | Solve for x: 5x - 32 = -17 | 3 | Add 32 to both sides: 5x = -17+32=15. Then x = 15/5 = 3. | linear_equation |
731,861 | algebra | medium | Solve for x: x^2 - 2x - 35 = 0 | x = -5, 7 | Factor: (x - -5)(x - 7) = x^2 -(2)x + -35 = 0. So x = -5 or 7. Check sum = 2, product = -35. | quadratic |
731,862 | algebra | medium | Solve for x: x^2 - 1x - 2 = 0 | x = 2, -1 | Factor: (x - 2)(x - -1) = x^2 -(1)x + -2 = 0. So x = 2 or -1. Check sum = 1, product = -2. | quadratic |
731,863 | arithmetic | easy | What is 14 + 33 * 42? Remember order of operations. | 1400 | Order of operations (PEMDAS): first 33*42=1386, then 14+1386=1400. | basic_operations |
731,864 | arithmetic | easy | What is 946 - 815? | 131 | Subtract: 946 - 815 = 131. | basic_operations |
731,865 | algebra | medium | Solve for x: x^2 + 1x - 12 = 0 | x = -4, 3 | Factor: (x - -4)(x - 3) = x^2 -(-1)x + -12 = 0. So x = -4 or 3. Check sum = -1, product = -12. | quadratic |
731,866 | algebra | medium | Solve for x: x^2 - 3x - 40 = 0 | x = -5, 8 | Factor: (x - -5)(x - 8) = x^2 -(3)x + -40 = 0. So x = -5 or 8. Check sum = 3, product = -40. | quadratic |
731,867 | calculus | medium | What is the indefinite integral of x^1 dx? | x^2/2 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^1 = x^2/2 + C. | integral |
731,868 | statistics | easy | What is the mean (average) of 53, 93, 67, 73, 3? | 57.8 | Mean = sum/count. Sum = 53+93+67+73+3=289. Count=5. Mean=289/5=57.8. | mean |
731,869 | calculus | medium | What is the derivative of 1x^4 with respect to x? | 4x^3 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [1x^4] = 1*4*x^3 = 4x^3. | derivative |
731,870 | calculus | medium | What is the indefinite integral of x^1 dx? | x^2/2 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^1 = x^2/2 + C. | integral |
731,871 | arithmetic | easy | What is 13 * 22? | 286 | Multiply: 13 * 22 = 286. | basic_operations |
731,872 | roots | easy | What is the square root of 625? | 25 | Find number that when squared gives 625. 25*25=625, so sqrt(625)=25. | square_roots |
731,873 | arithmetic | easy | What is 38688 / 93? | 416 | Divide: 38688 ÷ 93 = 416 because 93*416=38688. | division |
731,874 | arithmetic | easy | What is 2040 / 30? | 68 | Divide: 2040 ÷ 30 = 68 because 30*68=2040. | division |
731,875 | percentages | easy | What is 41% of 795? | 325.95 | Calculate 41/100 * 795 = 0.41*795 = 325.95. | percentages |
731,876 | algebra | medium | Solve for x: x^2 + 14x + 49 = 0 | x = -7 | Factor as (x - -7)^2 = 0, so root is -7 (double root). Sum of roots = -14, product = 49. | quadratic |
731,877 | word_problems | easy | If you have 60 apples and you buy 49 more apples, how many apples do you have in total? | 109 | Add initial 60 plus bought 49: 60+49=109. | addition_word |
731,878 | percentages | easy | What is 36% of 668? | 240.48 | Calculate 36/100 * 668 = 0.36*668 = 240.48. | percentages |
731,879 | calculus | medium | What is the derivative of 4x^4 with respect to x? | 16x^3 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [4x^4] = 4*4*x^3 = 16x^3. | derivative |
731,880 | arithmetic | easy | What is 892 - 590? | 302 | Subtract: 892 - 590 = 302. | basic_operations |
731,881 | arithmetic | easy | What is 553 - 178? | 375 | Subtract: 553 - 178 = 375. | basic_operations |
731,882 | algebra | easy | Solve for x: 4x - 40 = -72 | -8 | Add 40 to both sides: 4x = -72+40=-32. Then x = -32/4 = -8. | linear_equation |
731,883 | algebra | medium | Solve for x: x^2 - 16x + 60 = 0 | x = 10, 6 | Factor: (x - 10)(x - 6) = x^2 -(16)x + 60 = 0. So x = 10 or 6. Check sum = 16, product = 60. | quadratic |
731,884 | algebra | easy | Solve for x: 7x + 22 = 71 | 7 | Subtract 22 from both sides: 7x = 71-22=49. Then divide by 7: x = 49/7 = 7. | linear_equation |
731,885 | algebra | easy | Solve for x: 2x - 34 = -70 | -18 | Add 34 to both sides: 2x = -70+34=-36. Then x = -36/2 = -18. | linear_equation |
731,886 | arithmetic | easy | What is 89 * 75? | 6675 | Multiply: 89 * 75 = 6675. | basic_operations |
731,887 | fractions | medium | What is 16/9 - 16/18? Give as simplified fraction. | 8/9 | Common denominator 162. Numerator 288-144=144. So 144/162 simplifies to 8/9. | fraction_operations |
731,888 | arithmetic | easy | What is 537 + 51? | 588 | Add the two numbers: 537 + 51 = 588. | basic_operations |
731,889 | algebra | easy | Solve for x: 6x - 28 = -136 | -18 | Add 28 to both sides: 6x = -136+28=-108. Then x = -108/6 = -18. | linear_equation |
731,890 | algebra | medium | Solve for x: x^2 - 8x = 0 | x = 0, 8 | Factor: (x - 0)(x - 8) = x^2 -(8)x + 0 = 0. So x = 0 or 8. Check sum = 8, product = 0. | quadratic |
731,891 | algebra | easy | Solve for x: 18x - 24 = -258 | -13 | Add 24 to both sides: 18x = -258+24=-234. Then x = -234/18 = -13. | linear_equation |
731,892 | arithmetic | easy | What is 69 * 67? | 4623 | Multiply: 69 * 67 = 4623. | basic_operations |
731,893 | exponents | easy | What is 4^4? | 256 | 4^4 means multiply 4 by itself 4 times: 4*4*4*4 = 256. | exponents |
731,894 | arithmetic | easy | What is 75 * 34? | 2550 | Multiply: 75 * 34 = 2550. | basic_operations |
731,895 | calculus | medium | What is the indefinite integral of x^3 dx? | x^4/4 + C | Power rule for integration: integral x^n dx = x^(n+1)/(n+1) + C. So integral x^3 = x^4/4 + C. | integral |
731,896 | arithmetic | easy | What is 968 + 386 * 11? Remember order of operations. | 5214 | Order of operations (PEMDAS): first 386*11=4246, then 968+4246=5214. | basic_operations |
731,897 | calculus | medium | What is the derivative of 5x^7 with respect to x? | 35x^6 | Power rule: d/dx [x^n] = n*x^(n-1). So d/dx [5x^7] = 5*7*x^6 = 35x^6. | derivative |
731,898 | fractions | medium | What is 8/15 * 2/3? Give as simplified fraction. | 16/45 | Multiply numerators: 8*2=16. Denominators: 15*3=45. Simplify by gcd 1 to get 16/45. | fraction_operations |
731,899 | algebra | easy | Solve for x: 10x + 18 = -162 | -18 | Subtract 18 from both sides: 10x = -162-18=-180. Then divide by 10: x = -180/10 = -18. | linear_equation |
731,900 | number_theory | medium | What is the LCM (least common multiple) of 20 and 69? | 1380 | LCM = |20*69| / GCD(20,69). GCD=1, so LCM=1380/1=1380. | lcm |
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